Characterizing population-level short-term waning of newcastle disease humoral immunity of MDA-positive broiler chicks with day-old HB1 vaccination in Nigeria

Highlights

• •High anti-ND GMTs and serologic protection achieved by Day 1.
• •Significant GMT drop and protective antibody coverage loss by Day 7–21.
• •Population-level anti-ND protection lasts for 4.01 days (power-law model estimate).
• •Power-law decay model outperforms exponential models.

Abstract

Broiler chicks supplied by hatcheries across Nigeria are often vaccinated at day-old with the Hitchner B1 (HB1) vaccine and come from breeder hens with up-to-date Newcastle disease (ND) immunization. In Nigeria, virulent ND virus strains continue to circulate, making it imperative to assess the early population-level anti-ND humoral immune kinetics of broiler birds supplied to poultry farmers. In this study, we employed a hybrid approach integrating serological analysis with quantitative immunokinetic decay modelling to characterize short-term population-level ND humoral immunity waning in broiler chicks sourced from five major Nigerian hatcheries. Findings from this study show a rapid decline in anti-ND antibody levels, with a loss of putative population-level serologic protection observed within the first week of life in MDA-positive broiler chicks with day-old HB1 vaccination. Power-law modelling best captured the short-term non-linear pattern of anti-ND antibody waning in our study, estimating that population-level GMTs remained above the moderately protective threshold for approximately four days of life. These results point to the existence of a potential window of ND susceptibility, indicating an early population-level risk of ND infection for MDA-positive broiler birds under routine day-old HB1 vaccination in Nigeria. Overall, the study highlights the importance of accounting for MDA levels and optimizing vaccination timing to enhance early-life protection against ND in our region.

1. Introduction

Newcastle disease virus (NDV), also known as avian paramyxovirus (AP) type 1, is an enveloped, negative-sense, single-stranded RNA virus within the Orthoavulavirus genus of the family Paramyxoviridae and is the etiological agent of Newcastle disease (ND) (Brown et al., 2021; Rima et al., 2019). NDV is the most significant pathogen among the 22 known AP serotypes, affecting many different bird species (domestic and wild) worldwide, with chickens being more vulnerable to the disease (Dimitrov, 2024).

ND continues to be a major constraint on extensive poultry production in rural communities, as well as on the more semi-intensive and intensive production systems operated by poultry farmers in urban and peri‑urban communities of many low- to middle-income countries (Andrews et al., 2021). At the moment, vaccination and biosecurity remain the cornerstones of ND prevention (Bertran et al., 2018; Deka et al., 2020; Dimitrov et al., 2017), and effective vaccination programs are critical to the sustenance of poultry health and productivity.

In Nigeria, ND vaccination schedules often begin at the hatchery, with day-old broiler chicks receiving the Hitchner B1 (HB1) vaccine via aerosol spray (Oni & Adedipe, 2012). These chicks come from breeder flocks with up-to-date NDV immunization and therefore carry maternally derived antibodies (MDA) against ND. Anti-ND MDA have been said to be high and protective during the first ten days of life (Abdulrasol et al., 2024). These high early anti-ND MDA levels, however, can neutralize vaccine antigen following vaccination, particularly live vaccines such as HB1 (Gough & Allan, 1976; Van Eck et al., 1991). This neutralization has been reported to suppress vaccine-induced seroconversion and accelerate the decline of protective anti-ND MDA, resulting in an “immune gap” during which chicks become increasingly vulnerable to ND infection (Deka et al., 2020; Liu et al., 2023; Oni & Adedipe, 2012; Vrdoljak, 2017).

A protective level of humoral immunity, alongside cell-mediated and mucosal immunity, is critical for protecting birds against ND during the early stages of life and beyond (Kapczynski et al., 2013). However, no study has quantitatively characterized the short-term population-level pattern of anti-ND antibody waning in MDA-positive broiler birds under routine day-old HB1 vaccination in Nigeria. Consequently, there is a critical need for a quantitative population-level understanding of early anti-ND humoral immune dynamics in broiler chicks supplied to poultry farmers. In this study, we therefore employed a hybrid approach integrating serology with quantitative immunokinetic decay modelling to characterize population-level humoral immune kinetics in broiler chicks supplied by major hatcheries across the country. We hypothesized that population-level anti-ND humoral immunity in MDA-positive broiler chicks vaccinated with HB1 at day-old declines rapidly during early life, leading to an early loss of putative serologic protection. By addressing this hypothesis, this study aims to provide empirically grounded insights into early anti-ND humoral immunity waning, informing evidence-based strategies for optimizing early protective immunity and minimizing the devastating impact of ND on the Nigerian poultry industry.

2. Methodology

2.1. Study design & population

This study adopted a non-longitudinal population-level design in which 450 day-old broiler chicks sourced from five major hatcheries in Nigeria were allocated into five groups (A–E) of 90 chicks each. Within each group, 15 chicks were randomly selected for terminal sampling on days 1, 7, 10, 14, 17, and 21 over the 21-day study period. The sample size (15 chicks per day and 90 chicks per group) was determined as a convenience sample based on logistics and available resources, while ensuring that it significantly exceeded the 25 chicks per group used by Oni and Adedipe (2012) in a similar study conducted in Nigeria. To compensate for possible sample size limitation, a robust bootstrapping analysis was employed in the statistical analysis section of our study. In this study, an additional five chicks per group from the corresponding hatchery batch were kept as a source of replacement in case mortality was recorded. Such age-matched replacements were required on days 10 (two replacements), 14 (one replacement), and 21 (three replacements) for groups B, C, and E, respectively. Birds (19 chicks) remaining after the study period were kept until 8 weeks of age and subsequently sold.

