Backward and Hopf bifurcation analysis of an SEIRS COVID-19 epidemic model with saturated incidence and saturated treatment response

In this work, we further the investigation of an SEIRS model to study the dynamics of the Coronavirus Disease 2019 pandemic. We derive the basic reproduction number R ₀ and study the local stability of the disease-free and endemic states. Since the condition R ₀ < 1 for our model does not determine if the disease will die out, we consider the backward bifurcation and Hopf bifurcation to understand the dynamics of the disease at the occurrence of a second wave and the kind of treatment measures needed to curtail it. Our results show that the limited availability of medical resources favours the emergence of complex dynamics that complicates the control of the outbreak.