Modeling and optimal control of dengue disease with screening and information

Abstract

This study presents a mathematical model for dengue transmission which quantifies two very important aspects: one, the impact of information-based behavioural response, and the other, the segregation of infected human population into two subclasses, ‘detected’ and ‘undetected’. For the proposed model, the sensitivity analysis is conducted to identify the key model parameters which not only influence the basic reproduction number, but also regulate the transmission of dengue. Further, in order to find the optimal pathways for suitable control interventions that reduce the dengue prevalence and economic burden, an optimal control problem is proposed by considering information-induced behavioural change, quarantine, screening, use of repulsive measures and culling of mosquitoes as control interventions. A weighted sum of various costs incurred in applied controls and the cost due to dengue disease (productivity loss) is incorporated in the proposed cost functional. The analysis of control system using Pontryagin’s maximum principle leads the existence of the optimal control profiles. Further, an exhaustive comparative study for seven different control strategies is conducted numerically. Our findings emphasize that every individual control strategy has their own impact on reducing the cumulative count of infection as well as cost. The combined impact of all control interventions is highly effective and economically viable in controlling the prevalence of dengue. We also investigated the effect of the basic reproduction number on the designed control strategies and observed that the comprehensive use of controls keeps a strong tab on the infective even if the severity of epidemic is high.