An epidemic model of malaria without and with vaccination. Pt 1. A model of malaria without vaccination

We propose a mathematical model of the malaria epidemic in the human population (host), where the transmission of the disease is produced by a vector population (mosquito) known as the malaria mosquito. The malaria epidemic model is defined by a system of ordinary differential equations. The host population at any time is divided into four sub-populations: susceptible, exposed, infectious, recovered. Sufficient conditions for stability of equilibrium without disease and endemic equilibrium are obtained using the Lyapunov's function theory. We define the reproductive number characterizing the level of disease spreading in the human population. Numerical modeling is made to study the influence of parameters on the spread of vector-borne disease and to illustrate theoretical results, as well as to analyze possible behavioral scenarios.