All study birds had a history of day-old HB1 intraocular vaccination and originated from parent stock that had received up-to-date NDV immunization. The study birds were housed in five different brooding sections (groups A–E), prepared according to standard recommendations, in the Poultry Section of the Veterinary Teaching Hospital, Joseph Sarwuan Tarka University, Makurdi (JoSTUM). The birds were provided with feed (Ultima® Plus Super Starter for the first 2 weeks, followed by Ultima® Starter for the next 1 week) and water (tap water) ad libitum, with no additional vaccines or drugs administered during the 21-day study period.

2.2. Sample collection

Chicks were randomly selected for sampling at each time-point, and they were sacrificed through manual cervical dislocation, followed by blood collection directly via cardiac puncture, using a slight modification of the method described by Kelly and Alworth (2013). The sacrificed bird was placed in right lateral recumbency, feathers over the collection site were gently removed, and the area was disinfected with 70 % alcohol. A volume of ≥0.5 mL to ≤1.0 mL of blood was collected using a 21 G needle attached to a 2 mL syringe, inserted between the ribs perpendicular to the skin at the approximate location of the heart. Blood samples were transferred into plain sample bottles, labeled appropriately, and left to clot at room temperature. The serum was then separated into labeled cryovials corresponding to groups A–E and the respective sampling days (1, 7, 10, 14, 17, and 21) and stored at −20 °C in the Veterinary Microbiology Laboratory of JoSTUM, until serological analysis.

2.3. Generation of serological data

2.3.1. Serology

The hemagglutination inhibition (HI) test was performed according to the WOAH Manual of Diagnostic Tests and Vaccines for Terrestrial Animals (WOAH, 2021), using 4 hemagglutinating units (HAU) of in-house prepared vaccinal NDV antigen. Two-fold serum dilution (1:2, 1:4, 1:8, 1:16, 1:32, ……, 1:2048, 1:4096) was employed for the HI test, and the test was performed in the Veterinary Microbiology Laboratory of JoSTUM.

2.3.2. HI titers, seropositive counts, and coded titres

HI titers for each positive serum sample corresponding to groups A–E and the respective sampling days (1, 7, 10, 14, 17, and 21) were expressed as the reciprocal of the highest serum dilution (HI endpoint) that inhibited agglutination of 1 % chicken red blood cells by vaccinal NDV antigen. E.g., if the HI endpoints for three study birds were 1:4, 1:8, and 1:16, then the HI titers for the samples translated to 4, 8, and 16, respectively. The complete anti-ND HI titers for this study are provided in sheet 1 of Supplementary File 1 (SF 1). Anti-ND seropositive counts (number of serum samples with determined HI titers) were recorded for each of groups A–E across all sampling days (1, 7, 10, 14, 17, and 21), and these can be found in Table 1. Anti-ND HI titers were log₂-transformed to generate coded titres (sheet 2 of SF 1), as described by Thrusfield (2005, p. 306). E.g., if 2, 4, 8, and 16 were the HI titers of some samples in the study, transformation of these coded titers into the log₂-titer space yields 1, 2, 3, and 4, respectively.

Table 1.

Analysis of Anti-ND Antibody Seropositivity in MDA-positive Broiler Chicks with Day-old HB1 Vaccination.

Days	N	Group A	Group B	Group C	Group D	Group E
1	15	1514,17,21 (100 %, 76.14–100)	15 (100 %, 76.14–100)	1521 (100 %, 76.14–100)	1517,21 (100 %, 76.14–100)	1314 (86.7 %, 60.86–97.52)
7	15	1514,17,21 (100 %, 76.14–100)	15 (100 %, 76.14–100)	1521 (100 %, 76.14–100)	1321 (86.7 %, 60.86–97.52)	1314 (86.7 %, 60.86–97.52)
10	15	1021 (66.67 %, 41.5–85.04)	12 (80 %, 54.1–93.72)	1321 (86.7 %, 60.86–97.52)	1417,21 (93.3 %, 68.2–99.9)	1514,17,21 (86.7 %, 60.86–97.52)
14	15	81,7,21 (53.3 %, 30.11–75.2)	15 (100 %, 76.14–100)	10 66.67 %, 41.5–85.04)	12 (80 %, 54.1–93.72)	31,7,10 (20 %, 6.28–45.95)
17	15	61,7 (40 %, 19.75–64.3)	12 (80 %, 54.1–93.72)	1421 (93.3 %, 68.2–99.9)	61,10 (40 %, 19.75–64.3)	710 (46.67 %, 24.80–69.89)
21	15	01,7,10,14 (0 %, 0.00–23.86)	14 (93.3 %, 68.2–99.9)	41,7,10,17 26.67 %, 10.5–52.4)	51,7,10 33.3 %, 14.96–58.5)	710 (46.67 %, 24.80–69.89)
χ2 df p-value (p) ***		45.56	10.07	36.36	30.18	31.81
		5	5	5	5	5
		1.12e-08	0.07	8.05e-07	1.35e-05	6.48e-06
		Yes	No	Yes	Yes	Yes

This table presents anti-ND antibodies seropositive counts among study birds (terminal sampling) across days by group, followed by associated calculated percentages and 95 % confidence intervals (CI) determined by modified Wald method using GraphPad QuickCalcs. N: Sample size, χ2: Chi-Square test statistic value, df: Degrees of freedom, *** Comment on statistical significance (if p < 0.05, Yes), Numerical superscripts: within group exact point (s) of statistical significance for ND seropositive counts between pair of days as indicated by Z-test pair-wise comparison.

