Effect of reinfection on the spread of COVID-19 evaluated by a flexible compartment model

Individuals infected with COVID-19 acquire infection-induced immunity after the recovery period and then become recovered individuals who are resistant to COVID-19 infection and return to the community. With an increase in the number of recovered individuals in the community, the contact rate between infected individuals and susceptible individuals is reduced by the contact of infected individuals with recovered individuals, causing a decrease in the total number of infected individuals. However, infection-induced immunity in recovered individuals decreases gradually, and when it decreases to below a certain threshold several weeks and/or several months after recovered individuals return to the community. Recovered individuals whose infection-induced immunity drops below a certain threshold substantially get back to susceptible individuals and can be infected with reinfections, which are infections that occur in individuals who have been infected once and have recovered from infection. The number of susceptible individuals is affected not only by the change in the number of infected individuals but also by the change in the number of individuals who get back to susceptible individuals from recovered individuals. The increase in susceptible individuals due to getting back to susceptible individuals from recovered individuals can increase not only the number of individuals who could be infected but also the contact rate between infected individuals and susceptible individuals, resulting in a marked increase in the number of infected individuals. Reinfections, which are infections that occur in individuals who have been infected once and have recovered, indicate an increase in the number of ‘spreaders’ and may increase the number of infected individuals. Will the changes in the number of infected individuals in the case of reinfection show the same trend as the changes in the cases of initial infection? Using a flexible compartment model specific to COVID-19, changes in the number of reinfected individuals were calculated. The model includes the duration of infection-induced immunity, which indicates the validity period of the effectiveness of infection-induced immunity, and the ‘back to rate’, which indicates the ratio of the number of individuals who get back to susceptible individuals from recovered individuals as independent variables in the calculation equations. The change in the number of infected individuals was examined in relation to the duration of infection-induced immunity. The results revealed that the occurrence of reinfection depends on the duration of infection-induced immunity, and that the duration of infection-induced immunity required for reinfection to occur varies depending on the symptomatic rate and/or the potential (biological) infectious capacity of the coronavirus. When reinfection occurs, not only do reinfections occur, but also ‘normal infections’, which are the first-time infections that occur in ‘original’ susceptible individuals, necessarily occur. As a result, the number of infected individuals increases significantly, and the duration of infection becomes significantly longer. Therefore, it is necessary to reduce the occurrence of reinfection in the early stages of infection through vaccination, PCR testing, and other medical and policy cares.