Simulation of the SIR model on networks

Abstract

The standard model of epidemics of illnesses that make people immune upon recovery is the Susceptible–Infectious–Recovered (SIR) model. It’s important to understand the role of networks in revealing who could infect whom and when these encounters take place. There are four different network models for implementation of the SIR model on networks: (1) the random network (Erdos-Renyl model); (2) the small-world network (Watts-Strogatz beta model); (3) the scale-free network (Barabasi-Albert model), and (4) the complete network. The small-world method is like the lock-down method used in the COVID19 pandemic. Fewer connections and less connection strength will cause the pandemic to spread more slowly and thus be contained. Where there are more connections, such as scale-free networks (the Barabasi-Albert model) and full networks, the prevalence is much higher and may lead to the collapse of the healthcare system. When predicting the transmission of infectious diseases, simulations have demonstrated that taking a network approach can provide useful information. We've shown how integrating some regularly observed network patterns can significantly alter the model's behavior, altering disease propagation rates and long-term health effects. A network model also better informs the debate of targeted policies like contact tracing and testing, which have been used successfully to help manage infectious diseases by accounting for patterns of interaction among a population.