Stability Research of an SEIR Model with Distinct General Contact Rates and Infectious Force in Latent and Recovered Period

Abstract

In this work, an SEIR infectious model with distinct general contact rates and infectious force in latent and recovered period is established, and the stability of the model is studied using theoretical and numerical methods. First, we derive the basic reproduction number R0, which determines whether the disease is extinct or not. Second, using the LaSalle’s invariance principle, we show that the disease-free equilibrium is globally asymptotically stable and the disease always dies out when R0<1. On the other hand, by Routh-Hurwitz criterion theory, we also prove that the disease-free equilibrium is unstable and that the unique endemic equilibrium is locally asymptotically stable when R0>1. Third, through the method of autonomous convergence theorem, we obtain that the unique endemic equilibrium is globally asymptotically stable and the disease persists at this endemic equilibrium when R0>1. Finally, numerical simulations are carried out to confirm the theoretical analysis.