Abstract
: In this paper, we report an application for the mathematical theory of dynamic optimization for design of optimal strategies that account for daily commuting of human residents, aiming to reduce vector-borne infections (dengue) among human populations. Our analysis is based on a two-patch dengue transmission model amended with control variables that represent personal protection measures aimed at reduction of the number of contacts between mosquitoes and human hosts (e.g., the use of repellents, mosquito nets, or insecticide-treated clothing). As a result, we have proposed and numerically solved an optimal control problem to minimize the costs associated with the application of control measures, while also minimizing the total number of dengue-infected people in both residential areas. Our principal goal was to identify an optimal strategy for personal protection that renders the maximal number of averted human infections per unit of invested cost, and this goal has been accomplished on the grounds of cost-effectiveness analysis.
Highlights
Population mobility is one of the factors that have historically influenced the spread of epidemics.An infection that affects individuals in some geographically isolated area can reach other locations due to people traveling
We have addressed the role of personal protection measures on dengue transmission, while considering people commuting between two zones, both located in a dengue-endemic area
We have tried to model two realistic situations regarding daily commuting and to analyze strategies of personal protection aiming to reduce the number of contacts between human hosts and vector transmitters of the disease
Summary
Population mobility is one of the factors that have historically influenced the spread of epidemics. We focus on the transmission of dengue infections that are spread by the female mosquito, mainly of the species Aedes aegypti, while accounting for population mobility. We introduce the personal protection measures that can be assumed by (a share of) human populations residing in both patches in order to avoid mosquito bites, and to reduce the risk of infection with dengue virus. Such measures are modeled by two exogenous dynamical variables widely known as control functions, and these variables are patch-specific.
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