Modeling and Simulation of Modified SIR Epidemic  Model with Immigration and Non–monotonic  Incidence Rate under Treatment

D. Jasmine; E. C. Henry Amirtharaj

Volume : III, Issue : VII, July - 2013

Modeling and Simulation of Modified SIR Epidemic Model with Immigration and Non–monotonic Incidence Rate under Treatment

D. Jasmine, E. C. Henry Amirtharaj

Abstract :

An epidemic model with non–monotonic incidence rate under a limited resource for treatment is proposed to understand the effect of the capacity of the treatment. This model is investigated by considering modified non–monotonic incidence rate with immigration. It is assumed that the treatment rate is proportional to the number of infective when it is below the capacity and is a constant when the number of infective is larger than the capacity. Existence and stability of the disease free and endemic equiliium are investigated for both the cases. Some numerical simulations are given to illustrate the analytical results.