Disease-induced resource constraints can trigger explosive epidemics

TL;DR

This paper presents a mathematical model showing that resource constraints can cause epidemic outbreaks to become explosive and uncontrollable, even when the disease would otherwise die out, highlighting a critical transition in epidemic dynamics.

Contribution

It introduces a novel model linking resource limitations to epidemic spread, revealing conditions for explosive outbreaks and providing analytical expressions for critical thresholds.

Findings

Epidemics can become explosive due to resource constraints.

Critical cost thresholds determine the transition to explosive spread.

The model applies to various contagion processes beyond diseases.

Abstract

Advances in mathematical epidemiology have led to a better understanding of the risks posed by epidemic spreading and informed strategies to contain disease spread. However, a challenge that has been overlooked is that, as a disease becomes more prevalent, it can limit the availability of the capital needed to effectively treat those who have fallen ill. Here we use a simple mathematical model to gain insight into the dynamics of an epidemic when the recovery of sick individuals depends on the availability of healing resources that are generated by the healthy population. We find that epidemics spiral out of control into "explosive" spread if the cost of recovery is above a critical cost. This can occur even when the disease would die out without the resource constraint. The onset of explosive epidemics is very sudden, exhibiting a discontinuous transition under very general assumptions. We find analytical expressions for the critical cost and the size of the explosive jump in infection levels in terms of the parameters that characterize the spreading process. Our model and results apply beyond epidemics to contagion dynamics that self-induce constraints on recovery, thereby amplifying the spreading process.