Modeling and Optimal Control Analysis for Malaria Transmission with Role of Climate Variability

Abstract

In this paper, we present a nonlinear deterministic mathematical model for malaria transmission dynamics incorporating climatic variability as a factor. First, we showed the limited region and nonnegativity of the solution, which demonstrate that the model is biologically relevant and mathematically well-posed. Furthermore, the fundamental reproduction number was determined using the next-generation matrix approach, and the sensitivity of model parameters was investigated to determine the most affecting parameter. The Jacobian matrix and the Lyapunov function are used to illustrate the local and global stability of the equilibrium locations. If the fundamental reproduction number is smaller than one, a disease-free equilibrium point is both locally and globally asymptotically stable, but endemic equilibrium occurs otherwise. The model exhibits forward and backward bifurcation. Moreover, we applied the optimal control theory to describe the optimal control model that incorporates three controls, namely, using treated bed net, treatment of infected with antimalaria drugs, and indoor residual spraying strategy. The Pontryagin’s maximum principle is introduced to obtain the necessary condition for the optimal control problem. Finally, the numerical simulation of optimality system and cost-effectiveness analysis reveals that the combination of treated bed net and treatment is the most optimal and least-cost strategy to minimize the malaria.