2.4. Calculation of outcome variables

2.4.1. Arithmetic mean titre (AMT)

AMTs for sampling days (1, 7, 10, 14, 17, and 21) across groups A–E and the pooled dataset (overall) were calculated from the coded titres as described by Thrusfield (2005, p. 306) using the formula below. The AMT in this study is simply the average of the anti-ND coded titers per day, and it is also in the log₂-titer space.

$$AMT=\frac{\text{Sum}\text{of}\text{Coded}\text{Titers}\text{Per}\text{Day}}{\text{Number}\text{of}\text{Coded}\text{Titers}\text{for}\text{that}\text{Day}}$$

AMT values across groups A–E and the pooled dataset can be found in Sheet 1 of SF 2, and the pooled AMTs in the log₂-titer space were also employed in population-level quantitative immunokinetic modelling of antibody waning in Section 2.6.

2.4.2. Geometric mean titre (GMT)

GMTs for sampling days (1, 7, 10, 14, 17, and 21) across groups A–E and the pooled dataset were calculated from the determined AMTs as described by Thrusfield (2005, p. 306) using the formula below. Calculation of GMTs simply involved back-transformation of the AMTs into the real titer space.

$$GMT=2^{AMT}$$

Observed GMT values and associated 95 % bootstrapped confidence intervals (CI) can be found in Sheet 2 of SF 2 and are also presented graphically (with 95 % CI displayed as error bars) across sampling days for each of groups A–E and the pooled dataset in Fig. 1.

Fig. 1.

Temporal progression of early anti-newcastle disease antibody profiles of MDA-positive broiler chicks with day-old HB1 vaccination.

Panels show plots of individual groups A–E observed anti-ND GMT and the observed pooled (Overall) anti-ND GMT, with associated bootstrapped 95 % CIs to reflect uncertainty around these observed anti-ND GMT values . Serum samples were collected on days 1, 7, 10, 14, 17, and 21, and HI titres were measured. HI titres were log₂-transformed to obtain coded titres, from which AMTs were calculated for each day and subsequently used to determine GMTs via back-transformation. GMT values are plotted on a continuous timeline here. The dashed line indicates the moderately protective titre level (GMT = 16) based on literature.

2.4.3. Moderately protective titre (%)

The percentage moderately protective titer [mPT (%)] for sampling days (1, 7, 10, 14, 17, and 21) across groups A–E and the pooled dataset were calculated using the formula below. The mPT (%) is simply the proportion of coded titers ≥4 for a specific day in a group. An HI titer of ≥16 (coded titer ≥4) has been putatively considered to be moderately protective against ND (Bordoloi et al., 2021; Ferreira et al., 2021; Liu et al., 2023).

$$mPT(\%)=\frac{\text{Counts}\text{of}\text{Coded}\text{Titers}\ge 4\text{Per}\text{Day}}{\text{Counts}\text{of}\text{Coded}\text{Titers}\text{for}\text{that}\text{Day}}\times 100$$

Observed mPT (%) and associated 95 % bootstrapped CI, displayed as error bars across sampling days for each of groups A–E and the pooled dataset, can be found in Fig. 2.

Fig. 2.

Percentage distribution of Anti-ND moderately protective antibody titers of MDA-positive broiler chicks with day-old HB1 vaccination.

Percentage moderately protective titres [mPT(%)] of anti-ND antibodies across days for study groups A-E, and the pooled data, with 95 % bootstrapped CIs. For each day, mPT was calculated as the proportion of coded titres ≥4. Differently coloured bars show observed mPT(%) values for groups A–E and the pooled data (Overall), while the bootstrapped 95 % CIs indicate the uncertainty around these estimates.

2.5. Statistical analysis

2.5.1. Analysis of seropositive counts

The association between anti-ND seropositivity and sampling days across groups A–E was evaluated using the Chi-square test of independence. Where statistically significant associations were detected (p < 0.05), post-hoc Z-test pairwise comparisons to pin-point exact days contributing to the statistical significance were performed between sampling days within groups, with Bonferroni correction applied to adjust for multiple comparisons. Also for each day, anti-ND seropositive counts were also expressed as percentages and the 95 % CI was determined by the modified Wald method using GraphPad QuickCalcs. Table 1 presents anti-ND seropositive counts across days by group, with corresponding determined proportions and 95 % CI.

2.5.2. Analysis of coded titers

Normality of the anti-ND coded antibody titers for each day within each group and the pooled data was assessed using the Shapiro–Wilk test. As normality assumptions were not satisfied (SF 3) for most of the days across groups A-E, and the pooled dataset, two independent Kruskal–Wallis (KW) analyses were used for between groups comparisons of anti-ND coded titres for a specific day, and within a group (A-E, and the pooled data) comparison across days to assess significant differences in anti-ND median coded antibody titres. In cases of statistical significance (p < 0.05) in each case of the KW analysis, the Dunn’s post-hoc test with Bonferroni correction was subsequently applied to identify groups contributing to the day-specific statistically significant anti-ND median coded titres, and to identify the exact days within a group contributing to the determined statistical significance. Additionally, 10,000 non-parametric bootstrap resampling of anti-ND coded titres for each sampling day across study groups A-E and the pooled dataset was performed to determine the 95 % CI (2.5th and 97.5th percentiles). Table 2 presents across groups (A-E, and pooled) day-specific observed anti-ND median coded titre distribution, bootstrapped 95 % CIs for the median coded titers, H-statistic, p-values, and exact points (alphabetical and numerical superscripts) of statistical significance.

Table 2.

Analysis and comparison of median Anti-ND coded titers of MDA-positive broiler chicks with day-old HB1 vaccination.

