A stochastic $\theta$-SEIHRD model: adding randomness to the COVID-19 spread

TL;DR

This paper extends a deterministic COVID-19 spread model to a stochastic framework by incorporating randomness into model coefficients, allowing for more realistic simulations and uncertainty quantification.

Contribution

It introduces a stochastic version of the $ heta$-SEIHRD model, enabling the analysis of uncertainties and the computation of confidence intervals and worst-case scenarios.

Findings

Model variables are represented by stochastic processes.

Confidence intervals for key variables are computed.

The stochastic model captures additional uncertainties.

Abstract

In this article we mainly extend the deterministic model developed in [10] to a stochastic setting. More precisely, we incorporated randomness in some coefficients by assuming that they follow a prescribed stochastic dynamics. In this way, the model variables are now represented by stochastic process, that can be simulated by appropriately solve the system of stochastic differential equations. Thus, the model becomes more complete and flexible than the deterministic analogous, as it incorporates additional uncertainties which are present in more realistic situations. In particular, confidence intervals for the main variables and worst case scenarios can be computed.