Mathematics

CLC number: O175

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

Department of Common Course, Anhui Xinhua University, Hefei 230088, Anhui , China

Received: 22 December 2021

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.