The role of ducks in detecting Highly Pathogenic Avian Influenza in small-scale backyard poultry farms

Steven Xingyu Wu; Christopher N Davis; Mark Arnold; Michael J Tildesley

doi:10.1371/journal.pcbi.1013357

. 2026 Jan 9;22(1):e1013357. doi: 10.1371/journal.pcbi.1013357

The role of ducks in detecting Highly Pathogenic Avian Influenza in small-scale backyard poultry farms

Steven Xingyu Wu ^1,^2,^*, Christopher N Davis ^1,^2,³, Mark Arnold ⁴, Michael J Tildesley ^1,^2,³

Editor: Qiangguo Jin⁵

PMCID: PMC12810905 PMID: 41512009

Abstract

Previous research efforts on highly pathogenic H5N1 avian influenza (HPAI) suggest that different avian species exhibit a varied severity of clinical signs after infection. Waterfowl, such as ducks or geese, can be asymptomatic and act as silent carriers of H5N1, making detection harder and increasing the risk of further transmission, potentially leading to significant economic losses. For backyard hobby farmers, passive reporting is a common HPAI detection strategy. We aim to develop a computational, mechanistic model to quantify the effectiveness of this strategy by simulating the spread of H5N1 in a mixed-species, small-population backyard flock. Quantities such as detection time and undetected burden of infection in various scenarios are compared. Our results indicate that the presence of ducks can lead to a higher risk of an outbreak and a higher burden of infection. If most ducks within a flock are resistant to H5N1, detection can be significantly delayed. We find that within-flock infection dynamics can heavily depend on the species composition in backyard farms. Ducks, in particular, can pose a higher risk of transmission within a flock or between flocks. Our findings can help inform surveillance and intervention strategies at the flock and local levels.

Author summary

We addressed the gap in our understanding of within-flock transmission dynamics of H5N1, particularly for small-scale, backyard farms, where it is reasonably realistic for multiple species of birds to be housed together. These smaller flocks may differ from their larger, industrialised counterparts in their structure and management, and may play a key role in the persistence and spread of H5N1. Notably, we know from the literature that waterfowl, such as ducks, can be asymptomatic after contracting H5N1 and thus act as ‘silent carriers’ of the virus, which could amplify the risk posed to other species of birds, mammals, and humans. We used a stochastic mechanistic model that accounted for such possibilities and simulated the possible outcomes of an outbreak. We found that while the presence of chickens is more likely to lead to high mortality upon infection, ducks can make H5N1 harder to detect within a flock, and thus cause a greater burden of infection, which increases the risk of potential between-flock and between-site transmissions. Our findings are consistent with the current literature and can help inform surveillance and control strategies.

Introduction

Highly Pathogenic Avian Influenza (HPAI), the H5N1 subtype, remains a threat to global health security as of 2025. The current H5N1 strain (A/goose/Guangdong/1/96) was first isolated from a domestic goose in China in 1996. Since then, numerous large outbreaks occurred in various countries in Asia in 2003, and subsequently led to cases found in Africa, Europe, and the Americas in the following decades, including nationwide outbreaks in many countries [1,2]. Although infections are most commonly found among birds, mammals and humans can also be affected. For example, a notable incident occurred in Hong Kong in 1997, where six people died after contracting an infection [2]. In 2024, an outbreak was identified in the US in which dairy cows and two humans contracted H5N1 [3]. Other mammals, including household pets, can also be susceptible to H5N1, as evident in an outbreak in a mink farm in Spain, 2023 [4], and in two cat shelters in South Korea, 2023 [5]. These events are examples of HPAI H5N1 causing significant economic losses and disrupting food security. The rare but significant bird-to-human spillover cases shows its pandemic potential, which is further signified by the recent cases of mammalian infections. Backyard and smallholder flocks are a unique concern in the context of HPAI H5N1 epidemiology, since they are widespread globally, often have limited biosecurity compared to commercialised farms, and potentially have consistent surveillance measures. These factors make them a persistent reservoir of viral circulation and a risk for widespread transmissions and zoonotic exposure. Therefore, understanding the transmission dynamics of the virus is vital in designing effective control and prevention strategies, and minimising potential human exposure to H5N1, especially in backyard flocks.

HPAI H5N1 is known to have a varied effect depending on the species and breed of the infected bird. Many existing studies, such as Bouma et al. [6] and Yu et al. [7], have shown that species such as chickens and turkeys are likely to exhibit noticeable clinical signs and die within days of an infection. In comparison, there exists some evidence that waterfowl such as ducks and geese can be asymptomatic to H5N1, meaning that no clinical signs would be observed in some cases, while still being highly infectious. This means that ducks can potentially act as ‘silent carriers’ of H5N1, making infections and outbreaks harder to detect promptly [8]. The presence of asymptomatic but infectious birds within a flock may also significantly alter the trajectory of an outbreak. Despite this, relatively few studies have investigated the epidemiological implications of housing multiple bird species together, particularly in small-scale backyard farms where such an arrangement is reasonably realistic [9]. One of the goals of this study is to investigate the potential risk of ‘silent spread’ of H5N1 resulting from the presence of ducks in a small, mixed-species flock, and how the infection dynamics changes for flocks with different species population distributions.

Mathematical and computational models have been widely used to study the spread of infectious diseases, including HPAI H5N1, providing insights into key epidemiological parameters such as the transmission rate and infectious period. In the context of HPAI, several studies have focused on fitting mathematical models to mortality data in large commercial flocks [10,11], while others have used experimental data to estimate key parameters such as transmission rate, latency period, and infectious period under controlled conditions [12,13]. A recent review by Kirkeby et al. [14] collected parameter estimates from previous work on HPAI of all subtypes, which were then used for a simulation study [15] to characterise the different epidemiological effects of HPAI subtypes, including H5N1. These works have been instrumental in the design of detection strategies and intervention policies. However, existing current research typically focuses on single-species flocks and overlooks the potentially varied outcomes introduced in mixed-species settings. Furthermore, most current models are geared towards high-density industrialised farms, leaving a gap in our understanding of disease dynamics in small-scale backyard flocks. Between October 2021 and April 2022, approximately a quarter of all HPAI-infected premises in the UK are considered ‘smallholding’ or ‘backyard’ [9]. In Southeast Asian countries such as Indonesia, backyard farms were found to have a higher contact rate than other types of flocks and were most at risk for transmissions of HPAI [16], demonstrating the significance of studying these types of flocks. In this study, we aim to address the current gap in literature by focusing on backyard, mixed-species flocks and investigating the effectiveness of passive surveillance. By developing a mechanistic model that allows the possibility of inter-species interactions and infection dynamics in mixed-species flocks, we explore how different population compositions of species influence outbreak probability, detection time, and infection burden.

In this study, we develop a stochastic, mechanistic model to simulate the within-flock spread of HPAI H5N1 in small, mixed-species populations. By varying the proportion of species such as chickens and ducks, we aim to evaluate how species composition influences: (i) the overall disease dynamics assuming no intervention, (ii) the time to HPAI detection via passive surveillance based on mortality signals, and (iii) the total burden of infection, measured by the total time birds spent infectious, up to the point of detection. The potential output of the model can inform the effectiveness of passive surveillance as an HPAI detection strategy, and is of practical relevance for designing early warning systems, optimising surveillance strategies, and implementing intervention policies such as vaccinations or culling. Ultimately, our goal is to improve our understanding of how heterogeneity in species susceptibility, clinical signs, and mortality rate can influence the trajectory and detectability of HPAI outbreaks in non-industrial poultry settings.

