A New Susceptible-Infectious (SI) Model With Endemic Equilibrium
Abstract
The focus of this article is on the dynamics of a new susceptible-infected model which consists of a susceptible group (S) and two different infectious groups (I1 and I2). Once infected, an individual becomes a member of one of these infectious groups which have different clinical forms of infection. In addition, during the progress of the illness, an infected individual in group I1 may pass to the infectious group I2 which has a higher mortality rate. In this study, positiveness of the solutions for the model is proved. Stability analysis of species extinction, I1-free equilibrium and endemic equilibrium as well as disease-free equilibrium is studied. Relation between the basic reproduction number of the disease and the basic reproduction number of each infectious stage is examined. The model is investigated under a specific condition and its exact solution is obtained.