Optimal Control and Cost-Effectiveness Strategies of Malaria Transmission with Impact of Climate Variability

Abstract

We proposed in this study a deterministic mathematical model of malaria transmission with climate variation factor. In the first place, fundamental properties of the model, such as positivity of solution and boundedness of the biological feasibility of the model, were proved whenever all initial data of the states were nonnegative. The next-generation matrix method is used to compute a basic reproduction number with respect to the disease-free equilibrium point. The Jacobian matrix and the Lyapunov function are used to check the local and global stability of disease-free equilibriums. If the basic reproduction number is less than one, the model's disease-free equilibrium points are both locally and globally asymptotically stable; otherwise, an endemic equilibrium occurs. The results of the sensitivity analysis of the basic reproduction numbers were obtained, and its biological interpretation was provided. The existence of bifurcation was discussed, and the model exhibits forward and backward bifurcations with respect to the first and second basic reproduction numbers, respectively. Secondly, using the maximum principle of Pontryagin, the optimal malaria reduction strategies are described with three control measures, namely, treated bed nets, infected human treatment, and indoor residual spraying. Finally, based on numerical simulations of the optimality system, the combination of treatment and indoor spraying is the most efficient and least expensive strategy for malaria eradication.