The spread of infectious diseases from a physics perspective

Abstract

Abstract This article deals with the spread of infectious diseases from a physics perspective. It considers a population as a network of nodes representing the population members, linked by network edges representing the (social) contacts of the individual population members. Infections spread along these edges from one node (member) to another. This article presents a novel, modified version of the SIR compartmental model, able to account for typical network effects and percolation phenomena. The model is successfully tested against the results of simulations based on Monte-Carlo methods. Expressions for the (basic) reproduction numbers in terms of the model parameters are presented, and justify some mild criticisms on the widely spread interpretation of reproduction numbers as being the number of secondary infections due to a single active infection. Throughout the article, special emphasis is laid on understanding, and on the interpretation of phenomena in terms of concepts borrowed from condensed-matter and statistical physics, which reveals some interesting analogies. Percolation effects are of particular interest in this respect and they are the subject of a detailed investigation. The concept of herd immunity (its definition and nature) is intensively dealt with as well, also in the context of large-scale vaccination campaigns and waning immunity. This article elucidates how the onset of herd-immunity can be considered as a second-order phase transition in which percolation effects play a crucial role, thus corroborating, in a more pictorial/intuitive way, earlier viewpoints on this matter. An exact criterium for the most relevant form of herd-immunity to occur can be derived in terms of the model parameters. The analyses presented in this article provide insight in how various measures to prevent an epidemic spread of an infection work, how they can be optimized and what potentially deceptive issues have to be considered when such measures are either implemented or scaled down.