Methods

Model construction

We considered a backyard farm that housed either chickens, ducks, or a mixture of both. For the purpose of simulations, we used a fixed number of 40 total birds to simulate a smallholder backyard premises, where the birds can be either layers or broilers. A Susceptible–Exposed–Infectious–Recovered–Dead (SEIRD) model was used as a baseline with added possibilities for a bird to be asymptomatic while infectious. Therefore, individual birds were divided into the following compartments: susceptible (S), exposed (E), infectious and symptomatic (I), infectious and asymptomatic (I^*), recovered (R), and dead (D). A subscript was used to denote the species of the bird: c for chickens and d for ducks (e.g. S_c(t) denotes the number of susceptible chickens at time t). An exposed bird would become infectious at the rate $σ_{s}$ , with the probability of being symptomatic p_s, for $s = c, d$ , where the species was chickens or ducks, respectively. An infectious bird would recover or die with the rate $γ_{s}, γ_{s}^{*}$ , and the probability of death $δ_{s}, δ_{s}^{*}$ , based on the bird species and the existence of clinical signs. The model assumed a homogeneously mixing bird population with a density-dependent contact rate, which is more appropriate for small populations on backyard premises. Therefore, as justified in Fournie et al. [17], the force of infection at time $t \geq 0$ on species $x \in {c, d}$ was given by:

λ_{x} (t) = \frac{1}{N - 1} (β_{c x} I_{c} (t) + β_{c x}^{*} I_{c}^{*} (t) + β_{d x} I_{d} (t) + β_{d x}^{*} I_{d}^{*} (t))

where N = 40 was the initial size of the flock (The –1 was required because a bird cannot ‘contact’ itself), and $β_{y x}, β_{y x}^{*}$ were the transmission rate from symptomatic and asymptomatic birds of species y to species x, respectively. We assumed all other inter-compartment transitions occur with an exponentially distributed waiting time. Thus, we had the transition rules for chickens:

S_{c} \overset{λ_{c} (t)}{\to} E_{c} E_{c} \overset{σ_{c}}{\to} I_{c} I_{c} \overset{γ_{c}}{\to} D_{c}

and for ducks:

S_{d} \overset{λ_{d} (t)}{\to} E_{d} E_{d} \overset{p_{d} σ_{d}}{\to} I_{d} E_{d} \overset{(1 - p_{d}) σ_{d}}{\to} I_{d}^{*} I_{d} \overset{δ_{d} γ_{d}}{\to} R_{d} I_{d} \overset{(1 - δ_{d}) γ_{d}}{\to} D_{d} I_{d}^{*} \overset{γ_{d}^{*}}{\to} R_{d}

The explanations for the rate parameters are found in Table 1, and the compartmental diagram that captures the transition rules is presented in Fig 1. Note that some transition rules are omitted due to the redundancy caused by the choice of parameters, which can be inferred from Table 1.

Table 1. Parameter values used in the model, based on literature sources or specified assumptions.

Parameter	Description	Value	Source
$β_{c c}$	Chicken-to-chicken transmission rate	1.15 (1.02–1.30)	[6,10]
$σ_{c}^{- 1}$	Chicken latency period	0.24 (0.099–0.48)	[6]
$γ_{c}^{- 1}$	Chicken infectious period	2.1 (1.8–2.3)	[6]
p _c	Chicken symptomatic probability	1	Assumed [8]
$δ_{c}$	Chicken case-fatality probability	1	Assumed [8]
$β_{d d}$	Symptomatic duck-to-duck transmission rate	4.1 (2.8–5.8)	[11]
$σ_{d}^{- 1}$	Duck latency period	0.17 (0.03–0.38)	[11]
$γ_{d}^{- 1}$	Symptomatic duck infectious period	4.3 (2.8–5.7)	[11]
p _d	Duck symptomatic probability	0, 0.2, 0.4, 0.6, 0.8	Assumed
$δ_{d}$	Symptomatic duck case-fatality probability	0.70 (0.61–0.78)	[11]
$κ$	Rescaling for asymptomatic duck parameters	3 (1-5)	Assumed
$β_{d d}^{*}$	Asymptomatic duck-to-duck transmission rate	$\frac{β_{d d}}{κ}$	Assumed
$γ_{d}^{* - 1}$	Asymptomatic duck infectious period	$κ γ_{d}^{- 1}$	Assumed
$δ_{d}^{*}$	Asymptomatic duck case-fatality probability	0	Assumed
$β_{c d}, β_{d c}, β_{d c}^{*}$	Cross-species transmission rates	$β_{d d}, β_{c c}, \frac{β_{c c}}{κ}$	Assumed

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Parameter values reflect published estimates where available, with assumptions and derived formulas applied to asymptomatic and cross-species transmission parameters. The rate unit is day⁻¹. Sensitivity analysis includes variation in symptomatic probability and rescaling factor $κ$ .

Fig 1 — A compartmental diagram of the disease dynamics of a mixed-species flock. The top and bottom parts represent the chicken and duck populations, respectively. We assumed that all infected chickens became symptomatic, while ducks might not exhibit clinical signs with probability (1−p_d).

Parameter values

Owing to a lack of real-world data on within-flock infection dynamics for backyard farms, we relied on parameter estimations from the literature to inform our parameter choices. The baseline parameters on chicken infection dynamics ( $β_{c c}, σ_{c}, γ_{c}$ ) were chosen based on results by Bouma et al. [6] and Tiensin et al. [10]. Specifically, Bouma et al. [6] presented an experimental study that aimed to provide a parameter estimation of an SEIR model for chickens, and Tiensin et al. [10] used Thailand field data to estimate the transmission rate for different values of the infectious period in an SIR model by using the back-calculation method. The values for $σ_{c}$ and $γ_{c}$ were taken directly from the experimental study. However, the estimated value for $β_{c c}$ from the experimental study was based on an inoculated chicken and a susceptible chicken in the same cage, which might not reflect field scenarios. Hence, the value for $β_{c c}$ was taken from the field study, using the assumed $γ_{c}^{- 1} = 2$ , which matched with the experimental study. However, it is worth noting that different breed of chicken may exhibit different susceptibility to infections [18], so the actual parameter set may slightly differ from our chosen value.

Almost all relevant studies suggested that H5N1 is highly lethal to chickens. Experimental results by Bouma et al. [6], Jeong et al. [19], and Forrest et al. [20], as well as reviews such as the work from Kim et al. [8], implied a 100% mortality rate for infected chickens. While works from Spekreijse et al. [13] and Yu et al. [7] demonstrated that a small proportion of chickens might be asymptomatic depending on the strains of H5N1, but near 100% mortality rate for chickens with clinical signs was still observed. Therefore, we assumed in our model that chickens would always show clinical signs and eventually die of H5N1. For ducks, it was found that the possibility of showing clinical signs and dying from H5N1 varies depending on the breed of the duck [8,21], the strains of the virus [7,21–23], or the route of infection [19]. Therefore, we conducted a sensitivity analysis on the duck symptomatic probability (p_d) to account for the different scenarios, choosing values p_d = 0,0.2,0.4,0.6, and 0.8.

