Saddle–node bifurcation of limit cycles in an epidemic model with two levels of awareness

In this paper we study the appearance of bifurcations limit cycles in an epidemic model with two types aware individuals. All transition rates are constant except for alerting decay rate most individuals and creation less individuals, which depend on disease prevalence a non-linear way. For ODE model, numerical computation their stability made by means Poincaré map. Moreover, sufficient conditions existence endemic equilibrium also obtained. These involve rather natural relationship between transmissibility that awareness. Finally, stochastic simulations under very low imported cases used to confirm scenarios bistability (endemic cycle) observed solutions model.