Managing disease outbreaks: The importance of vector mobility and spatially heterogeneous control.

Management strategies for control of vector-borne diseases, for example Zika or dengue, include using larvicide and/or adulticide, either through large-scale application by truck or plane or through door-to-door efforts that require obtaining permission to access private property and spray yards. The efficacy of the latter strategy is highly dependent on the compliance of local residents. Here we develop a model for vector-borne disease transmission between mosquitoes and humans in a neighborhood setting, considering a network of houses connected via nearest-neighbor mosquito movement. We incorporate large-scale application of adulticide via aerial spraying through a uniform increase in vector death rates in all sites, and door-to-door application of larval source reduction and adulticide through a decrease in vector emergence rates and an increase in vector death rates in compliant sites only, where control efficacies are directly connected to real-world experimentally measurable control parameters, application frequencies, and control costs. To develop mechanistic insight into the influence of vector motion and compliance clustering on disease controllability, we determine the basic reproduction number R0 for the system, provide analytic results for the extreme cases of no mosquito movement, infinite hopping rates, and utilize degenerate perturbation theory for the case of slow but non-zero hopping rates. We then determine the application frequencies required for each strategy (alone and combined) in order to reduce R0 to unity, along with the associated costs. Cost-optimal strategies are found to depend strongly on mosquito hopping rates, levels of door-to-door compliance, and spatial clustering of compliant houses, and can include aerial spray alone, door-to-door treatment alone, or a combination of both. The optimization scheme developed here provides a flexible tool for disease management planners which translates modeling results into actionable control advice adaptable to system-specific details.