When Few Mosquitoes Are Enough: Dengue outbreaks in non-endemic areas

Abstract

Dengue is no longer limited to tropical regions, as recent outbreaks in Southern Europe show. In 2024, nearly 150 local cases were reported in Fano, Italy, raising concerns that dengue could become established in temperate areas. In this work, we question the common belief that large outbreaks require high numbers of mosquitoes and a high basic reproduction number ($R_0$). We show that significant outbreaks can happen even when $R_0$ is below one, triggered by the random introduction of infected travelers. Using a mathematical model that includes imported cases and mosquito populations, we explain how rare but possible transmission events can cause substantial local spread, even under conditions usually thought too weak for sustained outbreaks. Our findings point out an important gap in current risk assessments, which often rely only on fixed invasion thresholds and basic reproduction numbers. By considering the complex interactions between human travel, mosquito ecology, and the environment, our work supports the One Health approach to understanding disease emergence. We recommend combining stochastic modeling, data on human movement, and mosquito surveillance in early warning systems to better predict outbreaks’ risk and improve preparedness in regions not traditionally affected by dengue.

1. Introduction

Dengue is a viral disease transmitted by Aedes mosquitoes, typically causing mild or asymptomatic infections but sometimes leading to severe, life-threatening illness. Once confined to tropical regions, dengue is now emerging in temperate areas, including Europe, a shift mirrored by the global spread of Aedes-borne diseases such as chikungunya, Zika, and yellow fever [1].

This growing threat, driven by climate change, global mobility, limited vaccine protection, and reactive outbreak control, highlights the need for an integrated approach to mosquito-borne disease preparedness. The emergence of these diseases reflects interconnected environmental, ecological, and social factors. Warmer climates and changing rainfall expand vector ranges, while international travel introduces viruses to new areas at unprecedented rates. Integrated surveillance of human, vector, and environmental data is essential, and a One Health framework can support effective cross-sector collaboration to anticipate, prevent, and mitigate arboviral risks [2].

In 2023 alone, mainland France reported six independent clusters of autochthonous dengue across three regions between July and October [3], [4], [5]. By 2024, Spain’s Catalonia region also recorded non–travel-associated cases in Tarragona [6], signaling that dengue is no longer just a visitor in Europe but is beginning to establish a foothold.

Europe’s dengue burden has traditionally been driven by importation through international travel to endemic areas [7], [8], [9]. Many viremic imported cases are asymptomatic, often escaping surveillance yet still capable of infecting competent mosquito vectors and enabling local transmission [10]. When these cases overlap with established vector populations, local outbreaks become possible. Although historically sporadic and limited, such events are now increasing in frequency and scale [11], [12], [13]. Recent studies show that dengue virus can alter mosquito behavior, increasing persistence during blood feeding and thus enhancing transmission likelihood [14]. In parallel, environmental variability has been shown to shape vector traits dynamically, as Aedes albopictus exhibits phenotypic plasticity that enhances its capacity to transmit dengue under diverse ecological conditions [15]. These biological and behavioral factors imply that imported-driven outbreaks can emerge even under subcritical vector densities (i.e., for densities below the critical levels ensuring endemic transmission), giving each imported case a disproportionate potential to seed local transmission. Consequently, classical models may underestimate the virus’s effective reproductive potential, especially in non-endemic regions.

According to the European Centre for Disease Prevention and Control (ECDC), Aedes albopictus, a competent dengue vector, is now well established across many European regions, including Italy [16]. This combination of a largely susceptible population, widespread vectors, and increasing imported cases creates ideal conditions for local dengue emergence.

Italy stands at the forefront of this shift. Over recent years, the country has experienced a marked rise in local transmission, such that autochthonous cases outnumbered imported ones in 2024 [17], [19] (Fig. 1(a)). Since 2020, three major outbreaks have occurred: the first in Vicenza Province (Veneto), linked to travel from Indonesia [20]; a broader resurgence in 2023 with 82 cases across Lombardy and Latium [21], [22], [23], [24], [25]; and a record-breaking outbreak in Fano in 2024 (Fig. 1(a)).

