Study on the Global Stability for a Generalized SEIR Epidemic Model

Abstract

In the current study, a generalized SEIR epidemic model is studied. The generalized fractional-order SEIR model (susceptible-infected-recovered (SIR) epidemic) model differentiated the population into susceptible population, exposure population, infected population, and rehabilitation population and has fundamental mentoring importance for the forecast of the probable outburst of infectious ailments. The fundamental duplicated quantity $R_0$ is inferred. When $R_0<1$ , the disease-free equilibrium (DFE) is particular and tending towards stability. When $R_0>1$ , the endemic equilibrium is sole. In addition, certain circumstances are set up to make sure the local progressive stability of disease-free and endemic equilibrium. Considering the influence of the individual behavior, a broader SEIR epidemic model is raised, which classified the population into susceptible, exposure, infected, and rehabilitation. What is more, the basic reproduction number, that regulates whether the infection will die out or not, is obtained by the spectral radius of the next-generation matrix; moreover, the global stability of DFE and endemic equilibrium are analyzed by a geometry method.