Current literature on parameter estimation of infection dynamics in duck flocks is scarce. One study on HPAI H5N8 from Vergne et al. [11] estimated using field data that the transmission rate was 4.1, the latency period was 0.17, the infectious period was 4.3, and the case-fatality rate was 0.7. Although the HPAI serotype was different, the results from the study were reasonably in agreement with an experimental study from van der Goot et al. [12]. The estimated R₀ number for duck flocks was also significantly larger than that of chicken flocks, in agreement with a recent review by Kirkeby et al. [14]. Given the high case-fatality rate assumed in the study, we assumed that the viral strain of focus in the work from Vergne et al. [11] was highly pathogenic to ducks, so the parameter estimations provided would apply specifically to symptomatic ducks.

For asymptomatic ducks, there was a lack of parameter estimation for the transmission rate or infectious period. Based on the work from Hulse-Post et al. [22], we expected that the infectious period for asymptomatic ducks could be as long as 17 days. Therefore, we defined a rescaling factor $κ = 3$ , where we assumed that the transmission rate $β_{d d}^{*}$ and infectious period $γ_{d}^{*}$ from asymptomatic ducks were $\frac{β_{d d}}{κ}, κ γ^{- 1}$ respectively, which ensured the value for R₀ was fixed. While $κ = 3$ will be assumed for all simulations and results except for the sensitivity analysis, see S5 Fig and S6 Fig from supporting information). Finally, given the homogeneous-mixing population assumption, we set the cross-species transmission rate $β_{c d} = β_{d d}, β_{d c} = β_{c c},$ and $β_{d c}^{*} = \frac{β_{c c}}{κ}$ , assuming the same contact rate between any two birds and the probability of infection dependent on the receiving bird.

Simulations and analysis

The model was simulated using the Gillespie algorithm [24]. Given a set of parameter choices, we set the number of chickens in the population to be 0, 10, 20, 30, and 40, out of 40 total birds, with the remainder being ducks. For the initial condition, one bird was chosen at random to become exposed, and the rest of the flock remained susceptible. The simulation then continued until no disease was present in the system. We performed 5000 realisations of the simulation model and stored them as a time series for each set of parameter choices and species compositions, which can be directly analysed by extracting summary statistics.

Among the 5000 simulations, we considered those that resulted in five or more birds ever being infected as an outbreak. We then filtered out the time series with no outbreaks and considered the interquartile range of the detection time: the day when the farm owner detects a certain number of deaths in the flock. We emulated the behaviours of different types of farm owners based on the level of cautiousness and likelihood of compliance, by considering scenarios where they would report a detection when two, four, or six birds died in the flock. The detection time for each detection rule was then recorded. We also calculated the undetected burden of infection within the flock, defined by the total time birds spent infectious up to the time of detection, measured in bird-days. This was done for every simulation with the death threshold for detection set at two, four, or six, similar to the detection time calculation.

We conducted sensitivity analysis on transmission rates $(β_{c c}, β_{d d})$ , latency $(σ_{c}^{- 1}, σ_{d}^{- 1})$ and infectious $(γ_{c}^{- 1}, γ_{d}^{- 1})$ periods, duck case-fatality probability $(δ_{d})$ , and the rescaling factor for asymptomatic duck parameters $(κ)$ using the Latin Hypercube Sampling (LHS) method [25], within the ranges specified in Table 1. For each parameter, its range was divided into 50 equal-probability intervals, and one value was sampled from each interval. Samples across parameters were combined via LHS to ensure uniform coverage of the multidimensional parameter space without repetition. Model outputs were then used to quantify parameter sensitivity by computing Spearman rank correlations (PRCC-style) between sampled parameter values and model outcomes: final deaths, detection time, and burden of infection. We tested outcomes for scenarios with p_d = 0.2 and chicken population sizes of 0 and 40.

In addition, we examined the effect of flock size on detection time and burden of infection. Flock size was varied from 20 to 200 birds in increments of 20, and for each flock size, simulations were conducted with chicken proportions of 0, 0.25, 0.5, 0.75, and 1, with other parameters held constant and p_d = 0.2.

The Python code that achieves the simulations can be found on GitHub: https://github.com/stevewu2001/Within-flock-simulation.

Results

Summary statistics

We investigated the final size of the simulations, recording the final death number (Figs 2 and 3 for each simulation. In most cases, most birds in the flock would be infected at some point during a successful outbreak (meaning that they will be either dead or recovered in the end). A higher duck symptomatic probability tends to lead to a larger number of deaths in a flock. This is evident from both the histograms in Figs 2 and 3 and the heat map in Fig 4. Interestingly, Fig 4 suggests that flocks with 30 chickens and 10 ducks result in the highest average number of deaths for all values of duck symptomatic probability.

Fig 2 — Histogram of distribution of final death numbers with varied number of chickens in flocks of size 40. Duck symptomatic probability set to 0.2.

Fig 3 — Histogram of distribution of final death numbers with varied number of chickens in flocks of size 40. Duck symptomatic probability set to 0.8.

Fig 4 — Heat map showing the average number of deaths in all simulation results given the parameter combinations of chicken populations and duck asymptomatic probability.

Detection time

We found that the outbreak detection time was highly dependent on the choice of parameters in the sensitivity analysis, specifically the probability of a duck showing clinical signs upon infection. Firstly, as per expectations, farmers who are able to detect H5N1 with lower death thresholds had an overall shorter detection time since the initial infection, as shown in Fig 5. We found that the difference between detection thresholds in duck-only flocks is most significant if the duck’s symptomatic probability is small (Fig 6 and top plot of Fig 5). We also found that duck-only flocks can result in overall longer detection times, with H5N1 left undetected for 10 days (median), and for as long as 40+ days in the worst-case scenarios. In comparison, the detection time is lower if chickens are present in the flock. Notably, detection is expected within approximately 7 days since the initial infection for chicken-only flocks. However, if the duck symptomatic probability is high, then the overall mortality rate will also increase, and thus the detection time is significantly lowered (bottom plot of Fig 5). The presence of chickens instead increases the detection time slightly, but the overall expected detection time is still fewer than approximately 7 days.

Fig 5 — Detection time for different death thresholds for detection and chicken population out of 40 total birds. Top plot: the duck’s symptomatic probability p_d = 0.2; Bottom plot: the duck’s symptomatic probability p_d = 0.8. The boxes indicate the interquartile range (25th and 75th percentiles), and the whiskers indicate the 2.5th and 97.5th percentiles. The white dot in the box indicates the average detection time, which also corresponds to the fourth and first row of Fig 6 (for detection after 2 deaths).

Fig 6 — Heat map showing the average detection time (with detection occurring when two deaths have occurred) in all simulation results given the parameter combinations of chicken populations and duck symptomatic probability. Note that no detection would occur for duck flocks with duck symptomatic probability equal to zero (Black grid).

Burden of infection

In general, due to the long infectious period, the transmissibility of H5N1, and the potentially delayed detection time in duck flocks, their presence in a flock contributes more to the burden of infection compared to chickens. If the duck symptomatic probability is low, the total time birds spend infectious is significantly higher in duck-only flocks, approximately 18 times higher than that of chicken-only flocks (top plot of Fig 7). While the number is reduced in the case of high duck symptomatic probability, a duck-only flock would still have approximately 4 times the burden of infection than chicken-only flocks (bottom plot of Fig 7). Note that we only accounted for time series with detected outbreaks, so if an outbreak occurred but detection failed, then the burden of infection accounting for such cases will be higher in duck-only flocks. As before, the heat map for the burden of infection before detection is shown in Fig 8. The result is consistent with the findings in Fig 7 for other sets of parameter choices. We have chosen to investigate only detected outbreaks, as undetected outbreaks are rare except for the p_d = 0.2 case in duck-only flocks, where detection evasion occurs due to the higher likelihood of having asymptomatic ducks. The burden of infection would then be calculated over the entire outbreak. This will not affect the qualitative result, as this case already yields the largest burden of infection with only detected outbreaks, as demonstrated by Fig 8.