Fig. 1.

Overview of dengue incidence trends and spatial patterns in Italy during the 2024 season, with a focus on the Fano outbreak. (a) Annual national trends in dengue incidence from imported (blue) and autochthonous (red) cases in Italy. Source: [17]. (b) Weekly time series of dengue cases in Fano, showing cumulative cases (red) and weekly new cases (blue). The green shaded area indicates the period during which mosquito control interventions were implemented. Sources: [17], [18]. (c) Spatial distribution of cumulative dengue incidence in 2024 across Italian regions (EU-NUTS2 level), with autochthonous cases shown on the left and imported cases on the right. Source [17].

Between August and October 2024, Fano reported 146 confirmed autochthonous dengue cases [17], [18], [26], marking the largest dengue outbreak recorded in Italy and one of the most significant in Europe (Fig. 1(b)). The outbreak was driven by favorable climatic conditions, the presence of Aedes albopictus, and a largely susceptible population. Clinical presentations ranged from mild fever to dengue with warning signs; no fatalities occurred. Public health authorities responded with intensified vector control, public education, and enhanced surveillance [18].

Existing studies attribute the outbreak to a supercritical transmission regime typical of endemic areas, estimating a basic reproduction number ($R_0$) above 2.0 and a peak effective reproduction number ($R_t$) of 3.53, with control attributed to increased awareness and interventions [18]. However, mosquito control efforts began on September 11th (week 37), just three days before the peak in new cases on September 14th (Fig. 1(b)). Given typical dengue and mosquito population dynamics, this timing suggests that the decline in cases was unlikely to result solely from these interventions. These findings imply that dengue dynamics in temperate Europe may be more complex than previously thought.

As of early July 2025, no autochthonous dengue cases have been reported in mainland Europe. However, local transmission occurred in Madeira, where two cases were reported in February after dengue virus was detected in mosquitoes [27]. The ECDC notes that dengue risk in mainland Europe hinges on seasonal importation of viremic travelers to areas with established vectors, mainly Aedes albopictus and, to a lesser extent, Aedes aegypti, which is limited to Cyprus, Madeira, and the eastern Black Sea. Autochthonous outbreaks in mainland Europe have historically occurred from June to November, coinciding with favorable climate and peak vector activity.

In this work, we propose an alternative explanation for dengue emergence in non-endemic areas, such as Italy and other European countries, by focusing on the role of chance events near the critical transmission threshold, the point at which disease spread either dies out or grows exponentially into an outbreak. Using a stochastic SIRUVY model [28], [29], which extends the classic SIR framework to include uninfected (U) and infected (V) mosquitoes and accounts for viremic imported human cases (Y), we show how outbreaks can arise even when transmission conditions are generally too low to sustain an epidemic (known as subcritical) or just barely high enough (marginally supercritical), due to random fluctuations and imported cases. Differently from [29], which focuses on spatio-temporal risk mapping in Northern Spain during 2023, our study investigates the mechanisms driving outbreak emergence under near-critical conditions, using the largest continental European outbreak in 2024 (Fano, Italy) as a case study. We show that intermediate vector abundance combined with frequent introductions of viremic imported cases can jointly sustain autochthonous transmission, even under subcritical regimes. While both studies build on the stochastic SIRUVY framework [28], our contribution provides a generalizable methodological foundation for understanding stochastic outbreak patterns in non-endemic regions, moving beyond regional risk assessment toward a broader theory of epidemic variability near the transmission threshold.

Our approach offers a novel framework to better understand and predict dengue risk in Europe’s evolving landscape, emphasizing the need for integrated surveillance and early warning systems that go beyond average reproduction numbers alone.

2. Results

From the theory of critical phenomena, it is well understood that when a system is near a tipping point, where a disease can either die out or grow into a large outbreak, its behavior can be dominated by random fluctuations. These fluctuations often appear similar across different time and size scales, a property known as self-similarity. Additionally, the size of outbreaks near this threshold tends to follow power-law distributions, where small outbreaks are common and large ones are rare but still possible, following a mathematically predictable pattern [28], [30].

