A mathematical model for repetitive behaviors of Covid-19

Abstract Covid-19 pandemic waves have been hitting us again and again in the past couple years in many countries, while the reason why they come in such repetitive manners remains unexplained, which have brought us with lingering anxieties and economic stagnations. We proposed a mathematical model to describe the mechanism of the repetitive appearance of the number of new cases based upon the SIQR model in which Q (quarantined infectors) were distinguished from I (un-quarantined ones). The repetitive behavior of the pandemic was simulated by an activator-inhibitor system around a fixed point in a phase space as a kind of self-organized oscillations. Periods between each wave were confirmed to be approximately similar. Repetitive behaviors were also observed in actual Covid-19 data. Practical policies and actions were discussed on the ways to effectively control the repetition of pandemic, and proactive PCR test especially after the peak-out stage is highly recommended.