Fig 7 — Undetected burden of infection (total time birds spent infectious up to the point of detection) for different death thresholds for detection and chicken population out of 40 total birds. Top plot: the duck’s symptomatic probability p_d = 0.2; Bottom plot: the duck’s symptomatic probability p_d = 0.8. The boxes indicate the interquartile range (25th and 75th percentiles), and the whiskers indicate the 2.5th and 97.5th percentiles. The white dot in the box indicates the average detection time, which also corresponds to the fourth and first row of Fig 8 (for detection after 2 deaths).

Fig 8 — Heat map showing the average undetected burden of infections (with detection occurring when two deaths have occurred) in all simulation results given the parameter combinations of chicken populations and duck asymptomatic probability. Note that no detection would occur for duck flocks with duck symptomatic probability equal to zero (Black grid).

Sensitivity analysis

As explained in the Methods section, we briefly explored the impact of the uncertainties of the parameters and total flock size on our results. The Spearman correlations (denoted as $ρ$ ) between the values of the sampled parameters and key statistics were shown in Figs 9 and 10. For chicken-only flocks, we found weak correlations for all parameters $(| ρ | < 0.15)$ . Parameters such as $κ$ , which are biologically irrelevant in the all-chicken setting, nonetheless showed small correlations $(| ρ | \approx 0.1)$ when considering detection times, which we attribute to sampling noise and stochasticity in simulation outcomes. For duck-only flocks, detection times were found to be moderately sensitive $(| ρ | \approx 0.3)$ to the duck-to-duck transmission rate $β_{d d}$ and $κ$ . Likewise, final deaths and burden of infections were mostly influenced by symptomatic duck case-fatality probability $δ_{d}$ and infectious period $γ_{d}^{- 1}$ respectively, albeit with less significance $(| ρ | \approx 0.15$ and 0.2).

Discussion

Our study differs from current literature with our unique focus on backyard, mixed-species flocks, the biological differences of each species, and the effectiveness of passive surveillance. To our knowledge, this is the first modelling study to quantify H5N1 transmission and passive surveillance performance in backyard mixed-species flocks, explicitly incorporating species-specific differences in infectiousness, symptoms, and mortality. We showed that ducks, or other similar species, may pose a substantial risk in the context of within-flock infections of HPAI. In particular, duck-only flocks have a higher chance of having an H5N1 outbreak (see S3 Fig and S4 Fig from supporting information), causing delayed detection (Figs 5 and 6) and increasing the risk of undetected outbreaks, and having a significantly higher burden of infection up to the point of detection (Figs 7 and 8), especially if ducks are more likely to be asymptomatic and thus can act as a ‘hidden’ source of infection. The undetected outbreaks and silent transmissions are signs to focus on duck flocks if alternative surveillance strategies such as active surveillance is utilised. Additionally, having a small population of ducks in a chicken-dominant flock can amplify mortality, as shown in Fig 4, where maximum final deaths are observed for flocks with 30 chickens and 10 ducks given a fixed duck symptomatic probability. The simulation results match expectations, as ducks have a longer infectious period and lower mortality rate. These biological traits directly influence our simulation outcomes, as the prolonged infectious period allows ducks to infect other birds over an extended time frame, while the lower mortality means outbreaks can remain undetected for longer under a passive surveillance system that triggers on deaths. We hypothesise that ducks can act as a more persistent intermediate source of infection, which could lead to more widespread infections when a larger chicken population coexists with the ducks. We also found that ducks tend to contribute to a higher unnoticed burden of infection, again driven by the longer infectious period and lower mortality rate, which explains the higher cumulative infection burden, delayed detection, and increased potential for between-flock transmission and zoonotic exposure through direct or indirect contact between flocks and humans. It is important to note that our analysis focuses on detected outbreaks, which may underestimate the true burden of infection, particularly in duck-only flocks. The undetected outbreaks, while only occurring in duck flocks under certain parameter assumptions, could prolong viral circulation and increase the risk of transmission to nearby flocks. In general, our findings are consistent with many other studies, in which ducks are shown or implied to be a more significant risk factor for HPAI H5N1 transmission [8,11,26].

The most sensitive parameter in our study is p_d, the probability that a duck will show clinical signs after infection. Specifically, detection evasion tends to only occur in duck-only flocks if p_d is small. This is likely due to low duck mortality, and most birds in the flock will recover without being detected. For larger values of p_d, we found that the detection time becomes shorter in duck-dominant flocks than in chicken-dominant flocks. A possible explanation is that ducks have a higher transmission rate and a longer infectious period, increasing the rate of death among birds. We also saw a lower infection burden when we increased the value of p_d, which is potentially due to the reduced detection time. In the additional sensitivity analysis, we found that some parameters, such as $β_{d d}, κ,$ and the total flock size, may have a moderate impact on the outcome upon detection. The choice of having 40 birds in our main simulations may also lead to an overestimation of detection time and burden of infection. However, we can also conclude that those parameters did not affect the result of our qualitative comparison between different configurations in a mixed-species flock.

One of our main assumptions regarding detection time is the criteria for detection. We assumed that a passive surveillance approach, where farmers voluntarily report a suspected infection in their flocks, has been implemented. We had chosen this approach as opposed to other strategies recommended for larger commercial flocks [26], because we believe that backyard farmers are more likely to have direct contact with the birds and therefore can observe signs and/or death reasonably efficiently. In particular, we believe that age-related mortalities are less likely to be identified as a sign of HPAI presence by backyard farmers. However, farmers’ knowledge and attitudes towards HPAI can vary significantly and are difficult to quantify. A recent survey study by McClaughlin et al. [9] highlighted the lack of knowledge of the clinical signs of HPAI among UK birdkeepers. Another investigation by Elbers et al. shows that irregular mortality rate is one of the main criteria for voluntary reporting in the Netherlands [27]. Hence, we have chosen the detection criterion to be ‘a certain number of deaths found in the flock’. We chose the threshold to be two, four, or six deaths to represent a likely range of farmer behaviour. These death thresholds are intended to reflect likely farmer behaviour in small backyard flocks, where voluntary reporting is common, whereas for commercial flocks it is often viable to have regulatory surveillance and laboratory confirmation, which may detect infection at lower relative mortality or earlier clinical signs. However, a highly knowledgeable bird owner may be able to identify clinical signs in birds before their deaths, and a less knowledgeable farmer may only report when there is a large number of deaths. Some farmers may also be hesitant to report if the signs of HPAI is not sufficiently clear [28], or try to rapidly harvest and sell birds during an outbreak [29]. This may result in a larger variance in detection time than what the simulation result suggests. Farmers’ sensitivity to observed deaths can also lead to varied outcomes. Factors such as delayed reporting can delay the detection time, resulting in an underestimation of detection time and burden of infection from our results. To address the uncertainties of the detection criteria, more surveys and investigations are required to better quantify farmers’ behaviours. For example, using surveys or interviews to group farmers by their knowledge level, reporting tendency, or response to flock mortality, as similarly demonstrated in Hill et al. [30].

