A single-agent extension of the SIR model describes the impact of mobility restrictions on the COVID-19 epidemic

Nicoletta Gnan,Marco Salvetti,Francesca Grassi,Matteo Paoluzzi,Andrea Crisanti,Nicola Vanacore

doi:10.1038/s41598-021-03721-x

Abstract

Mobility restrictions are successfully used to contain the diffusion of epidemics. In this work we explore their effect on the epidemic growth by investigating an extension of the Susceptible-Infected-Removed (SIR) model in which individual mobility is taken into account. In the model individual agents move on a chessboard with a Lévy walk and, within each square, epidemic spreading follows the standard SIR model. These simple rules allow to reproduce the sub-exponential growth of the epidemic evolution observed during the Covid-19 epidemic waves in several countries and which cannot be captured by the standard SIR model. We show that we can tune the slowing-down of the epidemic spreading by changing the dynamics of the agents from Lévy to Brownian and we investigate how the interplay among different containment strategies mitigate the epidemic spreading. Finally we demonstrate that we can reproduce the epidemic evolution of the first and second COVID-19 waves in Italy using only 3 parameters, i.e , the infection rate, the removing rate, and the mobility in the country. We provide an estimate of the peak reduction due to imposed mobility restrictions, i. e., the so-called flattening the curve effect. Although based on few ingredients, the model captures the kinetic of the epidemic waves, returning mobility values that are consistent with a lock-down intervention during the first wave and milder limitations, associated to a weaker peak reduction, during the second wave.

Highlights

Mobility restrictions are successfully used to contain the diffusion of epidemics
We show that the proposed model is able to account for the non-exponential epidemic growth induced by mobility restrictions and to reproduce real data from the first and the second COVID-19 epidemic wave in Italy, using a minimal set of parameters
The agent-based lattice model considered here reduces to a standard SIR model when the well-mixed population condition is satisfied, i. e. when large jumps dominate the dynamics (Fig. 2)

Summary

Introduction

Mobility restrictions are successfully used to contain the diffusion of epidemics. In this work we explore their effect on the epidemic growth by investigating an extension of the Susceptible-InfectedRemoved (SIR) model in which individual mobility is taken into account. Mobility data have been derived from mobile phone traffic c hanges[1,2,3,4,5,6] and remarkably good fits of the observations have been obtained using compartmental models These models describe the spread of infectious diseases among homogeneous compartments with different health status. To take into account the complexity of disease evolution, the basic SIR model has been generalized in several ways, introducing various sub-populations and describing, by different reaction rates, the conversion among interacting compartments. Contacts within and among groups determine the values assigned to SIR reaction rates for each group Reference values for these contact matrices have recently been proposed for the European population as a part of the POLYMOD p roject[14] and used to forecast the spread of several pandemic outbreaks, such as avian influenza in 200814 and Covid-1915. Values have been recalculated during different phases of Covid-19 pandemic in some countries

Methods

Results

Conclusion