Nonlinear dynamics of a time-delayed epidemic model with two explicit aware classes, saturated incidences, and treatment.

Whenever a disease emerges, awareness in susceptibles prompts them to take preventive measures, which influence individuals' behaviors. Therefore, we present and analyze a time-delayed epidemic model in which class of susceptible individuals is divided into three subclasses: unaware susceptibles, fully aware susceptibles, and partially aware susceptibles to the disease, respectively, which emphasizes to consider three explicit incidences. The saturated type of incidence rates and treatment rate of infectives are deliberated herein.

A mathematical and numerical study of a SIR epidemic model with time delay, nonlinear incidence and treatment rates.

A novel nonlinear time-delayed susceptible-infected-recovered epidemic model with Beddington-DeAngelis-type incidence rate and saturated functional-type treatment rate is proposed and analyzed mathematically and numerically to control the spread of epidemic in the society. Analytical study of the model shows that it has two equilibrium points: disease-free equilibrium (DFE) and endemic equilibrium (EE). The stability of the model at DFE is discussed with the help of basic reproduction number, denoted by [Formula: see text], and it is shown that if the basic reproduction number [Formula: see text] is less than one, the DFE is locally asymptotically stable and unstable if [Formula: see text] is greater than one.