Abstract
This article aims to study the global dynamics and control strategies of an epidemic model system for dengue fever. At first, we analyze the model considering the controls as constants. The biological feasibility of the model system is examined. The existence and stability of the equilibrium states are studied concerning the basic reproduction number. Both the local and the global asymptotic stability of the system’s equilibrium states are considered. Next, we introduce the time-dependent controls, namely, prevention for dengue infection, treatment for the infected persons, and spraying the insecticides against mosquitoes into the model. A control problem is proposed and solved analytically. The necessary conditions for the effective control of the disease are derived by applying Pontryagin’s maximum principle. Moreover, several possible combinations of the controls are considered, and also their productiveness is compared through the several numerical illustrations. It is suggested from the simulation works that the best strategy to minimize the transmission of dengue virus is to adopt all the three controls optimally among the considered strategies.
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