Eur. Phys. J. Plus (2017) 132: 208
https://doi.org/10.1140/epjp/i2017-11476-x

Regular Article

Global stability analysis of two-strain epidemic model with bilinear and non-monotone incidence rates

Near East University, TRNC, Lefkoşa, Turkey

^* e-mail: Isa.baba@neu.edu.tr

Received: 26 March 2017
Accepted: 2 April 2017
Published online: 8 May 2017

Abstract

In this article we studied an epidemic model consisting of two strains with different types of incidence rates; bilinear and non-monotone. The model consists of four equilibrium points: disease-free equilibrium, endemic with respect to strain 1, endemic with respect to strain 2, and endemic with respect to both strains. The global stability analysis of the equilibrium points was carried out through the use of Lyapunov functions. Two basic reproduction ratios R ¹ ₀ and R ² ₀ are found, and we have shown that if both are less than one, the disease dies out, and if both are greater than one epidemic occurs. Furthermore, epidemics occur with respect to any strain with a basic reproduction ratio greater than one and disease dies out with respect to any strain with a basic reproduction ratio less than one. It was also shown that any strain with highest basic reproduction ratio will automatically outperform the other strain, thereby eliminating it. Numerical simulations were carried out to support the analytic result and to show the effect of the parameter k in the non-monotone incidence rate, which describes the psychological effect of general public towards infection.