Global analysis of a time-delayed two-strain epidemic model with general incidence rates and therapy

The talk is about mathematical study of a time-delayed epidemic model with general incidence rates and therapy. The main four compartments of our model represent the densities of the susceptible, the first strain infected, the second strain infected and the recovered individuals. The time delays represent the needed time during the period of incubation for each strain. The therapy administration for each strain is assumed. The wellposedness of the tackled model will be established in terms of proving the results of existence, positivity and boundedness. The global stability of the disease-free equilibrium, the first strain endemic equilibrium, the second strain equilibrium and the both strains endemic equilibrium is fulfilled. It was remarked that the global stability of the equilibria depends mainly on the each strain basic reproduction number. Numerical tests are performed to show the stability of the equilibria for two different incidence functions. In our numerical tests, we will restrict ourselves to only two cases of incidence functions, namely, two bilinear incidence functions and two non-monotonic incidence rates. It was concluded that therapy efficiency plays an essential role in reducing the infection severity. Moreover, it was observed that any stain therapy efficiency increase or decrease can change the nature of the equilibrium stability. To control the spread of the infection in a two strain environment, it would be important to act on both strains treatment efficiencies.