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

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.