Epidemic model with nonlinear incidence rate and three-infectious individual classes

In this paper, we formulate the epidemic model that describes the dynamics of the spread of infectious transmission in the host population. This epidemic model combines three classes of infectious individuals with different infectivity and the nonlinear incidence rate. We investigated the basic reproductions number. We found that this model has two equilibrium points, one of them is free-equilibrium point and the other is endemic equilibrium point. By analyzing the existence and stability of the equilibria, we observed that the disease- free equilibrium is globally asymptotically stable when the basic reproduction number R0 is less than or equal unity, that is the disease dies out. While the endemic equilibrium point is locally asymptotically stable when the reproduction number is more than unity. The local and global stability for all possible equilibria are carried out with the help of Lyapunov function and LaSalle’s invariant principle. The global stability of the endemic equilibrium is discussed.