Development of a probabilistic model for Covid-19 dynamics with consideration of non-severe and severe infections

Covid-19 has triggered a massive global challenge with 1,576,069 overall confirmed cases, 1,545,429 recovered cases, and 30,640 deaths across Pakistan. Epidemiological models have always played an important role in understanding the dynamics of such infectious diseases. The severity of Covid-19 infection depends on several factors such as immune system and virus variants. Although detailed epidemiological models which consider these factors are generally more accurate, their complexity limits their application due to the unavailability of comprehensive historical data. Therefore, in this paper, we proposed a Susceptible-Non-severely Infected-Severely Infected-Recovered-Deceased model, for the prediction of Covid-19 infections. The proposed model broadly classifies Covid-19 infections into non-severe and severe infections. This classification is based on the overall effect of virus variants and individual immune systems. The important epidemiological proprieties of the model such as equilibrium points, stabilities and bifurcation analysis are discussed. The model is fitted to the Covid-19 data of Pakistan to predict the non-severe and severe infections over the next four months. The comparison of predicted and actual infections shows the forecasting efficiency of the model. Moreover, the prediction of a severely-infected population in the upcoming months can be of significant help to policy-makers in the efficient management of hospitalization services.