Global Stability of Multi-Strain SEIR Epidemic Model with Vaccination Strategy

A three-strain SEIR epidemic model with a vaccination strategy is suggested and studied in this work. This represented by system of nine nonlinear ordinary differential equations that describe the interaction between susceptible individuals, strain-1-vaccinated strain-1-exposed strain-2-exposed strain-3-exposed strain-1-infected strain-2-infected strain-3-infected recovered individuals. We start our analysis establishing existence, positivity, boundedness all solutions. In order to show global stability, has five equilibrium points: The first one stands for disease-free equilibrium, second strain-1 endemic third describes strain-2 fourth represents strain-3 point, last called total equilibrium. establish stability each point using some suitable Lyapunov function. depends on reproduction number R01, basic R02, R03. Numerical simulations are given confirm theoretical results. It shown eradicate infection, numbers strains must be less than unity.