Abstract
Although deterministic compartmental models are useful for predicting the general trend of a disease’s spread, they are unable to describe the random daily fluctuations in the number of new infections and hospitalizations, which is crucial in determining the necessary healthcare capacity for a specified level of risk. In this paper, we propose a stochastic SEIHR (sSEIHR) model to describe such random fluctuations and provide sufficient conditions for stochastic stability of the disease-free equilibrium, based on the basic reproduction number that we estimated. Our extensive numerical results demonstrate strong threshold behavior near the estimated basic reproduction number, suggesting that the necessary conditions for stochastic stability are close to the sufficient conditions derived. Furthermore, we found that increasing the noise level slightly reduces the final proportion of infected individuals. In addition, we analyze COVID-19 data from various regions worldwide and demonstrate that by changing only a few parameter values, our sSEIHR model can accurately describe both the general trend and the random fluctuations in the number of daily new cases in each region, allowing governments and hospitals to make more accurate caseload predictions using fewer compartments and parameters than other comparable stochastic compartmental models.
Highlights
Over the past year, the coronavirus disease 2019 (COVID-19) pandemic has placed enormous stress on healthcare systems worldwide
We develop a stochastic version of the modified SEIHR compartmental model established in [8], which allows one to accurately model the random fluctuations in the number of daily new cases in the COVID-19 epidemic process
We developed a model described by a system of stochastic differential equations to describe a stochastic SEIHR process
Summary
The coronavirus disease 2019 (COVID-19) pandemic has placed enormous stress on healthcare systems worldwide. The severity of the pandemic, given the fact that it takes a long time to develop effective vaccines, has imposed tremendous pressures and responsibilities onto the healthcare systems in all countries and regions, especially those with limited medical resources such as available staff, equipment and facilities. Differing from most infectious diseases found to date, COVID-19 is especially violent, aggressive and fast-spreading, and even among those deemed “recovered” from the disease, there are many for which adverse effects have lingered for months after the initial symptoms [1]. Failure to meet the demand for hospital resources can lead to resource saturation and a growing backlog of infectious patients requiring hospitalization, in turn increasing the total transmission rate due to unisolated infectious individuals and causing an adverse feedback loop
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