The Importance of Being Hybrid for Spatial Epidemic Models:A Multi-Scale Approach

Abstract

This work addresses the spread of a disease within an urban system, definedas a network of interconnected cities. The first step consists of comparing two differentapproaches: a macroscopic one, based on a system of coupled Ordinary DifferentialEquations (ODE) Susceptible-Infected-Recovered (SIR) systems exploiting populations onnodes and flows on edges (so-called metapopulational model), and a hybrid one, couplingODE SIR systems on nodes and agents traveling on edges. Under homogeneous conditions(mean field approximation), this comparison leads to similar results on the outputs on whichwe focus (the maximum intensity of the epidemic, its duration and the time of the epidemicpeak). However, when it comes to setting up epidemic control strategies, results rapidlydiverge between the two approaches, and it appears that the full macroscopic model is notcompletely adapted to these questions. In this paper, we focus on some control strategies,which are quarantine, avoidance and risk culture, to explore the differences, advantages anddisadvantages of the two models and discuss the importance of being hybrid when modelingand simulating epidemic spread at the level of a whole urban system.

Keywords

• agent-based modeling
• city systems
• disease spread
• mobility
• model coupling
• metapopulation
• network
• ODE