Modeling COVID-19 spread and non-pharmaceutical interventions in South Africa: A stochastic approach

The COVID-19 pandemic has exerted a pervasive worldwide influence, including on South Africa, which stands out as one of the African nations most substantially impacted. As of March 20, 2021, the nation has encountered a multitude of obstacles in its efforts to contain the virus's transmission. Conventional approaches to forecasting the transmission of contagious illnesses frequently prove inadequate when it comes to comprehending the intricate dynamics of COVID-19, specifically with regard to stochastic disruptions and the efficacy of non-pharmaceutical interventions. The deficiency in predictive modeling has impeded the capacity to effectively evaluate and execute measures to reduce the spread of the virus. The principal objective of this study is to construct a novel stochastic model, denoted as SEIHR, that can effectively forecast the transmission of COVID-19 in South Africa while also assessing the efficacy of diverse non-pharmacological interventions. By conducting an extensive data analysis spanning from April 17, 2020, to September 13, 2021, this research endeavors to provide a comprehensive and nuanced comprehension of the dynamics of the epidemic, with a particular focus on its early surges. Using the idea of stochastic Lyapunov function theory, this study aims to find out if there is and isn't a solution in the given model. It also wants to find out what conditions must be met in order to get rid of diseases when there are random disturbances, such as white noise. Using this model, the efficacy of interventions such as lockdowns in preventing the spread of the virus during the epidemic will also be critically evaluated. The primary objective is to furnish policymakers and health authorities with invaluable insights and tools that will enable them to more effectively manage and alleviate the COVID-19 crisis in South Africa and comparable settings.