A major challenge in interpreting the small dengue outbreaks reported across various Italian provinces, as well as in other European countries like France and Spain in 2024, is determining whether the large outbreak observed in Fano could be explained as a system operating near, but just below, this critical threshold.

To explore this, we simulated three scenarios of dengue transmission dynamics near the epidemic threshold given by Eq. (14)

For convenience, we label the scenarios using a basic reproduction number ($R_0$) analogous to a deterministic system. These $R_0$ values are computed using the standard deterministic formula applied to each choice of $k$, and are used only as convenient labels.

All scenarios shared the same baseline parameters, except for mosquito abundance, represented by the parameter $k$.

The first scenario represents a fully supercritical regime with its initial exponential growth ($R_0\approx 2$, with $k=1$), where transmission is sustained, analogous to an endemic region, using parameters from [18]. Our stochastic simulations showed that the fully supercritical regime (Fig. 2a,b) produced substantially larger outbreaks, often in the order of 100 times higher in cumulative incidence and weekly active cases than observed in Fano, consistent with patterns typically seen in endemic regions.

Fig. 2.

Comparison of stochastic SIRUVY simulations with observed dengue dynamics in Fano (2024) under three transmission scenarios. Shown are the 10 largest stochastic realizations (blue) out of 100 runs, together with reported data (black). Each row corresponds to a different regime (for convenience, scenarios are labeled by $R_0$ values computed from the deterministic formula without importation): (Top) fully supercritical ($R_0=2$), displayed on both the simulation scale (a,b) and the data scale (c,d); (Middle) marginally supercritical ($R_0=1.02$); (Bottom) subcritical ($R_0=0.98$). Left panels show cumulative autochthonous cases; right panels show active cases. Parameter values used in all simulations are listed in Table 1. $R_0$ values were obtained by adjusting $k$, the relative mosquito abundance: $k=1$ (top), $k=0.51$ (middle), and $k=0.49$ (bottom).

In contrast, the marginally supercritical scenario (Fig. 2c,d; $R_0\approx 1.02$) and the subcritical scenario (Fig. 2e,f; $R_0\approx 0.98$), corresponding respectively to $k=0.51$ and $k=0.49$, occasionally generated large, clustered outbreaks in some simulation runs. These dynamics closely matched the observed data from Fano in both the total number of cases over the year and the timing of infections, particularly under the subcritical setting.

In our stochastic SIRUVY model with importation, the parameter $k$ modulates the effective vector abundance and thus the effective transmission rate (as shown in Eq. (12)), but does not define a deterministic $R_0$. Imported cases ($Y$) act as an external source of infection, and no simple linear relationship exists between $R_0$ and the number of imported cases. These $R_0$ values therefore are used only as convenient labels to situate each scenario relative to familiar deterministic regimes (supercritical, marginally supercritical, and subcritical).

This finding suggests that even when average transmission conditions are not strong enough to sustain an epidemic, random chance events such as the introduction of a few viremic travelers can still lead to significant local spread. Most transmission chains die out quickly, but some, by chance, result in larger outbreaks. Furthermore, we found that outbreaks occurring just below or just above the classical epidemic threshold are statistically similar in size and timing, indicating that the transition between epidemic and non-epidemic regimes is not sharp but rather gradual.

An important feature of systems near the critical threshold is the wide range of possible outcomes. While most simulations produce few or no secondary cases, a smaller number lead to large outbreaks similar to the one observed in Fano. This variability reflects real-world dengue dynamics in non-endemic regions, where most imported cases do not result in local transmission, but some lead to substantial outbreaks. These findings challenge conventional deterministic models that assume transmission must exceed a fixed threshold to pose public health risks, and highlight the importance of incorporating stochasticity into models used for outbreak preparedness and early warning.

