Understanding Covid-19 Situation Using Mathematical Modeling

Abstract

In light of the absence of an effective vaccine or specific antiviral treatments, mathematical modeling assumes a crucial role in enhancing our comprehension of disease dynamics and in devising strategies to manage the rapid spread of infectious diseases. Particularly during this period, forecasting holds paramount significance for healthcare planning and for effectively addressing the COVID-19 pandemic. To elucidate the dynamics of the COVID-19 outbreak, this study introduces an extended SEIR compartment model, refined with the inclusion of contact tracing and hospitalization strategies. The model is calibrated employing daily COVID-19 data encompassing various Indian regions, including Kerala, Karnataka, Andhra Pradesh, Maharashtra, West Bengal, and the entirety of India. Employing the least squares method, we estimate sensitive parameters after conducting a sensitivity analysis, which we approach using partial rank correlation coefficient techniques. Our exploration focuses on the relative significance of system parameters, with a dedicated sensitivity analysis centered on the reproductive number R₀. To assess the model's resilience across parameter variations, we compute R₀ sensitivity indices. Our findings underscore the effectiveness of strategies that involve reducing disease transmission coefficients (s) and clinical outbreak rates (qa) in controlling COVID-19 outbreaks. Our study generates short-term predictions for daily and cumulative confirmed COVID-19 cases across the five Indian provinces. These projections reveal distinct trends, with certain states demonstrating steady exponential growth, while others exhibit a decline in daily new cases. Examining the long-term perspective, our model predicts oscillatory dynamics for COVID-19 cases in India, suggesting the potential for the disease to follow a seasonal pattern. Consequently, our simulation points towards a power law trend in coronavirus cases in India by the close of September 2020, further contributing to our understanding of the disease's progression.