Mitigating the outbreak of an infectious disease over its life cycle: A diffusion-based approach

Abstract

We first qualitatively divide the cycle of an infectious disease outbreak into five distinct stages by following the adoption categorization from the diffusion theory. Next, we apply a standard mechanistic model, the susceptible-infected-recovered model, to simulate a variety of transmission scenarios and to quantify the benefits of various countermeasures. In particular, we apply the specific values of the newly infected to quantitatively divide an outbreak cycle into stages. We therefore reveal diverging patterns of countermeasures in different stages. The stage is critical in determining the evolutionary characteristics of the diffusion process. Our results show that it is necessary to employ appropriate diverse strategies in different stages over the life cycle of an infectious disease outbreak. In the early stages, we need to focus on prevention, early detection, and strict countermeasure (e.g., isolation and lockdown) for controlling an epidemic. It is better safe (i.e., stricter countermeasures) than sorry (i.e., let the virus spread out). There are two reasons why we should implement responsive and strict countermeasures in the early stages. The countermeasures are very effective, and the earlier the more total infected reduction over the whole cycle. The economic and societal burden for implementing countermeasures is relatively small due to limited affected areas, and the earlier the less burden. Both reasons change to the opposite in the late stages. The strategic focuses in the late stages become more delicate and balanced for two reasons: the same countermeasures become much less effective, and the society bears a much heavier burden. Strict countermeasures may become unnecessary, and we need to think about how to live with the infectious disease.