Analytical tool for COVID-19 using an SIR model equivalent to the chain reaction equation of infection

Insights from data analysis of existing cases are important to prevent future outbreaks of coronavirus disease 2019 (COVID-19). Although mathematical models are expected to be useful for this purpose, the adequacy of reproducibility of these models is difficult to confirm because they are based on hypotheses. For example, using the time variation of the parameter of the basic reproduction number for the time variation of complex data on the number of infected persons is a change of expression and does not capture the substance of the problem. We previously showed that the simplest Susceptible, Infected, Recovered (SIR) model alone, without any complex models, exhibits acceptable reproducibility. By clarifying the rationale for this reproducibility, quantifiable characteristics regarding the infection spread, such as the duration of the pandemic and the mechanism of occurrence of several large waves, can be uncovered and this can contribute to countermeasures. Here, we show this method equals the chain reaction equation for infection, allowing the parameters (infection rate, population) of the mathematical models to be extracted from the data. Once a model that reproduces the actual situation is determined, much of the information becomes apparent. As an example, we present three characteristics of the spread of infection effective in controlling COVID-19: the time of onset of infection, the rapidity of the spread, and the time to acquisition of herd immunity. Acquiring this information is likely to increase the predictive accuracy of the model.