3. Materials and methods

Model framework

To evaluate the impact of imported dengue cases in non-endemic regions, we extend the classical SIRUV [31] model by incorporating an additional class for imported infectious individuals ($Y$), resulting in the SIRUVY model [28]. The human population of size $N$ is divided into susceptible ($S$), infectious ($I$), and recovered ($R$) individuals. The mosquito population of size $mN$ is structured into uninfected ($U$) and infected ($V$) vectors. Viremic imported cases ($Y$) represent individuals infected abroad who enter the population at a per-capita rate $\tilde{\varrho }$ and recover at rate $\gamma$.

The deterministic system is defined as:

$$\frac{dS}{dt}=\alpha R-\frac{\beta }{mN}SV,$$ (1)

$$\frac{dI}{dt}=\frac{\beta }{mN}SV-\gamma I,$$ (2)

$$\frac{dR}{dt}=\gamma I-\alpha R,$$ (3)

$$\frac{dU}{dt}=\psi \left(k\right)-\frac{\vartheta }{N}U(I+Y)-\nu U,$$ (4)

$$\frac{dV}{dt}=\frac{\vartheta }{N}U(I+Y)-\nu V,$$ (5)

$$\frac{dY}{dt}=\tilde{\varrho }N-\gamma Y,$$ (6)

where $\psi \left(k\right)=k\nu mN$ is the mosquito recruitment rate modulated by a relative abundance factor $k$, defined as:

$$k=\frac{\text{vector abundance in non-endemic area}}{\text{vector abundance in a typical endemic area}}.$$ (7)

Table 1.

Model parameters used in the stochastic SIRUVY simulations. Parameter values were retrieved from [28].

Parameter	Value	Description
$N$	$60000$	Human population size
$\gamma$	$52{\text{y}}^{-1}$	Recovery rate (1 week infectious period)
$\alpha$	$0.1{\text{y}}^{-1}$	Waning immunity (10-year duration)
$\beta$	$0.8\gamma$	Human infection rate (from mosquito to human)
$\nu$	$36.5{\text{y}}^{-1}$	Mosquito mortality (10-day lifespan)
$\vartheta$	$2.5\nu$	Mosquito infection rate (human to mosquito)
$m$	10	Mosquito-to-human ratio in endemic baseline
$\varrho$	$10/\mathrm{N}{\text{y}}^{-1}$	Importation rate of viremic travelers
$k$	$\{1,0.51,0.49\}$	Relative mosquito abundance
		(supercritical, marginally supercritical, subcritical)

This parameter is used to compare mosquito abundance between endemic and non-endemic regions, with non-endemic regions generally exhibiting lower vector densities. We assign $k\approx 1$ to endemic regions, while in non-endemic regions $k$ is smaller, and varying $k$ produces different transmission regimes, from subcritical to supercritical, as demonstrated in [28]. This approach provides a compact and intuitive representation of transmission conditions near the conventional epidemic threshold ($R_0\approx 1$). The same $k$ values are used in both deterministic and stochastic models to ensure comparability; however, stochastic simulations introduce variability through random fluctuations and imported infections. Imported cases play a critical triggering role: even in subcritical or near-critical regimes, single viremic travelers can initiate self-limited or amplified transmission chains depending on the stochastic realization and the value of $k$. This explains the occurrence of sporadic local outbreaks despite low average transmission potential.

The imported class rapidly reaches a quasi-equilibrium, $Y^{\ast }=\tilde{\varrho }N/\gamma =\varrho N$, which follows directly from setting $\frac{dY}{dt}=0$ in Eq. (6): the inflow of imported infections ($\tilde{\varrho }N$) is balanced by recovery ($\gamma Y$). This supports a model simplification in which $Y$ is replaced by its equilibrium value $Y^{\ast }$ as a constant importation source, neglecting stochastic fluctuations.