Days	k	H (df)	p-value (p)	***	Group A	Group B	Group C	Group D	Group E	Overall**
1	5	9.16 (4)	0.057	No	47,14,17 (4 - 7)	514,17,21 (4 – 5)	67,10,14,21 (4 – 7)	67,10,14,17,21 (4 – 6)	610,14,17,21 (5 – 8)	57,10,14,21 (5 - 6)
7	5	32.93 (4)	1.23e-06	Yes	2b,c,e;1 (1 - 2)	3a;21 (3 – 4)	4a;1 (3–4)	2e;1 (1 – 4)	5a,d;17,21 (4 – 5)	31,14,17,21 (3 – 4)
10	5	15.56 (4)	0.0036	Yes	3 (1 – 4)	3.5d (2.5 – 4)	21,7 (1 – 3)	2b,e;1 (1 – 2)	3d;1 (2 – 4)	21,21 (2 – 3)
14	5	15.75 (4)	0.0034	Yes	21 (1 - 3)	3c;1 (1 – 4)	1b;1,7,17 (1 – 1)	21 (1.5 – 2)	11 (1–1)	21,7 (1 – 2)
17	5	24.27 (4)	7.06e-05	Yes	1c;1 (1–1.5)	2.5e;1 (2 – 4)	4.5a,d,e;14 (3 – 5)	1c;1 (1 −2)	1b,c;1,7 (1 – 1)	21,7 (1 – 3)
21	4	7.15 (3)	0.067	No	-	21,7 (1 – 2)	11 (1 – 2)	11 (1 – 1)	11,7 (1 – 2)	11,7,10 (1 – 2)
				k	5	6	6	6	6	6
				H (df)	30.35 (4)	33.60 (5)	45.28 (5)	40.95 (5)	44.58 (5)	148.92
				p	4.35e-06	2.86e-06	1.27e-08	9.63e-08	1.77e-08	2.27e-30
				***	Yes	Yes	Yes	Yes	Yes	Yes

This table presents day-specific anti-ND median coded titer (log-transformed) distribution and associated 95 % confidence intervals determined following 10,000 bootstrap analysis across study groups, H (df): Kruskal Wallis H test statistic value (degrees of freedom) for between groups comparisons for a specific day, and within a group day-wise comparison, **: Pooled data (overall), ***: Comment on statistical significance [if p-value (p) <0.05, Yes], alphabetical superscript (a,b,c,d,e): day-specific points of statistical significance between median coded titres for study groups as indicated by Dunn’s Post-hoc test (Dpht), numerical superscripts (1,7,10,14,17,21): within a group point of statistical significance between days as determined by Dpht.

2.5.3. Analysis of outcome variables

2.5.3.1. GMT analysis across time and intervals

Observed GMTs are plotted across sampling days for groups A–E and the pooled dataset in Fig. 1. To quantify uncertainty around these observed estimates, non-parametric bootstrap resampling (10,000) of anti-ND coded antibody titres was performed independently for each day within groups A–E and for the pooled data. Then from each bootstrap resample, AMTs were recalculated and back-transformed to GMTs (using the same formulas in 2.4.1 and 2.4.2), from which the 95 % CIs were derived and displayed as error bars alongside the observed GMTs in Fig. 1.

Percent changes in GMTs (Table 3) across consecutive sampling intervals (1–7, 7–10, 10–14, 14–17, and 17–21 days) were calculated for each of group A–E and for the pooled dataset. For each interval, the observed percent change in GMT was calculated directly from the GMTs using the formula below, where DI_ΔGMT is the Days Interval change in GMT.

$$\mathrm{D}{\mathrm{I}}_{\Delta \text{GMT}}=\frac{\text{GT}{\mathrm{M}}_{\text{End}}-\text{GM}{\mathrm{T}}_{\text{Start}}}{GM{T}_{Start}}\times 100$$

where $D{I}_{\Delta \text{GMT}}$ is the Days Interval change in GMT.

Table 3.

Observed Interval-specific percent changes in anti-ND GMTs in MDA-positive broiler chicks with day-old HB1 vaccination.

Days Interval	Group A (95 % CI)	Group B (95 % CI)	Group C (95 % CI)	Group D (95 % CI)	Group E (95 % CI)	Overall*** (95 % CI)
1–7	−90.1 (−94.8– −81.9)	−65.4 (−78.2– −45.2)	−81.1 (−90.1– −65.5)	−88.7 (−93.9– −78.2)	−69.1 (−83.7– −41.3)	−81.3 (−86.4– −74.3)
7–10	129.9 (4.7–452.8)	−9.9 (−50.6–62.5)	−59.8 (−76.1– −29.7)	−40.2 (−63.4–0.4)	−61.0 (−78.8– −27.4)	−27.8 (−48.3–0.8)
10–14	−45.5 (−79.7–46.4)	−26.8 (−64.6–58.7)	−51.9 (−67.4– −28.9)	14.1 (−16.6–56.1)	−80.2 (−87.5– −68.5)	−37.5 (−55.3– −11.6)
14–17	−48.6 (−74.3– −8.3)	−3.3 (−54.4–97.7)	611.7 (265.9–1252.1)	−29.2 (−50.0–0.0)	0.0 (0.0–0.0)	38.1 (−8.9–109.3)
17–21		−46.2 (−69.3– −7.2)	−84.4 (−92.0– −68.0)	−20.6 (−37.0–0.0)	34.5 (10.4–81.1)	−46.8 (−64.1– −23.0)

Values represent observed percent changes in anti-ND GMT . The associated 95 % confidence intervals were derived using non-parametric bootstrapping of coded titres (10,000 resamples) and are shown in parentheses.***Represents pooled data.

