Time evolution of epidemic disease on finite and infinite networks

TL;DR

This paper introduces a novel analytical framework that combines contact network structure and disease progression over time, applicable to both finite and infinite networks, advancing epidemic modeling beyond traditional methods.

Contribution

The authors develop a new analytical approach that integrates network topology and temporal dynamics of disease spread, bridging the gap between compartmental models and simulation-based methods.

Findings

Framework effectively models epidemic evolution on various network sizes.

Analytical method matches simulation results for different network structures.

Applicable to other percolation phenomena in science and technology.

Abstract

Mathematical models of infectious diseases, which are in principle analytically tractable, use two general approaches. The first approach, generally known as compartmental modeling, addresses the time evolution of disease propagation at the expense of simplifying the pattern of transmission. The second approach uses network theory to incorporate detailed information pertaining to the underlying contact structure among individuals while disregarding the progression of time during outbreaks. So far, the only alternative that enables the integration of both aspects of disease propagation simultaneously while preserving the variety of outcomes has been to abandon the analytical approach and rely on computer simulations. We offer a new analytical framework, which incorporates both the complexity of contact network structure and the time progression of disease spread. Furthermore, we demonstrate that this framework is equally effective on finite- and "infinite"-size networks. This formalism can be equally applied to similar percolation phenomena on networks in other areas of science and technology.