Dynamical analysis of the infection status in diverse communities due to COVID-19 using a modified SIR model

In this article, we model and study the spread of COVID-19 in Germany, Japan, India and highly impacted states in India, i.e., in Delhi, Maharashtra, West Bengal, Kerala and Karnataka. We consider recorded data published in Worldometers and COVID-19 India websites from April 2020 to July 2021, including periods of interest where these countries and states were hit severely by the pandemic. Our methodology is based on the classic susceptible-infected-removed (SIR) model and can track the evolution of infections in communities, i.e., in countries, states or groups of individuals, where we (a) allow for the susceptible and infected populations to be reset at times where surges, outbreaks or secondary waves appear in the recorded data sets, (b) consider the parameters in the SIR model that represent the effective transmission and recovery rates to be functions of time and (c) estimate the number of deaths by combining the model solutions with the recorded data sets to approximate them between consecutive surges, outbreaks or secondary waves, providing a more accurate estimate. We report on the status of the current infections in these countries and states, and the infections and deaths in India and Japan. Our model can adapt to the recorded data and can be used to explain them and importantly, to forecast the number of infected, recovered, removed and dead individuals, as well as it can estimate the effective infection and recovery rates as functions of time, assuming an outbreak occurs at a given time. The latter information can be used to forecast the future basic reproduction number and together with the forecast on the number of infected and dead individuals, our approach can further be used to suggest the implementation of intervention strategies and mitigation policies to keep at bay the number of infected and dead individuals. This, in conjunction with the implementation of vaccination programs worldwide, can help reduce significantly the impact of the spread around the world and improve the wellbeing of people.