Predicting the evolution of the COVID-19 epidemic with the A-SIR model: Lombardy, Italy and S\~ao Paulo state, Brazil

TL;DR

This study extends the A-SIR epidemiological model to fit COVID-19 data from Lombardy and São Paulo, highlighting uncertainties in key parameters and their impact on epidemic forecasts.

Contribution

It introduces a generalized A-SIR model and a parameter fitting scheme based on death data, applied to real-world cases to analyze epidemic evolution.

Findings

Good data fit up to present with large future prediction variability.

Uncertainty in symptomatic probability affects epidemic forecasts.

Social distancing measures significantly influence epidemic trajectories.

Abstract

The presence of a large number of infected individuals with few or no symptoms is an important epidemiological difficulty and the main mathematical feature of COVID-19. The A-SIR model, i.e. a SIR (Susceptible-Infected-Removed) model with a compartment for infected individuals with no symptoms or few symptoms was proposed by Giuseppe Gaeta, arXiv:2003.08720 [q-bio.PE] (2020). In this paper we investigate a slightly generalized version of the same model and propose a scheme for fitting the parameters of the model to real data using the time series only of the deceased individuals. The scheme is applied to the concrete cases of Lombardy, Italy and S\~ao Paulo state, Brazil, showing different aspects of the epidemics. For each case we show that we may have good fits to the data up to the present, but with very large differences in the future behavior. The reasons behind such disparate outcomes are the uncertainty on the value of a key parameter, the probability that an infected individual is fully symptomatic, and on the intensity of the social distancing measures adopted. This conclusion enforces the necessity of trying to determine the real number of infected individuals in a population, symptomatic or asymptomatic.