The role of network in the sir model

Abstract

Mathematical models have been often used to simulate the dynamics of the spread of infectious disease, as well as to test containment public policy proposals. The goal of this work is to study how a network structure can determine the evolution of an epidemic. For that, we use a usceptible Infected Recovered (SIR) macroeconomic model in the presence of a network nvironment. Network models have been important in the job search discussion. In our epidemiological model, the network structure is an important cause of the spread of the disease. Intuitively, more connected people in the social circle are the main vector of the virus. On the other hand, those people with few connections should be less exposed to the disease. We study the behavior of the pandemic for different types of network, from a low connected one to a high connected one. We find exactly the expected relationship: because more connected economies (economies with a higher average number of links) spread the virus faster, they face harder consequences in a pandemic scenario, such as a greater fall on aggregate consumption and hours worked due to both the higher number of deaths and the susceptible agents’ higher attempt to stay at home and avoid physical contacts. Susceptible agents are more cautious in regard to the decision of their level of consumption and hours worked as the economy becomes more socially connected, once the consequences of leaving home to consume or to work are harder in the higher connected economy because of its higher number of infected people.