Mathematical model of a SCIR epidemic system with migration and nonlinear incidence function

Abstract

In this paper, we proposed a generalization for a model that considers Susceptible, Infected, Carrier, and Recovered by introducing a general incidence rate and considering migration in all its populations. This model has the characteristic that carriers and infected can transmit the disease, besides it has not a disease-free equilibrium point and no basic reproductive number. The focus of this study is to show a generalized model and the conditions required to analyze the equilibrium point stability. Using an appropriate Lyapunov function and with suitable conditions on the functions involved in the general incidence, we showed that the disease equilibrium point is globally asymptotically stable. Also, we presented numerical simulations of two applications to illustrate the results obtained from the analytical part.