Stochastic SIR Model Predicts the Evolution of COVID-19 Epidemics from Public Health and Wastewater Data in Small and Medium-Sized Municipalities: A One Year Study

The level of unpredictability of the COVID-19 pandemics poses a challenge to effectively model its dynamic evolution. In this study we incorporate the inherent stochasticity of the SARS-CoV-2 virus spread by reinterpreting the classical compartmental models of infectious diseases (SIR type) as chemical reaction systems modelled via the Chemical Master Equation and solved by Monte Carlo Methods. Our model predicts the evolution of the pandemics at the level of municipalities, incorporating for the first time i) a variable infection rate to capture the effect of mitigation policies on the dynamic evolution of the pandemics ii) SIR-with-jumps taking into account the possibility of multiple infections from a single infected person and iii) data of viral load quantified by RT-qPCR from samples taken from Wastewater Treatment Plants. The model has been successfully employed for the prediction of the COVID-19 pandemics evolution in small and medium size municipalities of Galicia (Northwest of Spain).