Modeling the Role of Seasonal Variability On The Dynamics of Mosquito-Borne Diseases

Abstract

In this article, we have proposed an non-autonomous mathematical model to describe the dynamics of mosquito-borne diseases taking into account seasonal variation. In the proposed model, the disease transmission rate and the growth rate of aquatic mosquito populations are considered seasonally. The non-autonomous model is shown to have a disease-free, globally asymptotically stable cyclic state whenever the time-dependent reproduction number R_C(t) is less than unity. From the model analysis, we find that a unique positive endemic periodic solution of a non-autonomous system exists only when R_C(t) > 1. The persistence and severity of an epidemic can be described by a time-dependent periodic reproduction number R_C(t). Furthermore, it is shown that if R_C(t) <1, the disease will not spread and may eventually disappear. We also propose an optimal control problem applied to control the disease with two other parameters namely insecticide and spraying. It has been shown that a control strategy consisting of insecticides and combined spraying can have a synergistic effect in reducing the incidence of mosquito-borne diseases. Finally, numerical simulations are performed to illustrate the results of our analysis.