The full derivation is provided in [28]. The cumulative number of imported cases then evolves linearly:

$$\frac{d{C}_Y}{dt}=\tilde{\varrho }N.$$ (8)

Stochastic model and transition dynamics

To capture low-incidence variability and outbreak unpredictability near the epidemic threshold, we complement the deterministic model with a stochastic formulation simulated by the Gillespie algorithm [32]. The system’s state vector is $\underset{\_}{X}={(S,I,R,U,V,Y)}^{\top }$, and transitions are defined by the following rates and corresponding changes:

$w_1=\alpha R$,	${\underset{\_}{r}}_1={(-1,0,1,0,0,0)}^{\top }$,
$w_2=\frac{\beta }{mN}SV$,	${\underset{\_}{r}}_2={(-1,1,0,0,0,0)}^{\top }$,
$w_3=\gamma I$,	${\underset{\_}{r}}_3={(0,-1,1,0,0,0)}^{\top }$,
$w_4=\psi \left(k\right)$,	${\underset{\_}{r}}_4={(0,0,0,1,0,0)}^{\top }$,
$w_5=\frac{\vartheta }{N}U(I+Y)$,	${\underset{\_}{r}}_5={(0,0,0,-1,1,0)}^{\top }$,
$w_6=\nu U$,	${\underset{\_}{r}}_6={(0,0,0,-1,0,0)}^{\top }$,
$w_7=\nu V$,	${\underset{\_}{r}}_7={(0,0,0,0,-1,0)}^{\top }$,
$w_8=\tilde{\varrho }N$,	${\underset{\_}{r}}_8={(0,0,0,0,0,1)}^{\top }$,
$w_9=\gamma Y$,	${\underset{\_}{r}}_9={(0,0,0,0,0,-1)}^{\top }$.

Analytical results for imported cases

The dynamics of $Y$ follow a birth–death process with immigration:

$$\frac{d}{dt}p(Y,t)=\tilde{\varrho }Np(Y-1,t)+\gamma (Y+1)p(Y+1,t)-(\tilde{\varrho }N+\gamma Y)p(Y,t).$$ (9)

The cumulative imports $C_Y\left(t\right)$ follows a Poisson process with rate $\lambda =\tilde{\varrho }N=\varrho \gamma N$:

$$p(C_Y,t|C_Y\left(t_0\right))=\frac{{\left[\lambda (t-t_0)\right]}^{C_Y-C_Y\left(t_0\right)}}{(C_Y-C_Y\left(t_0\right))!}{e}^{-\lambda (t-t_0)},$$ (10)

with exponentially distributed inter-arrival times:

$$p\left(\tau \right)=\lambda e^{-\lambda \tau }.$$ (11)

Stochastic simulations show that $Y\left(t\right)$ fluctuates around its deterministic mean, producing bursts of imported cases. These temporal clusters can intermittently seed local transmission in systems near criticality.

Reduced model and epidemic threshold

Assuming quasi-stationary mosquito dynamics, we derive a reduced equation for the human infected class, $I\left(t\right)$, by substituting $V$ into the human equations:

$$\frac{dI}{dt}=(k{\beta }_{\text{eff}}-\gamma )I+k{\beta }_{\text{eff}}\varrho N,$$ (12)

where

$${\beta }_{\text{eff}}=\beta \frac{\vartheta }{\nu }\frac{S_0}{N},\varepsilon \left(k\right)=\gamma -k{\beta }_{\text{eff}}.$$ (13)

Here, $\varepsilon$ represents the distance from criticality, approaching the epidemic threshold from below. For positive values of $\varepsilon$, the system reaches a stationary state. Smaller values of $\varepsilon$ indicate proximity to the critical threshold, highlighting regimes where stochastic fluctuations and imported cases can trigger sporadic outbreaks.

The critical threshold for vector abundance, where endemic transmission becomes possible, is given by:

$$k_c=\frac{\gamma }{{\beta }_{\text{eff}}}.$$ (14)

In the underlying deterministic system, below this threshold all transmission can be traced back to importation. In the stochastic system, as $k$ approaches $k_c$, the system exhibits self-similarity and nonlinear amplification: even small increases in vector abundance can substantially elevate the probability and size of outbreaks [28].

