On an epidemiological model with nonlinear infection incidence: Local and global perspective

Though bilinear and standard incident rates have been used frequently in classical epidemic models, nonlinearity in infection incidence is considered to be an useful modification due to its proximity with various realistic situations of disease propagation among ecological populations. In the present research, we consider an epidemiological model with SIS disease in the population. Infection is assumed to propagate following nonlinear incidence. First, we perform a stability and bifurcation analysis of the system around different equilibria from a local perspective. It is observed that the infected incidence fraction (p) plays the key role in controlling the disease dynamics. Then, using an iteration scheme and comparison argument, we investigate the global stability criteria of the model system around the endemic state and infer that the disease will persist among the species in the long run. Numerical simulation study is also carried out to illustrate and augment the analytical findings.