Resumen de A short study of an SIR model with inclusion of an alert class, two explicit nonlinear incidence rates and saturated treatment rate
Abhishek Kumar, Nilam Rathi, Raj Kishor
In this paper, we present a susceptible–alert–infected–recovered (SAIR) epidemic model with the consideration of two explicit saturated incidence rates and Holling functional type II treatment rate. Awareness about the epidemic may play a vital role in the control of the spread of an epidemic. Hence, an alert compartment has been incorporated into the model. It strives us to take two incidence rates: one from the susceptible class to infected class and another from alert class to infected class. Holling functional type II treatment rate has been introduced to capture the effects of resource limitation in treating infectives. The model has a disease-free equilibrium (DFE), which is locally asymptotically stable when R0<1. Using the center manifold theory, we show that DFE exhibits the forward bifurcation at R0=1. Stability of the endemic equilibrium has also been analyzed and discussed. Numerical simulations have been done by MATLAB 2012b and the outcomes have been discussed with the help of graphs in the paper.