To quantify uncertainty around these observed estimates, again non-parametric bootstrap resampling of anti-ND coded titres was performed independently for the start and end of each interval (10,000 resamples). For each bootstrap resample, AMTs, corresponding GMTs, and the percent change in GMT were obtained, from which the associated 95 % CIs were derived.

2.5.3.2. mPT (%) per day

mPT(%) were calculated for each of group A–E and for the pooled dataset across sampling days using the formula mentioned above (2.4.3). To estimate uncertainty, non-parametric bootstrap resampling (10,000) of coded titres was performed independently for each day in a group. For each bootstrap resample, mPT was recalculated, and the 95 % CIs were derived. Observed mPT (%) are reported in Fig. 2 with bootstrap-derived 95 % CIs displayed as error bars.

2.6. Quantitative modelling of anti-ND humoral immunity

2.6.1. Models considered

We considered three different decay models (power-law model, single-phase and biphasic exponential decay models) that have been used in previous literature (Saha et al., 2025; Fraser et al., 2007) to see which provided the most parsimonious and empirically coherent description of observed short-term anti-ND antibody waning of MDA-positive birds with a history of day-old HB1 vaccination. In our context, these models were phenomenological in nature and aimed at only describing the non-longitudinal observed population-level pattern of antibody waning over time and not the underlying immune mechanisms. In the two previous studies, which were longitudinal human studies, model fitting was performed in log antibody titre space, and as such, all modelling in our study was done using AMTs in the log₂-titer space, with direct back-transformation to the GMT space (real titer space) for biological interpretation. Model fitting in our study was performed only on the pooled data, rather than on individual study groups, in order to minimize the observed group-specific anti-ND antibody profile variability. The three phenomenological models, as adapted to our context, were fitted using non-linear least squares via the curve_fit function in scipy.optimize using Python within the Google Colab environment. The models evaluated were mathematically defined as follows.

Power-law decay model

The power-law decay model was fitted in this study as:

$$AM{T}_{pop}\left(t\right)=k-\alpha {\log }_2\left(c+t\right)$$

where $AM{T}_{pop}\left(t\right)$ is the population-level AMT, k is the theoretical (model-estimated) baseline (Day 1) population-level AMT, α is the population-level AMT decline coefficient, t is time (days), and c is a constant set to 1 in our study. To aid numerical convergence of the model during non-linear least squares fitting, we specified neutral initialization values based on our data structure. The initial value for k was set as the maximum observed AMT (i.e. AMT value at Day 1), while the initial value for α was set at 0.5, and both parameters were constrained to non-negative values.

The power-law decay model’s direct analytical equivalence in the real GMT space is expressed below, and the mathematical procedure for the determination of the formula can be found in SF 4.

$$GM{T}_{pop}\left(t\right)=\frac{2^k}{{\left(c+t\right)}^a}$$

Single-phase exponential decay model

The single-phase exponential decay model was fitted as:

$$AM{T}_{pop}\left(t\right)=A-\lambda t$$

where A represents the model-estimated population-level baseline (Day 1) AMT and λ is the population-level AMT waning rate which was set at 0.3. As mentioned above, these values were neutral initialization parameters to facilitate convergence of the model. Again, both parameters were constrained to non-negative values during model fitting as done for the power-law decay model.

Biphasic exponential decay model

The biphasic exponential decay model was fitted as:

$$AM{T}_{pop}\left(t\right)=\{\begin{array}{cc}{\alpha }_1-{\lambda }_{1}t,\hfill & t\le t_{change}\\ {\alpha }_2-{\lambda }_2\left(t-t_{change}\right),\hfill & t>t_{change}\end{array}$$

where α₁ and α₂ represent the model-estimated population-level AMT scaling constants for the early phase and the late phase respectively, λ₁ and λ₂ represent the population-level anti-ND antibody waning rates (velocity) for the early and late phases, and t_change represents the estimated transition point between the two phases. To aid convergence as done for the other decay models above, neutral initialization parameters were specified as follows: α₁ was set at the AMT at day 1 (peak anti-ND humoral status), λ₁ to 0.3, α₂ which is the pivot titer for the model was set to half of day 1 AMT, λ₂ to 0.05, and t_change was set to day 7 based on our observed overall GMT plot which was also in line with biological expectations as reported in previous studies (Deka et al., 2020; Oni & Adipe, 2012; Jalil et al., 2009). Parameters constraint was also maintained as done for the other decay models.

2.6.2. Models comparison and selection

The performance of the considered decay models in our study was evaluated using ΔAIC as the primary selection criterion as done by Saha et al. (2025), in addition to other model evaluation metrics [coefficient of determination (R²), root mean square error (RMSE), Akaike information criterion (AIC), Bayesian information criterion (BIC), ΔBIC, and graphical inspection of residuals]. Following the ΔAIC interpretive framework reported by Saha et al. (2025), a ΔAIC < 4 indicates minimal evidence against a model, 4 ≤ ΔAIC < 10 indicates moderate evidence, and ΔAIC ≥ 10 indicates strong evidence against it relative to the model with the best fit (lowest AIC). The models assessment metrics employed in this study can be found in SF4 (page 4, Table 1), while the fitted decay curves and residual diagnostics for all models in the AMT (log₂ tier) space and equivalent GMT (real titer) space are presented in Fig. 3.

Fig. 3.

Decay models comparison for short-term Anti-ND humoral immunokinetics description in broiler chicks with day-old HB1 vaccination.

2.6.3. Characterization of short-term population-level anti-ND humoral immunity waning

The power-law decay model was therefore employed to characterize key features of population-level anti-ND antibody waning in our study, including the instantaneous (day-specific) log₂-scale decline rates, day-specific antibody halving time, and fold-change in GMT relative to day 1.

