The development of mathematical modeling of infectious diseases is a key research area in various fields including ecology and epidemiology. One aim of these models is to understand the dynamics of behavior in infectious diseases. For the new strain of coronavirus (COVID-19), there is no vaccine to protect people and to prevent its spread so far. Instead, control strategies associated with health care, such as social distancing, quarantine, travel restric-tions, can be adopted to control the pandemic of COVID-19. This article sheds light on the dynamical behaviors of nonlinear COVID-19 models based on two methods: the homotopy perturbation method (HPM) and the modi ed reduced differential transform method (MRDTM). We invoke a novel signal ow graph that is used to describe the COVID-19 model. Through our mathe-matical studies, it is revealed that social distancing between potentially infected individuals who are carrying the virus and healthy individuals can decrease or interrupt the spread of the virus. The numerical simulation results are in reasonable agreement with the study predictions. The free equilibrium and stability point for the COVID-19 model are investigated. Also, the existence of a uniformly stable solution is proved.