Our choice of simulation model differs from some other studies on commercial farms [11,26] as we have excluded natural deaths of birds in our model. Unlike in a commercial farm, where the process of raising birds can be highly automated, backyard hobby farmers tend to know and have close contact with their flocks. Hence, while natural and H5N1-induced mortality can be difficult to differentiate in a large-scale farm, we assumed that small-scale bird keepers can identify an ‘unnatural’ death with relative ease, so the existence of natural mortality in our model makes little impact. This assumption may slightly underestimate the total mortality rate of birds. However, background mortality rate is highly varied across different farm management styles and regions, making any assumed rates speculative and context dependent. We have added two plots in supporting information (S9 Fig) to show that for background mortality rate 0.001 days⁻¹ (approximately 30% yearly mortality without HPAI), the impact of background mortality is minimal and does not change our qualitative results in any significant ways.

A limitation of our study is the choice of parameters in our model. Many parameter choices for our simulation were taken from either experimental studies (e.g., Bouma et al. [6]) or estimations from field data (e.g., Tiensin et al. [10], Vergne et al. [11]). Such parameters may change depending on the biosecurity measures and housing conditions of each individual flock. Additionally, the breeds and types of birds (e.g., broiler or layer) may also influence key parameters, which we did not account for in our simulations.

In our model, we assumed density-dependent transmission, such that the spread of disease through the flock depends on the total number of birds on the premises. In countries such as the UK, backyard poultry are typically kept in enclosures, and as flock size increases, the potential for contact also increases. However, in South East Asia, while some smallholders keep their poultry similarly enclosed, on other premises, birds are allowed to roam across much larger areas. In these cases, it may be more appropriate to assume frequency-dependent transmission, as birds are more likely to interact with a fixed number of contacts. The habitable space of the flock can also influence contact rates, so larger farms may have lower overall transmission rates than smaller farms. Furthermore, the inter-species transmission rate may be lower than assumed if chickens and ducks are kept separately, which violates our assumption of a homogeneously mixing population of birds. Some parameters, such as the probability of chickens showing clinical signs and dying from H5N1, were based on literature evidence and may vary in real-world settings. Additionally, our model had limited consideration of variance in farming conditions and environmental factors, which may impact its accuracy in specific backyard settings.

From a policy-making perspective, our findings indicate that species composition within backyard flocks has important implications for HPAI control strategies. Since passive surveillance leads to delayed detection and a higher risk of undetected transmission in duck-dominant flocks, enhanced measures such as active surveillance should be prioritised for these settings where the objective is to minimise the number of affected farms. In contrast, if reducing overall mortality is the primary goal, particularly in contexts where vaccination is available, prioritising interventions for chicken-dominant flocks is likely to be more effective due to their greater susceptibility and faster mortality. Species-specific strategies informed by our results can therefore help reduce both farm-level losses and between-flock transmission risk. We also recommend improving H5N1 awareness and symptom recognition among smallholders, particularly hobby farmers, to reduce the detection time and subsequently the burden of infections using the passive surveillance approach. Overall, these findings highlight the need for tailored surveillance and control policies that account for biological differences between bird species in backyard systems.

In conclusion, this study presents an exploratory analysis of how species composition may influence the within-flock transmission dynamics of HPAI. Our finding suggests that ducks, or waterfowl in general, are likely to play a more significant role in transmitting HPAI, while chickens or other similar species tend to have faster and more frequent mortalities, which is consistent with the current literature. Future work on parameter estimation of infection dynamics between various species of birds can be useful for further investigation. The parameter estimation may be integrated with real-time surveillance data and can be used on extended models such as spatial simulations or agent-based models. Another potential direction of research is to consider alternative surveillance and control strategies by taking the different transmissibility of H5N1 from various bird species into account. For example, a multi-objective optimisation problem comparing the trade-off between reducing mortality and limiting transmission can be investigated in the context of multi-species flocks, which would enable a more systematic analysis of different surveillance strategies.

Supporting information

S1 Fig. Infectious birds time series.

Number of infectious birds over time, for fixed p_d = 0.2. Red trajectories shows the time series directly, and the black trajectory is plotted by calculating the average across all time series on each day. Top: all 40 birds are ducks, middle: 20 chickens and 20 ducks, bottom: all 40 birds are chickens.

(TIFF)

pcbi.1013357.s001.tiff^{(4.5MB, tiff)}

S2 Fig. Dead birds time series.

Number of dead birds over time, for fixed p_d = 0.2. Blue trajectories shows the time series directly, and the black trajectory is plotted by calculating the average across all time series on each day. Top: all 40 birds are ducks, middle: 20 chickens and 20 ducks, bottom: all 40 birds are chickens.

(TIFF)

pcbi.1013357.s002.tiff^{(6.7MB, tiff)}

S3 Fig. Histogram final p_d = 0.2.

Histogram of distribution of final removed numbers (dead or recovered) with varied number of chickens in flocks of size 40. Duck symptomatic probability set to 0.2. The vertical dashed line indicates time series that are considered an outbreak (To the right of the dashed line).

(TIFF)

pcbi.1013357.s003.tiff^{(4.5MB, tiff)}

S4 Fig. Histogram final p_d = 0.8.

Histogram of distribution of final removed numbers (dead or recovered) with varied number of chickens in flocks of size 40. Duck symptomatic probability set to 0.8. The vertical dashed line indicates time series that are considered an outbreak (To the right of the dashed line).

(TIFF)

pcbi.1013357.s004.tiff^{(4.5MB, tiff)}

S5 Fig. Violin plot LHS all-chicken flock.

Violin plot for the distribution of final deaths, detection time, and burden of infections among all LHS simulations (all-chicken flocks).

(TIFF)

pcbi.1013357.s005.tiff^{(3.4MB, tiff)}

S6 Fig. Violin plot LHS all-duck flock.

Violin plot for the distribution of final deaths, detection time, and burden of infections among all LHS simulations (all-duck flocks).

(TIFF)

pcbi.1013357.s006.tiff^{(3.4MB, tiff)}

S7 Fig. Bar plot outbreak/detection distribution.

Bar plot showing the probability of a simulation run resulting in an outbreak, and whether it would be detected with death thresholds 6, 4, or 2. This is fixed with p_d = 0.2. For p_d = 0.8 all outbreaks can be detected with the highest death threshold.

(TIFF)

pcbi.1013357.s007.tiff^{(2.7MB, tiff)}

S8 Fig. Result vs total population size.

The mean detection time (top) and burden of infection (bottom) until detection for different total flock sizes and the proportion of chickens in the flock. Other parameters, including p_d = 0.2, were fixed.

(TIFF)

pcbi.1013357.s008.tiff^{(1.9MB, tiff)}

S9 Fig. Simulation outcomes with natural mortality.

The detection time and burden of infection for the natural mortality rate 10⁻³ (approximately 30% yearly mortality without HPAI). This shows that the inclusion of natural mortality will not have any qualitative impact on our results.

(TIFF)

pcbi.1013357.s009.tiff^{(5MB, tiff)}

Data Availability

The code to generate all simulated data can be found in https://github.com/stevewu2001/Within-flock-simulation.

Funding Statement

SXW was funded by the Engineering and Physical Sciences Research Council (EPSRC) through the Mathematics of Systems Centre for Doctoral Training (MathSys CDT) [grant number EP/S022244/1] (website: https://www.ukri.org/councils/epsrc/). CND and MJT were supported by a joint Ecology and Evolution of Infectious Diseases (EEID) award from the U.S. National Science Foundation (NSF) and the Biotechnology and Biological Sciences Research Council (BBSRC) [grant number BB/X005224/1] and a BBSRC grant [BB/X016137/1]. (websites: https://www.nsf.gov/ and https://www.ukri.org/councils/bbsrc/). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

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PLoS Comput Biol. doi: 10.1371/journal.pcbi.1013357.r001

Decision Letter 0

Jennifer A Flegg, Qiangguo Jin

22 Aug 2025

PCOMPBIOL-D-25-01462

The role of ducks in detecting Highly Pathogenic Avian Influenza in small-scale backyard poultry farms

PLOS Computational Biology

Dear Dr. Wu,

Thank you for submitting your manuscript to PLOS Computational Biology. After careful consideration, we feel that it has merit but does not fully meet PLOS Computational Biology's publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.

