Vector Epidemic Model of Malaria with Nonconstant-Size Population

The paper presents the dynamic characteristics of a vector-host epidemic model with direct transmission. The malaria propagation model is defined 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 the Lyapunov functions, certain sufficient conditions for the global stability of the disease-free equilibrium and endemic equilibrium are obtained. The basic reproduction number that characterizes the evolution of the epidemic in the population was found. Finally, numerical simulations are carried out to study the influence of the key parameters on the spread of vector-borne disease.