SIR Dynamics with Vaccination in a Large Configuration Model

We consider an SIR model with vaccination strategy on a sparse configuration model random graph. We show the convergence of the system when the number of nodes grows and characterize the scaling limits. Then, we prove the existence of optimal controls for the limiting equations formulated in the framework of game theory, both in the centralized and decentralized setting. We show how the characteristics of the graph (degree distribution) influence the vaccination efficiency for optimal strategies, and we compute the limiting final size of the epidemic depending on the degree distribution of the graph and the parameters of infection, recovery and vaccination. We also present several simulations for two types of vaccination, showing how the optimal controls allow to decrease the number of infections and underlining the crucial role of the network characteristics in the propagation of the disease and the vaccination program.

Automated summary

In this study, an SIR model with vaccination strategy on a sparse configuration model random graph was considered. The convergence of the system as the number of nodes grows and the existence of optimal controls in game theory framework were shown. The influence of degree distribution on vaccination efficiency and epidemic final size was analyzed, along with simulations demonstrating the role of network characteristics in disease propagation and vaccination.