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Qiangguo Jin

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PLOS Computational Biology

Jennifer Flegg

Section Editor

PLOS Computational Biology

Journal Requirements:

1) Please ensure that the CRediT author contributions listed for every co-author are completed accurately and in full.

At this stage, the following Authors/Authors require contributions: Steven Xingyu Wu, Christopher N Davis, Mark Arnold, and Michael J Tildesley. Please ensure that the full contributions of each author are acknowledged in the "Add/Edit/Remove Authors" section of our submission form.

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Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Authors:

Please note here if the review is uploaded as an attachment.

Reviewer #1: In this manuscript, Wu et al. presents a well-designed simulation study examining the transmission dynamics of Highly Pathogenic Avian Influenza (HPAI) H5N1 within small-scale, mixed-species poultry flocks, with particular attention to backyard farming systems. The authors develop a computational model that simulates disease spread, incorporating factors such as species composition, chicken-to-duck ratios, mortality-based detection timing, and cumulative infectious burden prior to detection. This approach captures important complexities often overlooked in models designed for large, single-species commercial farms.

Overall, the manuscript is well written and addresses a timely and relevant topic. However, several aspects would benefit from further clarification and elaboration. Please see my comments below:

Major comments:

Abstract:

1. The authors could consider mentioning in the abstract that the authors have developed a computational model to simulate the spread of HPAI H5N1.

2. Including the GitHub link in the abstract would improve accessibility and encourage use of the model and data.

Introduction:

3. Add a brief (2–3 sentence) overview of why HPAI H5N1 matters globally and why backyard flocks are a unique concern.

4. Highlight novelty by emphasizing what makes your study different from existing research.

5. Briefly outline how the findings could inform public health or agricultural policy.

6. Discuss limitation by adding a short note on what the model does not capture (e.g., environmental factors, human intervention) adds credibility.

Methods:

7. The simulation-based approach is strong, with thoughtful use of the Gillespie algorithm and behavioral detection thresholds. However, the assumed flock size of 40 birds may limit generalizability. Absolute mortality thresholds (e.g., 2–6 birds) represent a large proportion of the flock and may not scale well to larger operations. Smaller flocks are also more susceptible to stochastic effects. To improve applicability, I suggest including simulations with larger flock sizes or a sensitivity analysis to assess how outcomes vary with population size.

8. The authors have acknowledged the key model assumptions such as homogeneous mixing and exclusion of natural mortality. It would be helpful to more clearly discuss how these assumptions might influence transmission dynamics and detection timing.

9. The authors have provided the GitHub link for data and code. To improve usability, they should consider adding a README file with clear instructions on how to run and interpret the model.

Results:

10. The differences between duck-only and chicken-only flocks are interesting. To strengthen the interpretation, the authors should more clearly explain how biological traits such as longer infectious periods or lower mortality in ducks relate to the simulation results.

11. The analysis of detection time at various death thresholds is valuable. To improve its practical relevance, it would help to discuss how these thresholds reflect real-world surveillance practices, particularly in smallholder and commercial settings.

12. Using bird-days to measure infectious burden is appropriate. To highlight its epidemiological importance, the authors could more clearly explain how a higher burden might increase the risk of transmission to nearby flocks or humans.

13. The decision to analyze only simulations with detected outbreaks may underestimate the true burden of infection, particularly in duck-only flocks. A brief discussion or sensitivity analysis of undetected outbreaks would provide a more complete picture.

Discussion:

14. The authors acknowledge variability in farmer behavior, which is commendable. However, the discussion could be strengthened by referencing more region-specific behavioral studies or proposing how behavioral heterogeneity could be modeled in future work.

15. The discussion mentions important assumptions, such as homogeneous mixing and the exclusion of natural mortality. However, their impact on the results should be explored in more depth. For instance, how could spatial separation or age-related mortality affect detection patterns?

16. The author could consider presenting the balance between reducing mortality and limiting transmission as a multi-objective optimization problem to strengthen the study’s computational relevance.

17. The proposed future work is appropriate but could be expanded to include agent-based models, spatial simulations, or integration with real-world surveillance data. Exploring these directions would broaden the study’s scope and enhance its impact.

Reviewer #2: The paper addresses an interesting research question related to modeling influenza transmission across different avian species. The manuscript is generally well written with a clear presentation of the methodology. However, after careful review, I have concerns regarding the significance of the problem, the novelty of the methodology, and the design of the numerical experiments.

Regarding the problem setup, the authors emphasize that interspecies transmission in avian populations has not been investigated. The focus of the article is on small backyard settings where there is limited or no data available to validate the parameter values used in the dynamical system models.

This raises concerns about the practical relevance and credibility of the simulation results. While small backyard scenarios are underexplored, higher-density industrial settings may be of greater interest from both scientific and public health perspectives.

Additionally, data from such settings may be available to support parameter estimation and model validation.

I think incorporating these would significantly enhance the attractiveness and trustworthiness of the study in real-world applications, or the authors should explain more clearly why they chose this setting given the limited data resources.

Regarding the methodology, the main novelty of the paper appears to lie in modeling transmission under a mixed-species structure. However, this novelty is weakened by the use of a simplified, uniform distribution of species.

Since this mixing structure is central to the contribution of the paper (putting aside the backyard setting), I suggest that the authors explore other mixing assumptions that reflect different contact probabilities or densities between species based on real-world scenarios. This would make the methodological contribution more convincing.

I do not see other significant methodological innovations that distinguish the manuscript, as the model is based on traditional compartmental formulations and simulations with parameter values drawn from previous references.

I think for a journal like PCB, some advances in computational methods should be proposed, or at least the authors should adopt other advanced existing computational frameworks to draw conclusions instead of relying solely on traditional methods.

For the numerical experiments, I have concerns about the validity of the results, as parameter values are taken from previous references that may not be fully suitable for backyard settings. Given that no data are available, the resulting conclusions have limited support from real-world scenarios.

I therefore suggest that the authors explore potential datasets to help validate the research findings, or change the problem settings to ones for which data validation is possible.

The design of the sensitivity analysis for some model parameters also confuses me, as only a few values are considered, which may be too simplistic for a highly nonlinear SEIR model with mixed densities assumed.

I suggest the authors switch to a continuous distribution for the sensitivity analysis instead of testing only a few points. Consider using Latin Hypercube Sampling if no data are available.

The purpose of sensitivity analysis should be to compare and identify parameters from the full set that are of interest. For example, people may be most interested in the transmission rate and asymptomatic probability, which are more sensitive and therefore more crucial for controlling the spread.

Based on this, a full comparison of sensitivities for all parameters is needed.

Reviewer #3: The review comments are uploaded as an attachment.

Reviewer #4: The paper by Wu et al. The role of ducks in detecting Highly Pathogenic Avian Influenza in small-scale backyard poultry farms, develops a SEIRD model and uses stochastic simulation to study avian influenza transmission between ducks and chickens in small mixed flocks. The parameters are drawn from literatures, and the simulations appear plausible. The work investigates the role of ducks in avian flu transmission in small population, which is interesting. And the authors have acknowledged the limitation of their work.