The power-law decay model as defined in 2.6.1. is:

$$AM{T}_{pop}\left(t\right)=k-\alpha {\log }_2\left(c+t\right)$$

The population-level day-specific log₂-scale decline rate ($r_{pop}$) at specific sampling time (t) in our study was defined as the negative (-) time derivative of the anti-ND population-level AMT as shown below:

$$r_{pop}\left(t\right)=-\frac{d}{dt}\left[AM{T}_{pop}\left(t\right)\right]$$

Differentiating the applied power-law decay model resulted in the formula below:

$$\frac{d}{dt}\left[AM{T}_{pop}\left(t\right)\right]=-\frac{\alpha }{\left(c+t\right)\ln \left(2\right)}$$

$r_{pop}\left(t\right)$ of the anti-ND population-level AMT at the respective sampling time in our study is therefore:

$$r_{pop}\left(t\right)=\frac{\alpha }{\left(c+t\right)\ln \left(2\right)}$$

$r_{pop}\left(t\right)$is only an age-specific descriptor, and do not represent intrinsic anti-ND antibody decay rates. Standard error for $r_{pop}\left(t\right)$ was derived from the covariance matrix of the fitted power-law model in nonlinear regression.

The detailed procedure for differentiating the power-law decay model and mathematical laws employed can be found in SF 4.

The day-specific population-level fold-changes in GMT $\left[F{C}_{pop}\left(t\right)\right]$ were calculated as the ratio of fitted GMT values at each sampling day relative to day 1 using the formula below.

$$F{C}_{pop}\left(t\right)=\frac{GM{T}_{fitted\left(t\right)}}{GM{T}_{fitted\left(Day1\right)}}$$

Additionally, the fitted power-law model was used to estimate the fractional day at which population-level anti-ND antibody levels reached the scientifically defined moderately protective level [GMT of 16, AMT of 4 since AMT is in the log₂ titer space], providing a quantitative indicator of the point at which broiler birds became theoretically susceptible to ND at the population-level in our study.

3. Results

Our study revealed a significant association (p-value < 0.05) between anti-ND seropositivity and days in all other groups except group B, with a general trend showing a decrease in seropositivity as days progressed, notably from Day 14 onwards (Table 1).

The anti-ND median coded titers in our study also revealed a general trend of decrease as days progressed. Anti-ND coded titer distributions differed significantly between groups A–E for some days (7, 10, 14, 17, and 21), and they also differed significantly within the respective groups across days. The exact groups contributing to the day-specific statistically significant anti-ND median coded titers, and the exact days on which anti-ND median coded titers differed significantly within a group, can be found in Table 2. Overall, there appears to be a heterogeneous anti-ND coded titer distribution across the groups, and the median anti-ND coded titers of all groups at Day 1 were ≥4, which has been described as moderately protective against ND (Bordoloi et al., 2021; Ferreira et al., 2021; Liu et al., 2023). After Day 1, only two groups (C and E) maintained a median coded titer value ≥4 up to Day 7, and not beyond that. The pooled data showed that by sampling Day 7, the study birds had a median anti-ND coded titer value of 3, which is below the commonly used threshold for moderately protective anti-ND antibody titres (coded titer ≥4).

In our study, on Day 1, none of the study groups had an anti-ND GMT below the moderately protective level (mPL) of ≥ 16 [(Fig. 1), mPL depicted as a horizontal dashed line], and 93.3 %–100 % of chicks across groups A–E achieved mPT (%) on Day 1 (Fig. 2). The pooled data (overall) showed that 97.3 % of the broiler birds in this study had a coded titer ≥4 (GMT of ≥ 16) on Day 1. Based on the sampling days, a significant drop in anti-ND GMT below the mPL was seen by Day 7 for groups A–D and by Day 10 for group E. The pooled data also mirrored this predominant trend among the groups (Fig. 1). Following this, mPT (%) fell significantly below the ≥85 % threshold commonly considered as indicative of ND herd immunity (van Boven et al., 2008) by Day 7 for the pooled data, and this decline was observed from Day 7 or 10 onwards to Day 17 or 21, depending on the group (Fig. 2). Using the power-law decay model, the estimated day at which population-level anti-ND antibody levels was last at exactly the protective threshold was 4.01 days. This indicates that population-level anti-ND antibody levels remained above the moderately protective threshold only until approximately Day 4, after which it fell below this threshold, suggesting increased population-level susceptibility to ND.

The overall anti-ND antibody profile in our study revealed an 81.3 % drop in GMT over the day interval 1–7, which subsequently slowed to −27.8 % and −37.5 % for days 7–10 and 10–14, respectively (Table 3). The overall antibody profile also captured a temporary surge in GMT of +38.06 % during the day interval 14–17. Examination of group-specific dynamics revealed this transient upward trend in anti-ND antibody levels in four out of five groups across different intervals, specifically during days 7–10 in group A, 10–14 in group D, 14–17 in group C, and 17–21 in group E. Although this short-lived humoral immunity boost is evident in our data, it does not negate or distract from the more dominant pattern of a general decline in the population-level anti-ND antibody profile among MDA-positive broiler birds with a history of day-old HB1 vaccination during the first 21 days of life in this study.

