Deterministic and stochastic approaches to modeling the second wave of COVID-19 transmission in India and Brazil

COVID-19 is a global pandemic that has significantly impacted societies and healthcare systems worldwide. Therefore, understanding its complex effects requires thorough analysis. This study focused on the second wave of COVID-19 in India and Brazil, utilizing a compartmental model that incorporated the Beddington-DeAngelis incidence and Holling Type-II treatment functions to better understand transmission dynamics and the effects of medical interventions. Data fitting was conducted using Python, while simulations and all other analyses, including sensitivity analysis to explore implications for disease control strategies, were performed using MATLAB. The study also extended the model to a stochastic framework by incorporating white noise, allowing a comparison between the deterministic and stochastic approaches. The deterministic model provided a baseline understanding of the transmission dynamics and stability, while the stochastic model captured potential variability in outcomes, including disease extinction and stochastic permanence.