Backward Bifurcation of Sir Epidemic Model with Non- Monotonic Incidence Rate under Treatment

Treatment is of great importance in fighting against infectious diseases. Backward bifurcation of SIR epidemic model with treatment rate is proposed and analyzed by Wang W. We have reinvestigated the above model by considering a backward bifurcation of SIR epidemic model with non-monotone incidence rate under treatment. It is assumed that the treatment rate is proportional to the number of patients as long as this number is below a certain capacity and it becomes constant when that number of patients exceeds this capacity. Mathematical models have become important tools in analyzing the spread and control of infectious diseases. It is shown that this kind of treatment rate leads to the existence of multiple endemic equilibria where the basic reproduction number plays a big role in determining their stability. Moreover, numerical calculations are support to analyze the global stability of unique endemic equilibrium.