A Mathematical Model for the COVID-19 Pandemic in Tokyo through Changing Point Calculus

The great social and economic impact that the COVID-19 pandemic has had on a global level has encouraged the development of new mathematical models that make it possible to better manage this and future pandemics. Here, we propose an extension of the classical epidemiological compartmental model SIR, the SEIAMD model (Susceptible–Exposed–Identified–Asymptomatic–iMmunized–Deceased), which considers the appearance of new virus variants, the use of vaccines, the existence of nonidentified asymptomatic individuals, and the loss of immunity acquired by infection or vaccination. Using an optimization model coded in Python that allows us to determine the change points that represent different behaviors of infected people, the SEIAMD model calculates, from official data, the different effective contact rates that were observed during the first seven waves of the COVID-19 pandemic in Tokyo due to the application of Non-Pharmaceutical Interventions (NPIs) and social habits. The closeness of the results obtained with our model and the real data, as well as the accuracy of predictions and observations, confirm the suitability of our model for studying the evolution of the COVID-19 pandemic in Tokyo.