Healthy-infected predator-prey models, a case study of Covid-19 infection rate

Since the first case of a novel coronavirus, called COVID-19, was found in Wuhan, China, in December 2019, the number of cases rapidly increased and spread to various urban areas in China as well as to many different countries in the world. The number of confirmed cases is proliferating on a daily basis and has been declared a pandemic lately. In this paper a new delayed healthy- infected model is investigated to analyze the COVID-19 epidemic. The global analysis of the model as well as boundedness and permanence properties are examined. Then we analyze the effect of time delay on the stabilization of the equilibria, i.e., we study whether time delay could change the stability of a co-existence point from an unstable mood to a stable one. The system undergoes a Hopf bifurcation when it passes a critical time delay. Finally, some numerical simulations are performed to support our analytic results.