Modelling and optimal control for Chikungunya disease.

Abstract

A generalized model of intra-host CHIKV infection with two routes of infection has been proposed. In a first step, the basic reproduction number [Formula: see text] was calculated using the next-generation matrix method and the local and global stability analyses of the steady states are carried out using the Lyapunov method. It is proven that the CHIKV-free steady state [Formula: see text] is globally asymptotically stable when [Formula: see text] and the infected steady state [Formula: see text] is globally asymptotically stable when [Formula: see text]. In a second step, we applied an optimal strategy via the antibodies' flow rate in order to optimize infected compartment and to maximize the uninfected one. For this, we formulated a nonlinear optimal control problem. Existence of the optimal solution was discussed and characterized using an adjoint variables. Thus, an algorithm based on competitive Gauss-Seidel-like implicit difference method was applied in order to resolve the optimality system. The theoretical results are confirmed by some numerical simulations.