I have a few concerns:

1. In the text, beta^*_dc=beta_cc/kappa, however, it is inconsistent with kappa*beta_cc in Table 1. Please double check this and the corresponding simulation.

2. In detection time section, the work states that ‘due to higher mortality rate for ducks’, which is misleading as they specifically mentioned that chicken has nearly 100% death rate while the duck actually has a lower case-fatality rate. I think this statement requires clarification with biological evidence.

**********

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Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Yes

Reviewer #4: Yes

**********

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Reviewer #1: Yes: Dr. Reema Singh

Reviewer #2: No

Reviewer #3: No

Reviewer #4: No

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PLoS Comput Biol. 2026 Jan 9;22(1):e1013357. doi: 10.1371/journal.pcbi.1013357.r002

Author response to Decision Letter 1

13 Oct 2025

Attachment

Submitted filename: Response to reviewers.pdf

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PLoS Comput Biol. doi: 10.1371/journal.pcbi.1013357.r003

Decision Letter 1

Jennifer A Flegg, Qiangguo Jin

13 Nov 2025

PCOMPBIOL-D-25-01462R1

The role of ducks in detecting Highly Pathogenic Avian Influenza in small-scale backyard poultry farms

PLOS Computational Biology

Dear Dr. Wu,

Please submit your revised manuscript by Jan 13 2026 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at ploscompbiol@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pcompbiol/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.

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We look forward to receiving your revised manuscript.

Kind regards,

Qiangguo Jin

Academic Editor

PLOS Computational Biology

Jennifer Flegg

Section Editor

PLOS Computational Biology

Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Authors:

Please note here if the review is uploaded as an attachment.

Reviewer #1: Thank you for addressing my comments. I appreciate the thoughtful revisions and the authors’ efforts to respond to the majority of the points raised. However, several comments appear to be only partially addressed and could benefit from further clarification or expansion to fully meet their intent.

1. Previous comment: Add a brief overview of why HPAI H5N1 matters globally and why backyard flocks are a unique concern.

New comment: The authors have partially addressed this by providing examples from the UK and Southeast Asia that highlight the elevated risk in backyard flocks. While this supports the concern about their vulnerability, it does not clearly explain the global significance of HPAI H5N1, such as its impact on public health, poultry industries, or zoonotic potential.

2. Previous comment: Highlight novelty by emphasizing what makes your study different from existing research.

New comment: Thank you for partially addressing this point. To more clearly highlight the novelty of your study, I recommend explicitly stating early in the discussion how your approach differs from prior work. For instance, you could emphasize the unique focus on backyard mixed-species flocks, your assumptions around passive surveillance, or specific modeling choices that distinguish your study.

3. Previous comment: Briefly outline how the findings could inform public health or agricultural policy.

New comment: Thank you for the additions that begin to connect your findings to policy relevance. To fully address the comment, I suggest summarizing how specific results, such as duck-related detection delays and species composition effects, could inform concrete public health or agricultural policies. A clear statement of practical implications would help readers understand how your findings can support decision-making.

4. Previous comment: The differences between duck-only and chicken-only flocks are interesting. To strengthen the interpretation, the authors should more clearly explain how biological traits such as longer infectious periods or lower mortality in ducks relate to the simulation results.

New comment: Thank you for adding a sentence to address this point. To strengthen the interpretation further, I suggest expanding the explanation of how these biological traits specifically influence simulation outcomes such as detection time, infection burden, and mortality patterns. This would help clarify the mechanisms driving the observed differences.

5. Previous comment: The analysis of detection time at various death thresholds is valuable. To improve its practical relevance, it would help to discuss how these thresholds reflect real-world surveillance practices, particularly in smallholder and commercial settings.

New comment: Thank you for partially addressing this comment. To improve practical relevance, I suggest briefly discussing how the selected death thresholds align with actual surveillance practices in both smallholder and commercial contexts. Referencing typical reporting criteria or known behavioral patterns could help contextualize the thresholds and strengthen the policy implications.

6. Previous comment: Using bird-days to measure infectious burden is appropriate. To highlight its epidemiological importance, the authors could more clearly explain how a higher burden might increase the risk of transmission to nearby flocks or humans.

New comment: Thank you for addressing this point. The added explanation strengthens the epidemiological relevance of bird-days. If applicable, consider briefly noting whether prolonged infectiousness in ducks could also elevate zoonotic risk to further clarify the public health implications.

7. Previous comment: The decision to analyze only simulations with detected outbreaks may underestimate the true burden of infection, particularly in duck-only flocks. A brief discussion or sensitivity analysis of undetected outbreaks would provide a more complete picture.

New comment: Thank you for including the bar plot in the supplementary materials. To fully address the comment, I suggest briefly discussing the implications of undetected outbreaks in the main text. For example, highlighting how these silent infections, especially in duck-only flocks, could influence surveillance strategies or underestimate transmission risk would reinforce the importance of your findings.

8. Previous comment: The authors acknowledge variability in farmer behavior, which is commendable. However, the discussion could be strengthened by referencing more region-specific behavioral studies or proposing how behavioral heterogeneity could be modeled in future work.

New comment: Thank you for citing relevant work on behavioral heterogeneity. To fully address the comment, I suggest referencing region-specific behavioral studies related to HPAI or smallholder poultry farming if available. Additionally, proposing how behavioral variability could be incorporated into future models, especially in the context of backyard flocks, would improve the relevance and depth of the discussion.

9. Previous comment: The discussion mentions important assumptions, such as homogeneous mixing and the exclusion of natural mortality. However, their impact on the results should be explored in more depth. For instance, how could spatial separation or age-related mortality affect detection patterns

New comment: Thank you for the update. To fully address the comment, I suggest briefly summarizing in the main text how key assumptions such as homogeneous mixing and exclusion of natural mortality might influence detection patterns. For example, spatial separation could slow transmission and delay detection, while age-related mortality might obscure outbreak signals. A clearer discussion of these mechanisms would help readers interpret the robustness of your findings.

10. Previous comment: The author could consider presenting the balance between reducing mortality and limiting transmission as a multi-objective optimization problem to strengthen the study’s computational relevance.

New comment: Thank you for acknowledging the suggestion. To fully address the comment, I recommend briefly elaborating on how the trade-off between reducing mortality and limiting transmission could be framed as a multi-objective optimization problem. Even a short mention of potential objectives, constraints, or modeling approaches would help clarify the computational relevance and open avenues for future work.

Reviewer #2: The manuscript has been substantially improved. I do not see any remaining issues and therefore accept the manuscript.

Reviewer #3: The authors have addressed most of my previous comments well. However, several of the responses require further discussion or additional clarification.

First, I am not fully convinced by the following response: “We believe that density-dependent models are more appropriate for small flocks. Unlike in large-scale farms, where each bird is more likely to have a fixed number of contacts regardless of population increase, in a small backyard the population size directly impacts the contact rate of birds.”

The extent of density-dependent transmission is influenced not only by the number of animals but also by the space available to them. While the combined effects of these factors are complex to understand, I believe that in backyard settings, birds are likely to have sufficient space to roam and express their social behaviours more freely. This could lead to more heterogenous mixing and frequency-dependent transmission, as birds would not need to interact with unrelated individuals against their social preferences. I acknowledge that when bird density is very high relative to the available space, movement may be restricted, and contacts may occur mostly among nearby individuals (so may have a fixed number of contacts regardless population increase as the authors wrote). However, such settings are unlikely to represent typical backyard settings I imagine. One could also favour the opposite dynamics (if density is high but birds can still move, they would have more contacts with related birds, resulting in density-dependent transmission).

