On Time-Delayed Two-Strain Epidemic Model with General Incidence Rates and Therapy

In this work, we will study 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. In our suggested model, the time delays will represent the needed time during the period of infection incubation for each strain. We will assume in our model therapy administration for each strain that its efficiency will be represented by two strictly positive constants η1 for the first strain and η2 for the second strain. 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. More precisely, when the first strain therapy efficiency η1 is increased, the first strain infected individuals are reduced considerably. Some remark is observed concerning the effect of the second strain therapy efficiency η2. Moreover, it was observed that any strain 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.