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

Abstract

Abstract In this paper, we study an epidemic model describing two strains with non-monotone incidence rates. The model consists of six ordinary differential equations illustrating the interaction between the susceptible, the exposed, the infected and the removed individuals. The system of equations has four equilibrium points, disease-free equilibrium, endemic equilibrium with respect to strain 1, endemic equilibrium with respect to strain 2, and the last endemic equilibrium with respect to both strains. The global stability analysis of the equilibrium points was carried out through the use of suitable Lyapunov functions. Two basic reproduction numbers R 0 1 and R 0 2 are found; we have shown that if both are less than one, the disease dies out. It was established that the global stability of each endemic equilibrium depends on both basic reproduction numbers and also on the strain inhibitory effect reproduction number(s) Rm and/or Rk. It was also shown that any strain with highest basic reproduction number will automatically dominate the other strain. Numerical simulations were carried out to support the analytic results and to show the effect of different problem parameters on the infection spread.