GLOBAL DYNAMICS AND OPTIMAL CONTROL FOR A VECTOR-BORNE EPIDEMIC MODEL WITH MULTI-CLASS-AGE STRUCTURE AND HORIZONTAL TRANSMISSION

Abstract

An age-structured vector-borne disease model with horizontal transmission is proposed and studied in this paper, where the incubation ages of both host and vector and the immunity age of host are also introduced to consider the effects of multi-class-age structure. The reproductive number [Formula: see text] is derived as a threshold value to determine the existence and stability of the disease-free and endemic steady states. Furthermore, by constructing suitable Lyapunov functionals, the global threshold dynamics of this model is established by [Formula: see text], that is, the disease-free equilibrium is globally asymptotically stable when [Formula: see text], while if [Formula: see text] the endemic equilibrium is globally asymptotically stable. In addition, considering the limited budget of the centers for disease control and prevention (CDC) in the process of disease control, we present an optimal control problem with a fixed total expenditure, and discuss the existence of the most control strategy for this disease. Finally, some numerical simulations are performed to support the theoretical results.