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 hence helps to reduce the epidemic’s health burden by lowering peak incidence. Therefore, this paper studies susceptible-aware-infected-recovered (SAIR) epidemic model with novel combinations of Michaelis-Menten functional type nonlinear incidence rates for unaware aware susceptible inclusion time delay as latent period saturated treatment rate infected people. The is analyzed mathematically describe disease transmission dynamics two obtained equilibria: disease-free endemic. We derive basic reproduction number $$R_0$$ investigate local global stability behavior equilibria . A bifurcation analysis performed using center manifold theory when there no delay, revealing forward varies from unity. Moreover, presence Hopf around EE shown depending on parameter delay. Lastly, numerical simulations validate analytical findings.