Control attenuation and temporary immunity in a cellular automata SEIR epidemic model

Abstract

Mathematical modeling is an important tool to analyze impacts and plan to mitigate epidemics in communities. In order to estimate the impact of control measures in a second wave of infections, we analyze the SEIR epidemic model based on stochastic cellular automata. The control measure is based on one of the key strategies to control the epidemic, which is the restriction of the mobility of individuals in space. For stronger restrictions, we observe a decrease larger than 15% in the total number of infected individuals during the epidemic. On the other hand, the total attenuation of control measures in the system can lead to a second wave scenario and even a situation in which the total number of infected individuals is close to the uncontrolled case. Additionally, we also include the possibility of reinfection, as the SEIRS model, where the recovered individuals can go to the susceptible state based on a fixed immunity time or a probabilistic rule. Our results show that an extinction of the epidemic occurs only for a fixed immunity time.