COVID-19 dynamical system and cellular automaton based on an extended compartment model of contact network and vaccination impact

Abstract

In this paper, we study a new round of novel coronavirus disease 2019 (COVID-19) infection scenarios due to a mutated strain in the middle of the epidemic. By considering the characteristics of the presence or absence of symptoms, the severity of symptoms, and vaccination, we develop an extended compartmental model containing 11 compartments and describe its compartmental transformation process from both discrete and continuous perspectives by probabilistic cellular automata and a system of ordinary differential equations. Further, we analyze the relevance of the endemic equilibrium points as well as the trajectory types corresponding to the ordinary differential equations. Based on the model, we simulate the reoccurrence of an outbreak in the United States in the winter of 2021, and the results fit well with the actual data and show the consistency between the two forms of Probabilistic Cellular automata and the system of Ordinary Differential Equations. The effects of contact network and vaccination are investigated by applying the model to different scenarios. The results show that premature relaxation of social isolation campaigns may lead to subsequent waves of infection and that widespread vaccination is effective in reducing the number of severe illnesses and deaths. The significance of this paper is to provide a model of infectious diseases for mid-epidemic and to assist in epidemic prevention policy-making through Probabilistic Cellular Automata.