A Stochastic Compartmental Model for COVID-19

TL;DR

This paper introduces two stochastic models for COVID-19 that incorporate lockdown measures and healthcare capacity, demonstrating how hospital actions can effectively control the epidemic's spread, especially when vaccines are not yet widely available.

Contribution

The paper generalizes previous models by integrating hospital capacity and lockdown effects, providing a more comprehensive stochastic framework for COVID-19 spread analysis.

Findings

Lockdown measures alone may lead to resurgence after removal.

Hospital capacity thresholds can suppress virus spread.

Model predictions align well with US and France COVID-19 data.

Abstract

We propose two stochastic models for the Coronavirus pandemic. The statistical properties of the models, in particular the correlation functions and the probability density function, have duly been computed. Our models, which generalises a model previously proposed and published in a specialised journal, take into account the adoption of the lockdown measures as well as the crucial role of the hospitals and Health Care Institutes. To accomplish this work we have analysed two scenarios: the SIS-model (Susceptible => Infectious => Susceptible) in presence of the lockdown measures and the SIS-model integrated with the action of the hospitals (always in presence of the lockdown measures). We show that in the case of the pure SIS-model, once the lockdown measures are removed, the Coronavirus will start growing again. However, in the second scenario, beyond a certain threshold of the hospital capacities, the Coronavirus is not only kept under control, but its capacity to spread tends to diminish in time. Therefore, the combined effect of the lockdown measures with the action of the hospitals and health Institutes is able to contain and dampen the spread of the SARS-CoV-2 epidemic. This result can be used during a period of time when the massive distribution of delivery of a limited number of vaccines in a given population is not yet feasible. By way of example, we analysed the data for USA and France where the intensities of the noise have been estimated by Statistical Mechanics. In particular, for USA we have analysed two possible hypotheses: USA is still subject to the first wave of infection by and USA is in the second (or third) wave of SARS-CoV-2 infection.The agreement between theoretical predictions and real data confirms the validity of our approach.