SIR Epidemics in Interconnected Networks: threshold curve and phase transition

Abstract

For simplicity of mathematical modelling of epidemic spreading, assumption is that hosts have identical rate of disease-causing contacts. However, in real world the scenario is different. The network-based framework allows us to capture the complex interdependencies and structural heterogeneity present in real-world systems. We examine two distinct scenarios involving the dynamics of Susceptible-Infected-Recovered (SIR) in interconnected networks. In the first part, we show how the epidemic threshold of a contact network changes as a result of being coupled with another network for a fixed infection strength. The model employed in this work considers both the contact networks and interconnections as generic. We have depicted the epidemic threshold curve for interconnected networks, considering the assumption that the infection could be initially present in either one or both of the networks. If the normalized infection strengths are above the threshold curve, the infection spreads, whereas if the normalized infection strengths are below the threshold curve, the disease does not spread. This is true for any level of interconnection. In the second part, we investigate the spillover phenomenon, where the disease in a novel host population network comes from a reservoir network. We have observed a clear phase transition when the number of links or the inter-network infection rate exceeds a certain threshold, keeping all other parameters constant. We observe two regimes for spillover: a major spillover region and a minor spillover region based on interpopulation links (fraction of links between two networks) and inter-network infection strength (infection rate between reservoir and host network). If the interpopulation links and inter-network infection strength are in the major spillover region, the spillover probability is high, while if the former parameters are in the minor spillover region, the spillover probability is low. When the number of infected individuals within a reservoir network is nearly equal, and the inter-network infection strength remains constant, the threshold number of links required to achieve the spillover threshold condition varies based on the network topology. Overall, this work contributes to the understanding of SIR dynamics in interconnected networks and sheds light on the behavior of epidemics in complex systems.