Competitive Coexistence in a Two-Strain Epidemic Model with a Periodic Infection Rate

Chentong Li,Yicang Zhou,Yingying Zhang

doi:10.1155/2020/7541861

Chentong Li, Yicang Zhou + Show 1 more

Open Access

https://doi.org/10.1155/2020/7541861

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Abstract

In this article, we study the global dynamical behavior of a two-strain SIS model with a periodic infection rate. The positivity and boundedness of solutions are established, and the competitive exclusion conditions are given for the model. The conditions for the global stability of the disease-free equilibrium and persistence of the model are obtained. The conditions of coexistence in this model are also found. Finally, the conditions of uniqueness of the solution are proved.

Highlights

Since the first work [1] about the mathematical epidemic model published, there were plenty of results of infectious diseases in modeling and dynamics. ese epidemic models usually include two important parameters, the infection rate and recovery rate
We introduce two basic reproductive numbers R10 and R20 for our two-strain model and use these two values as the thresholds to analyze the dynamic behaviors of model (1)
Numerical simulations are performed to illustrate the dynamic behaviors of model (1) and (21)

Summary

Introduction

Since the first work [1] about the mathematical epidemic model published, there were plenty of results of infectious diseases in modeling and dynamics. ese epidemic models usually include two important parameters, the infection rate and recovery rate. Is paper is organized as follows: In Section 2, we analyze the positivity and boundedness of model (1), as well as the global stability of the disease-free equilibrium. E condition Ri0 < 1(i 1, 2) implies that if e􏽒0 ((βi(t)SE/1+SE)− ki)dt < 1(i 1, 2), we claim that the disease-free equilibrium is globally asymptotically stable. As (b0S∗/1 + S∗) k1 > c1, m(b0S∗/1 + S∗) k2 > c2 and R10 > 1 implies dS∗ − λ > 0, so there exists unique positive equilibrium E1 (S∗, I∗) for model (28). For model (21), if R10 > 1 and β1(t) b0+ ε cos(t), where ε > 0 and small, there exists a asymptotically stable positive 2π-periodic solution (S(t), I(t)) for model (21)

Uniqueness of the Solution on the Surface

Numerical Simulation

Discussion