Mathematical modeling of pandemics under uncertainty using nonlinear stochastic differential equations

Abstract Mathematical models can provide insight into the evolution of a pandemic under some conditions and assumptions. The real world changes constantly, especially during a pandemic. Thus, oftentimes some parameters vary over time due to many factors, including social human behavior, interventions, and media awareness. Forecasting pandemics is a very complex task due to the uncertainty of the parameters’ values. In this paper, we construct and analyze a stochastic mathematical model, based on a system of nonlinear stochastic differential equations, to explain the complexity of COVID-19 pandemic forecasting, taking into account the fluctuations of human social behavior and non-pharmaceutical interventions. We study the proposed nonlinear stochastic model and determine the Covid disease extinction and persistence conditions. The results presented here provide insight about the difficulties that many studies have faced in forecasting the dynamics of the COVID-19 pandemic. We find the basic reproduction number for the stochastic model that is a crucial threshold parameter to understand the dynamics of pandemics and especially when the disease becomes extincts. Finally, we present some numerical simulations that support the theoretical results and provide insight into the uncertainty present in the dynamics of a pandemic.