Applied Mathematics & Information Sciences

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In this Zika virus disease model, we have incorporated a non-monotonic incidence rate for the human to human transmission, which describes the psychological effect from the behavioural change of the susceptible individuals and the crowding effect of the infected individuals. The proposed epidemic model has seven mutually exclusive sub-classes of humans and mosquitoes which are analyzed by a suitable approach to control the Zika virus. Transmission of Zika virus is of three types, which are between human to human, human to mosquito and mosquito to human. The existence, the local stability of the disease-free, and the endemic equilibrium have been investigated in detail. Our model also exhibits backward bifurcation which suggests that merely reducing the basic reproduction number $R_0$ below one is not enough to make disease-free equilibrium globally stable. We presented the sensitivity analysis of some key parameters of the basic reproduction number. Later, we extended the model to the optimal control problem and obtained control strategies to reduce the symptomatic and asymptomatic infection levels. Numerical simulation is performed to support our analytical results.

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