Path analysis method in an epidemic model and stability analysis

Abstract

In this paper, a new method for obtaining the basic reproduction number is proposed, called the path analysis method. Compared with the traditional next-generation method, this method is more convenient and less error-prone. We develop a general model that includes most of the epidemiological characteristics and enumerate all disease transmission paths. The path analysis method is derived by combining the next-generation method and the disease transmission paths. Three typical examples verify the effectiveness and convenience of the method. It is important to note that the path analysis method is only applicable to epidemic models with bilinear incidence rates. The Volterra-type Lyapunov function is given to prove the global stability of the system. The simulations prove the correctness of our conclusions.