DYNAMICS OF A DELAYED EPIDEMIOLOGICAL MODEL WITH NONLINEAR INCIDENCE: THE ROLE OF INFECTED INCIDENCE FRACTION

Abstract

We present and analyze an epidemiological model containing Susceptible (S(t)) and Infected (I(t)) populations. The incidence rate is assumed to be nonlinear in the infected fraction (Ip(t)) as well as the susceptible fraction (Sq(t)). The dynamical behavior of the system is investigated from the point of view of stability and bifurcation. To model the recovery time of infected populations, a recovery delay, both in distributed and discrete form is introduced. In all the cases, it is shown that the infected incidence fraction p plays a vital role in controlling the dynamical behavior of the system. Numerical simulations are performed to justify the analytical findings.