In this study, as shown in Fig. 3 and SF4 (page 4, Table 1), the comparative evaluation of the three considered decay models fitted to the pooled AMTs revealed that the power-law decay model provided the most parsimonious and empirically coherent description of the observed short-term population-level anti-ND antibody waning of MDA-positive birds with a history of day-old HB1 vaccination, although the biphasic exponential decay model was arguably equally competitive as it achieved a marginally higher R² (0.9710 vs 0.9651) and lower RMSE (0.2203 vs 0.2419). Based on the primary model selection criteria in our study, ΔAIC, the single-phase exponential decay model showed strong evidence against it (ΔAIC = 9.82 ≈ 10), while the biphasic exponential decay model demonstrated moderate evidence against it (ΔAIC = 4.88 ≈ 5) relative to the best-fitting model (the power-law decay model). The power-law decay model therefore emerged as our preferred model (ΔAIC = 0), as it also exhibited a high goodness-of-fit (R² = 0.9651) pointing to its ability to also explain much of the variability in our data.

Using the selected power-law decay model, k, which is the model-estimated baseline (Day 1) population-level anti-ND AMT was 6.58 ± 0.37, while α was 1.11 ± 0.11, indicating a rapid early decline in population-level anti-ND antibody levels followed by a progressive deceleration of waning over time. Consistent with the theoretical properties of the power-law model that we applied, the $r_{pop}\left(t\right)$was highest at Day 1 and declined monotonically as the age of study birds increased [SF4 (page 4, Table 2)]. Specifically, $r_{pop}\left(t\right)$ decreased from 0.80 ± 0.08 log₂ units per day at Day 1 to 0.07 ± 0.01 log₂ units per day by Day 21.

Back-transformation of the fitted power-law decay model into GMT space also showed close agreement between observed and fitted GMTs across sampling days, and this further supports the adequacy of the selected model in characterizing non-longitudinal short-term population-level waning of anti-ND humoral immunity of MDA-positive birds with a history of day-old HB1 vaccination. Relative to Day 1, fitted GMTs decreased sharply to 21.5 % of baseline by Day 7 corresponding to a 78.5% reduction (Table 3; SF4). This decline continued progressively, with fitted GMTs decreasing to 15.1 %, 10.7 %, and 7.0 % of Day 1 levels by Days 10, 14, and 21, respectively. Although a transient elevation in observed GMT was noted at Day 17 as mentioned above, the fitted GMTs continued to follow the overarching declining trajectory, and that reinforces the overall dominance of antibody waning at the population level.

4. Discussion

This study provides a detailed descriptive and quantitative evaluation of population-level early anti–ND humoral immunity waning in MDA-positive broiler chicks with a history of day-old HB1 vaccination in Nigeria. By integrating cross-sectional serological measurements with quantitative immunokinetic decay modelling, the study offers population-level insights into short-term anti-ND antibody profile of Nigeria’s poultry supply chain. While mathematical approaches have been widely applied to immunokinetic studies in both humans and animals, most of such work, which are predominantly long term longitudinal studies, has focused on human immunity (Andraud et al., 2012; Fraser et al., 2007; Le et al., 2015; Poehler et al., 2022; Quintela et al., 2014; Saha et al., 2025; Xiong et al., 2022), with relatively few studies addressing avian humoral kinetics (Andrew et al., 2021; Gharaibeh & Mahmoud, 2013; Hay et al., 2019; McKee et al., 2015; Olarte et al., 2011). To the best of our knowledge, this study represents the first attempt in Nigeria to combine serology with quantitative immunokinetic decay modelling to characterize population-level early (first 21 days) anti-ND antibody in broiler chicks supplied by major hatcheries across the country.

The findings from this study demonstrate that at Day 1, birds across all groups exhibited high anti-ND GMTs and a high proportion of study birds achieved moderately protective antibody titres, consistent with efficient vertical transfer of MDA from vaccinated breeder hens to hatched chicks. However, a pronounced decline in anti-ND antibody levels was observed within the first week of life in most groups and in the pooled dataset. This rapid decline is consistent with previous studies in MDA-positive broiler chicks vaccinated at day old, including reports from Bangladesh and Nigeria that documented significant reductions in anti-ND antibody levels by Day 7 following day-old vaccination under a longitudinal design (Jalil et al., 2009; Oni et al., 2012). Additionally, Vrdoljak (2017) reported delayed immune responses in NDV-vaccinated MDA-positive birds. Collectively, these findings points to the role of MDA-mediated interference with live vaccine-induced seroconversion, resulting in accelerated clearance of pre-existing MDA rather than simple passive maternal antibody decay.

The decline in population-level protective anti-ND antibody levels observed in this study appears to be more rapid than would be expected from MDA waning alone. Abdulrosol et al. (2024) reported that anti-ND MDA alone can remain protective for up to 10 days of life. In this study, using the power-law decay model applied to the pooled dataset, the estimated day at which population-level anti-ND antibody level was last at the protective threshold of 16 (coded titer 4) by day 4.01. This suggests that anti-ND humoral immunity may wane more rapidly in MDA-positive broiler birds under routine day-old HB1 vaccination than would be expected from passive immunity alone, thereby indicating an early risk of ND infection in this setting. Although transient increases in anti-ND antibody levels were observed at later time points in some groups and in the pooled data, these responses were short-lived and insufficient to restore serologic protective immunity. These transient increases may plausibly reflect limited replication of the HB1 vaccine virus following partial escape from MDA neutralization. As HB1 is a replicating antigen (Russell & Ezeifeka, 1995), low-level antigenic stimulation may occur as maternal antibody titres decline. Nevertheless, these responses were not sustained and does not alter the dominant population-level pattern of progressive anti-ND antibody waning during the first 21 days of life of MDA-positive broiler chicks vaccinated at day old.

