Vector-borne malaria epidemic model with vaccination

This paper presents the dynamic epidemic model of the direct transmission of the vector-host type. The malaria distribution model is determined by a system of ordinary differential equations. The host population is divided into four subpopulations: susceptible, exposed, infected, and recovered, and the vector population is divided into three subpopulations: susceptible, exposed, and infected. Using the theory of Lyapunov functions, certain sufficient conditions are achieved for the stability of the disease-free equilibrium and endemic equilibrium. The basic reproductive number $R_0$ has been found, it characterizes the epidemic development in the population. The part of the human population is vaccinated and we examine how this prevents the development of mosquitoes in the vector population. Finally, numerical modeling is carried out to study the influence of key parameters on the spread of vector-borne diseases.