A nonlinear SAIR epidemic model: Effect of awareness class, nonlinear incidences, saturated treatment and time delay

Awareness plays a vital role in informing and educating people about infection risk during an outbreak and hence helps to reduce the epidemic's health burden by lowering the peak incidence. Therefore, this paper studies a susceptible-aware-infected-recovered (SAIR) epidemic model with the novel combinations of Michaelis-Menten functional type nonlinear incidence rates for unaware and aware susceptible with the inclusion of time delay as a latent period and a saturated treatment rate for infected people. The model is analyzed mathematically to describe disease transmission dynamics in two obtained equilibria: disease-free and endemic. We derive the basic reproduction number R-0 and investigate the local and global stability behavior of obtained equilibria for the time delay (omega) over bar >= 0. A bifurcation analysis is performed using center manifold theory when there is no time delay, revealing the forward bifurcation when R-0 varies from unity. Moreover, the presence of Hopf bifurcation around EE is shown depending on the bifurcation parameter time delay. Lastly, the numerical simulations validate the analytical findings.