Epidemic spread on patch networks with community structure

Abstract

Predicting and preparing for the trajectory of disease epidemics relies on a knowledge of environmental and socioeconomic factors that affect transmission rates on local and global spatial scales. This article discusses the simulation of epidemic outbreaks on human metapopulation networks with community structure, such as cities within national boundaries, for which infection rates vary both within and between communities. We demonstrate mathematically, through next-generation matrices, that the structures of these communities, setting aside all other considerations such as disease virulence and human decision-making, have a profound effect on the reproduction rate of the disease throughout the network. In high modularity networks, with high levels of separation between neighboring communities, disease epidemics tend to spread rapidly in high-risk communities and very slowly in others, whereas in low modularity networks, the epidemic spreads throughout the entire network as a steady pace, with little regard for variations in infection rate. The correlation between network modularity and effective reproduction number is stronger in population with high rates of human movement. This implies that the community structure, human diffusion rate, and disease reproduction number are all intertwined, and the relationships between them can be affected by mitigation strategies such as restricting movement between and within high-risk communities. We then test through numerical simulation the effectiveness of movement restriction and vaccination strategies in reducing the peak prevalence and spread area of outbreaks. Our results show that the effectiveness of these strategies depends on the structure of the network and the properties of the disease. For example, vaccination strategies are most effective in networks with high rates of diffusion, whereas movement restriction strategies are most effective in networks with high modularity and high infection rates. Finally, we offer guidance to epidemic modelers as to the ideal spatial resolution to balance accuracy and data collection costs.

Keywords: Community networks; Disease epidemics; Metapopulation SIR; Patch networks; Super-spreader events.