A mathematical model of \textit{Culex} population abundance and the impact of vector control interventions in a patchy environment

TL;DR

This study develops a temperature-driven, multi-patch ODE model of Culex population dynamics that explicitly incorporates inter-patch dispersal and vector-control interventions in Cook County, Illinois. By coupling a four-stage life cycle (E, L, P, A) with a dispersal network and weather forcing, the authors quantify how spatial connectivity alters intervention efficacy and persistence thresholds via the Basic Offspring Number $R_0$ and its patch-specific counterparts $R_{0_i}$. The work shows that ignoring dispersal can overestimate control impact, while coordinated, early-season ULV spraying together with larvicide can synergistically reduce abundance and suppress $R_0$ more effectively across patches. These findings provide a practical, weather-informed framework to optimize spatially targeted vector-control strategies and mitigate disease risk in patchy urban landscapes. The framework is validated with 2018 trap data and can be extended to more patches, stochastic events, and health outcomes in future work, enabling adaptive, data-driven abatement planning.

Abstract

Recent mosquito-borne outbreaks have revealed vulnerabilities in our abatement programmes, raising concerns about how abatement-districts should choose optimal future control strategies. Spatial dissemination of vector-borne disease is strongly shaped by the movement of both hosts and mosquitoes, creating substantial overlap between vector activity and pathogen spread. We developed a mathematical model for Culex mosquito dynamics in a patchy landscape, integrating entomological observations, weather-driven factors, and the vector control practices of the Northwest Mosquito Abatement District (NWMAD) in Cook County, Illinois. By coupling a temperature-driven multi-patch ODE model with NWMAD's adulticide and larvicide interventions, we investigated how spatial heterogeneity and control timing influence mosquito abundance. We also evaluated how mosquito dispersal modifies intervention effectiveness by comparing single-patch and two-patch model outcomes. Our results showed that models ignoring spatial connectivity can substantially overestimate the impact of interventions or misidentify the thresholds of vector persistence. Through numerical simulations, we analysed continuous and pulsatile control approaches under varying spatial and temporal configurations. These findings provide insight into optimal strategies for managing Culex populations and mitigating mosquito-borne disease risk in weather-driven, spatially connected environments across Cook County, Illinois.

Figures (12)

• Figure 1: Culex population model \ref{['Eq1']}, \ref{['Eq2']} and \ref{['Eq3']} study area, displaying the locations of mosquito trap data. Figure (c) shows the locations of the trap data, represented by the red dots under the jurisdiction of NWMAD within the Cook county (Figure (b)), Illinois, USA (Figure (a)) serviced between $2014$ and $2019$. Two blue dots represent neighbouring trap locations (Figure (c)) and Figure (d) shows the street map features of these two adjacent sites with $7$ traps in each site.
• Figure 2: Time series of daily mean temperature and precipitation data for NWMAD County of $2018$, obtained from the PRISM Climate Group at Oregon State University, which provides gridded estimates at a $4$ km spatial resolution PRISMClimateGroup.
• Figure 3: (a) Schematic illustration of a metapopulation model and the associated movements amongst patches of adult mosquitoes. It represents different patches in a metapopulation weather-driven model and the connections linking them. It describes movement of adult individuals between patches in a compartmental model, where each patch hosts a population structured by distinct life stages. (b) Model diagram of Culex population dynamics in temperate climate. Aquatic stages are drawn in blue, adult females in grey. We depict an additional mortality rate due to flushing in larvae population in red ($\beta_W$) and additional death due to larvicide ($\eta$), an extra death due to the application of adulticide in blue ($\zeta$) and as described in \ref{['Eq1']}, \ref{['Eq2']} and \ref{['Eq3']}.
• Figure 4: Sobol indices.
• Figure 5: Sobol indices of second-order interactions.