Uncertainty Quantification of a Mathematical Model of COVID-19 Transmission Dynamics with Mass Vaccination Strategy

Olivares, Alberto; Staffetti, Ernesto

In this paper, the uncertainty quantification and sensitivity analysis of a mathematical model of the SARS-CoV-2 virus transmission dynamics with mass vaccination strategy has been carried out. More specifically, a compartmental epidemic model has been considered, in which vaccination, social distance measures, and testing of susceptible individuals have been included. Since the application of these mitigation measures entails a degree of uncertainty, the effects of the uncertainty about the application of social distance actions and testing of susceptible individuals on the disease transmission have been quantified, under the assumption of a mass vaccination program deployment. A spectral approach has been employed, which allows the uncertainty propagation through the epidemic model to be represented by means of the polynomial chaos expansion of the output random variables. In particular, a statistical moment-based polynomial chaos expansion has been implemented, which provides a surrogate model for the compartments of the epidemic model, and allows the statistics, the probability distributions of the interesting output variables of the model at a given time instant to be estimated and the sensitivity analysis to be conducted. The purpose of the sensitivity analysis is to understand which uncertain parameters have most influence on a given output random variable of the model at a given time instant. Several numerical experiments have been conducted whose results show that the proposed spectral approach to uncertainty quantification and sensitivity analysis of epidemic models provides a useful tool to control and mitigate the effects of the COVID-19 pandemic, when it comes to healthcare resource planning.