4. Discussion

The 2024 dengue outbreak in Italy’s Marche Region was unprecedented in temperate Europe, with nearly all cases being autochthonous. Conventional analyses, based on standard estimation of reproduction numbers, suggested sustained supercritical transmission (e.g., $R_0\gg 1$), possibly driven by favorable climatic conditions, with control attributed to swift intervention measures [18].

However, such interpretations may not fully capture the complexity of dengue dynamics in non-endemic regions. For example, why would dengue reproduction numbers be significantly elevated in one specific area but not in neighboring regions under seemingly similar conditions? Our proposed mechanism emphasizes the importance of stochasticity and the role of importations. Using a stochastic SIRUVY model, we demonstrate that sizeable outbreaks can emerge even when local transmission is subcritical, particularly when mosquito abundance is near the critical threshold and viremic imported cases are present.

From the perspective of critical phenomena theory, epidemic systems close to the transmission threshold can exhibit large and unpredictable fluctuations. These fluctuations often follow scale-invariant patterns, appearing similar across different time or population scales, and tend to obey power-law distributions, where small outbreaks are common and large ones, though rare, are still expected (i.e., more likely than predicted by thin-tailed distributions such as the Gaussian). These are characteristic of fat-tailed behavior.

This natural variability complicates interpretation of the generally low dengue activity reported in most Italian provinces and other European regions like France and Spain in 2024. A central question is whether the outbreak in Fano represents one such rare but statistically plausible event in a near-critical system.

Our results support this interpretation. While many stochastic simulations lead to rapid fadeout, a subset generates large outbreaks that align with the Fano epidemic. This suggests that sporadic, high-impact outbreaks can arise in temperate settings with moderate vector abundance, provided that viremic travelers introduce infections capable of initiating local transmission.

This fragmented pattern of contrasting outcomes is a distinctive feature of near-critical systems. It reflects real-world dengue dynamics in non-endemic areas, where most imported cases fail to spark onward transmission but a few lead to substantial outbreaks. This challenges deterministic models that assume persistently supercritical transmission conditions and large reproduction numbers.

In this light, our framework is parsimonious and offers several advantages. It directly links outbreak onset to the timing and number of imported infections modulated by seasonal variation in mosquito abundance. It also explains how similar ecological conditions can produce divergent outcomes due to random chance, without requiring abrupt transitions to highly efficient local transmission. Although the model has limitations, including assumptions about importation patterns and challenges in real-time parameterization, it offers a plausible and mechanistically grounded alternative to deterministic interpretations.

Finally, we note that our simulations intentionally do not incorporate explicit seasonal forcing in mosquito abundance or temperature. Because we focus on a short late-summer window during which environmental conditions change slowly, holding seasonality constant allows us to isolate the effects of stochastic introductions under near-threshold conditions. Incorporating full seasonal dynamics – once high-resolution entomological and climatic data become available – would be a natural extension of this work and would likely further suppress average transmission, making large outbreaks even more dependent on chance importation events.

5. Conclusion

Dengue emergence in temperate regions is no longer hypothetical. While local transmission may remain subcritical on average, imported cases can trigger significant outbreaks through stochastic interactions near ecological thresholds. Effective preparedness requires early detection, integrated surveillance, and rapid, targeted responses that incorporate a One Health perspective, recognizing the interconnected roles of human, animal, and environmental health. As climate change and global mobility reshape vector-borne disease landscapes, adopting a probabilistic, context-sensitive approach to outbreak risk is essential.

CRediT authorship contribution statement

Giulio Pisaneschi: Writing – review & editing, Writing – original draft, Methodology, Investigation, Formal analysis. Piero Manfredi: Writing – review & editing, Writing – original draft, Supervision, Methodology, Investigation, Formal analysis. Alberto Landi: Writing – review & editing, Supervision, Methodology, Investigation, Formal analysis, Data curation. Nico Stollenwerk: Writing – review & editing, Supervision, Methodology, Investigation, Formal analysis, Conceptualization. Maíra Aguiar: Writing – review & editing, Writing – original draft, Supervision, Project administration, Methodology, Investigation, Funding acquisition, Formal analysis, Conceptualization.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Data availability

Data will be made available on request.