The modelling component of this study provided additional biological resolution at the pooled population level and demonstrated that among the decay models evaluated, the power-law decay model most parsimoniously described the pooled anti-ND antibody waning of MDA-positive broiler chicks vaccinated at day old. This model outperformed both the single-phase and biphasic exponential decay models based on the primary selection criterion (ΔAIC) employed in this study, consistent with the approach and findings reported by Saha et al. (2025) who employed the model to describe the waning of humoral immunity over time following infection or vaccination, particularly for tetanus and diphtheria vaccines and live viral infections such as measles, vaccinia, and varicella-zoster virus. As noted by Saha et al., 2025 “similar power-law-like waning is also observed for data on antibody waning following vaccination with human papillomavirus, hepatitis A, and hepatitis B.” The power-law model captures the empirical observation that the rate of antibody waning, and consequently antibody half-life, changes over time (Saha et al., 2025). In our study, power-law model-based estimates aligned closely with observed trends. Back-transformation of the fitted power-law model into real titre (GMT) space demonstrated strong agreement between observed and predicted antibody levels. The model’s high R² value (0.9651) further indicates that it explained a substantial proportion of the variability in the pooled data. Collectively, these findings highlight the utility of the power-law decay model for describing population-level anti-ND humoral immunity waning of MDA-positive broiler birds with a history of day-old HB1 vaccination. The progressive decrease in model-estimated population-level antibody decline rate over the 21-day study period, alongside GMT fold changes and corresponding reductions derived from the model, reflects a marked progressive slowing of population-level anti-ND antibody waning in MDA-positive birds with a history of day-old HB1 vaccination as days progressed within the 21 day study period.

The practice of day-old HB1 vaccination in MDA-positive chicks remains a subject of debate in avian immunology. Some studies support early vaccination, arguing that it primes birds for stronger secondary responses, induces mucosal immunity not provided by maternal antibodies, and reduces vaccinal reactions during subsequent vaccinations (Chu & Rizk, 1975; Eidson et al., 1976; Gharaibeh et al., 2013; Giambrone et al., 1990; Klieve and Cumming, 1988; Morgan et al., 1993; Vrdoljak., 2017). In contrast, other studies report that high MDA levels can neutralize live vaccine virus, suppress seroconversion, and create an “immune gap” during which birds are vulnerable to infection (Deka et al., 2020; Jamil et al. (2009); Liu et al., 2023; Oni & Adedipe, 2012; Oni & Adedipe, 2012; El-Tayeb et al., 2014). While this study cannot definitively argue for or against the practice of day-old HB1 vaccination, the observed rapid loss of population-level protective anti-ND antibody levels without subsequent boosting highlights the presence of a potential window of susceptibility in early life. In this context, our findings align with existing evidence suggesting that appropriately timed booster vaccinations, such as those administered at days 7 and 21, may help mitigate this potential immune gap. Jalil et al. (2009) demonstrated improved immune responses and survival following challenge in broilers boosted at days 7 and 21. Furthermore, regular seromonitoring could support more precise vaccine scheduling tailored to MDA levels within specific production systems.

In conclusion, this study demonstrates that MDA-positive broiler chicks vaccinated at day old with the HB1 vaccine and without subsequent boosting experience rapid anti-ND humoral immunity waning and loss of serologic protection at the population-level within the first week of life and onwards. By integrating serological data with quantitative immunokinetic modelling, the study highlights the non-linear nature of anti-ND antibody waning under conditions of HB1 vaccination–MDA presence. While early vaccination remains essential for ND control, particularly in endemic settings such as Nigeria, our results underscore the need to account for MDA levels when designing vaccination programs. Monitoring MDA levels and optimizing vaccine timing may help mitigate vaccine interference and reduce early-life vulnerability to ND infection.

5. Limitations

Several limitations of this study must be acknowledged. The study describes short-term population-level anti-ND humoral immunokinetics and focused exclusively on humoral antibody responses; it did not assess cell-mediated immunity or protective efficacy through challenge experiments. In addition, the population-level waning of MDA alone was not evaluated in tandem. The absence of an unvaccinated MDA-only control group limits our ability to conclusively isolate the effects of HB1 day-old vaccination on the short-term population-level anti-ND humoral immunity waning within the Nigerian broiler poultry supply context. Also, the sample size used in this study was a convenience sample based on logistical constraints and available resources rather than an a priori power calculation. The robust bootstrapping employed in the study compensates partially for the possible sample size limitation in our study. Furthermore, the study employed a non-longitudinal design; as such, the modelling approach described population-level cross-sectional antibody waning rather than within-individual antibody kinetics. This cross-sectional humoral immunity modelling integrated pooled population dynamics rather than exclusively group-specific analyses. Nevertheless, pooling served to reduce group-specific variability, providing a robust characterization of population-level short-term anti-ND antibody waning of MDA-positive broilers with a history of HB1 vaccination in Nigeria.

Ethical statement

Ethical approval for the use of broiler chicks in this study was sought for and obtained (reference number: JOSTUM/CVM/ETHICS/2025/05) from the Animal Ethics & Welfare Committee of the College of Veterinary Medicine, Joseph Sarwuan Tarka University, Makurdi, Nigeria.

Consent

Not applicable.

Funding statement

This work received no external funding.

Data availability

All the data associated with our study have been provided in the published manuscript and the associated supplementary files.

CRediT authorship contribution statement

Nathaniel Rabo: Writing – review & editing, Writing – original draft, Visualization, Validation, Resources, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. Eunice Bako: Resources, Methodology, Investigation, Data curation, Conceptualization. Moses Audu: Writing – review & editing, Resources. John Ibu: Writing – review & editing, Supervision, Resources, Methodology, Investigation, Data curation, Conceptualization.

Declaration of competing interest

The authors declare that they have no competing interests.