Could you please provide a further justification for your assumptions regarding transmission mode and include that in the manuscript?

Second, please clarify why only layer chickens were chosen as the study population. Are layer chickens the most common type kept in backyard settings, and is this specific to the UK? I am not sure this assumption is generalisable, as in many Southeast Asian countries, for example, chickens are often raised primarily for meat production.

Finally, I remain unconvinced by the authors’ rationale for excluding background mortality. Background mortality is a key factor in passive surveillance on poultry farms, and detection time is one of the main outcomes of this study. If ducks and chickens have different background mortality rates, this could influence detection times to some extent. Exploring this aspect would strengthen the manuscript, or alternatively, please provide a more robust justification for not including it.

Reviewer #4: The authors have addressed my previous comments. I have no further comments.

**********

Have the authors made all data and (if applicable) computational code underlying the findings in their manuscript fully available?

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Yes

Reviewer #4: Yes

**********

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Reviewer #1: Yes: Dr. Reema Singh

Reviewer #2: No

Reviewer #3: No

Reviewer #4: No

Figure resubmission:

Reproducibility:

PLoS Comput Biol. 2026 Jan 9;22(1):e1013357. doi: 10.1371/journal.pcbi.1013357.r004

Author response to Decision Letter 2

13 Dec 2025

Attachment

Submitted filename: Review Response.pdf

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PLoS Comput Biol. doi: 10.1371/journal.pcbi.1013357.r005

Decision Letter 2

Jennifer A Flegg, Qiangguo Jin

23 Dec 2025

Dear Mr Wu,

We are pleased to inform you that your manuscript 'The role of ducks in detecting Highly Pathogenic Avian Influenza in small-scale backyard poultry farms' has been provisionally accepted for publication in PLOS Computational Biology.

Before your manuscript can be formally accepted you will need to complete some formatting changes, which you will receive in a follow up email. A member of our team will be in touch with a set of requests.

Please note that your manuscript will not be scheduled for publication until you have made the required changes, so a swift response is appreciated.

IMPORTANT: The editorial review process is now complete. PLOS will only permit corrections to spelling, formatting or significant scientific errors from this point onwards. Requests for major changes, or any which affect the scientific understanding of your work, will cause delays to the publication date of your manuscript.

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Thank you again for supporting Open Access publishing; we are looking forward to publishing your work in PLOS Computational Biology.

Best regards,

Qiangguo Jin

Academic Editor

PLOS Computational Biology

Jennifer Flegg

Section Editor

PLOS Computational Biology

***********************************************************

PLoS Comput Biol. doi: 10.1371/journal.pcbi.1013357.r006

Acceptance letter

Jennifer A Flegg, Qiangguo Jin

PCOMPBIOL-D-25-01462R2

The role of ducks in detecting Highly Pathogenic Avian Influenza in small-scale backyard poultry farms

Dear Dr Wu,

I am pleased to inform you that your manuscript has been formally accepted for publication in PLOS Computational Biology. Your manuscript is now with our production department and you will be notified of the publication date in due course.

The corresponding author will soon be receiving a typeset proof for review, to ensure errors have not been introduced during production. Please review the PDF proof of your manuscript carefully, as this is the last chance to correct any errors. Please note that major changes, or those which affect the scientific understanding of the work, will likely cause delays to the publication date of your manuscript.

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Thank you again for supporting PLOS Computational Biology and open-access publishing. We are looking forward to publishing your work!

With kind regards,

Anita Estes

Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Supplementary Materials

S1 Fig. Infectious birds time series.

(TIFF)

pcbi.1013357.s001.tiff^{(4.5MB, tiff)}

S2 Fig. Dead birds time series.

(TIFF)

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S3 Fig. Histogram final p_d = 0.2.

(TIFF)

pcbi.1013357.s003.tiff^{(4.5MB, tiff)}

S4 Fig. Histogram final p_d = 0.8.

(TIFF)

pcbi.1013357.s004.tiff^{(4.5MB, tiff)}

S5 Fig. Violin plot LHS all-chicken flock.

Violin plot for the distribution of final deaths, detection time, and burden of infections among all LHS simulations (all-chicken flocks).

(TIFF)

pcbi.1013357.s005.tiff^{(3.4MB, tiff)}

S6 Fig. Violin plot LHS all-duck flock.

Violin plot for the distribution of final deaths, detection time, and burden of infections among all LHS simulations (all-duck flocks).

(TIFF)

pcbi.1013357.s006.tiff^{(3.4MB, tiff)}

S7 Fig. Bar plot outbreak/detection distribution.

(TIFF)

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S8 Fig. Result vs total population size.

(TIFF)

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S9 Fig. Simulation outcomes with natural mortality.

(TIFF)

pcbi.1013357.s009.tiff^{(5MB, tiff)}

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Data Availability Statement

The code to generate all simulated data can be found in https://github.com/stevewu2001/Within-flock-simulation.

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PERMALINK

The role of ducks in detecting Highly Pathogenic Avian Influenza in small-scale backyard poultry farms

Steven Xingyu Wu

Christopher N Davis

Mark Arnold

Michael J Tildesley

Roles

Abstract

Author summary

Introduction

Methods

Model construction

Table 1. Parameter values used in the model, based on literature sources or specified assumptions.

Fig 1. Model compartmental diagram.

Parameter values

Simulations and analysis

Results

Summary statistics

Fig 2. Histogram final deaths pd = 0.2.

Fig 3. Histogram final deaths pd = 0.8.

Fig 4. Heat map final deaths.

Detection time

Fig 5. Box plot detection time.

Fig 6. Heat map detection time.

Burden of infection

Fig 7. Box plot burden of infection.

Fig 8. Heat map burden of infection.

Sensitivity analysis

Fig 9. The Spearman correlation between the sampled parameters and final deaths (left), detection time (middle), and burden of infection (right), respectively, with fixed pd = 0.2, and all 40 birds are chickens.

Fig 10. The Spearman correlation between the sampled parameters and final deaths (left), detection time (middle), and burden of infection (right), respectively, with fixed pd = 0.2, and all 40 birds are ducks.

Discussion

Supporting information

Data Availability

Funding Statement

References

Decision Letter 0

Jennifer A Flegg

Qiangguo Jin

Roles

Author response to Decision Letter 1

Decision Letter 1

Jennifer A Flegg

Qiangguo Jin

Roles

Author response to Decision Letter 2

Decision Letter 2

Jennifer A Flegg

Qiangguo Jin

Roles

Acceptance letter

Jennifer A Flegg

Qiangguo Jin

Roles

Associated Data

Supplementary Materials

Data Availability Statement

ACTIONS

PERMALINK

RESOURCES

Similar articles

Cited by other articles

Links to NCBI Databases

Fig 2. Histogram final deaths p_d = 0.2.

Fig 3. Histogram final deaths p_d = 0.8.

Fig 9. The Spearman correlation between the sampled parameters and final deaths (left), detection time (middle), and burden of infection (right), respectively, with fixed p_d = 0.2, and all 40 birds are chickens.

Fig 10. The Spearman correlation between the sampled parameters and final deaths (left), detection time (middle), and burden of infection (right), respectively, with fixed p_d = 0.2, and all 40 birds are ducks.