Dynamics of a time-delayed two-strain epidemic model with general incidence rates

Two-strain time-delayed epidemic model with general incidence rates is suggested and studied in this paper. The model consists of four compartments that describe the interaction between the susceptible, the first strain infected individuals, the second strain infected ones and the recovered individuals. In order to interpret the infection incubation period for each strain, two time delays will be incorporated into the studied model. Our first mathematical study will concern the wellposedness of the suggested model in terms of the classical existence, positivity and boundedness results. In order to perform the global stability, four equilibria of the problem are given. The first one stands for the disease-free equilibrium, the second describes first strain endemic equilibrium, the third one represents the second strain equilibrium and the last one is called the both strains endemic equilibrium. It was established that the global stability of each equilibrium depends on the strain 1 basic reproduction number R01 and on the strain 2 basic reproduction number R02. Numerical simulations are performed with a various incidence functions, namely, bilinear, Beddington–DeAngelis, Crowley–Martin and non-monotonic incidence rates. The bifurcation analysis have been conducted depending on time delays. We will limit ourselves to the theoretical study of the Hopf bifurcation results. The numerical results are in good agreement with the theoretical results dealing with the equilibria stability. Moreover, it was revealed that the time-delays may play an essential role in changing the nature of the equilibria stability.