Modeling and uncertainty quanti cation in the nonlinear dynamics of epidemiological phenomena: Application to Zika virus and COVID-19 outbreaks

Abstract

Outbreaks due infectious diseases has been drawing attention of the scientific community in the last few years. The recognition of the aggressive effects created for the health and economy of the population worldwide made researchers from the most diverse areas of knowledge turn their resources into projects inside the theme. The present work presents and apply a framework for uncertainty quantification in epidemiological models. This is based on use global sensitivity analysis by Polynomial Chaos Expansion-based Sobol indices, combined with the Maximum Entropy Principle. The first allows to identify the most relevant input parameters, while the second one orients the construction of least biased distributions for those inputs. Then, a Monte Carlo simulation is executed to analyze the outcome stochastic process obtained through the model. The framework was applied in the epidemiological scenarios of Zika virus in Brazil and COVID-19 in Rio de Janeiro city, allowing to extract some important statistics about each outbreak. A compartmental model is employed in the first scenario, while the multi-waves dynamics of the second scenario is described by a Beta logistic growth model. Before riding the robustness study, calibration results are performed to put the quantities of interest obtained from theses models in a shape closer to the real data. Additional discussions are made about how to use sensitivity analysis results to update the knowledge about the parameters, and guide model selection