Disease-Induced Resource Constraints Can Trigger Explosive Epidemics

24 Pages Posted: 16 Sep 2014 Last revised: 9 May 2015

See all articles by Lucas Böttcher

Lucas Böttcher

ETH Zürich

Olivia Woolley-Meza

ETH Zürich

Nuno A.M. Araujo

ETH Zürich

Hans J. Herrmann

ETH Zürich

Dirk Helbing

ETH Zürich - Department of Humanities, Social and Political Sciences (GESS)

Date Written: August 6, 2014

Abstract

Advances in mathematical epidemiology and network science have led to a better understanding of the risks posed by epidemic spreading and informed strategies to contain disease spread through prevention and treatment. 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 an epidemic would not be predicted by a standard model that does not consider the reduction in resource generation as individuals fall ill. Through simulations and analytical solutions we show that the onset of explosive epidemics is very sudden, exhibiting a discontinuous transition under very general assumptions. We also determine analytically 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 other contagion dynamics that self-induce constraints on recovery, thereby amplifying the spreading process.

Keywords: epidemics, networks, resource constraints

JEL Classification: I10

Suggested Citation

Böttcher, Lucas and Woolley-Meza, Olivia and Araujo, Nuno A.M. and Herrmann, Hans J. and Helbing, Dirk, Disease-Induced Resource Constraints Can Trigger Explosive Epidemics (August 6, 2014). Available at SSRN: https://ssrn.com/abstract=2496128 or http://dx.doi.org/10.2139/ssrn.2496128

Lucas Böttcher

ETH Zürich ( email )

Wolfgang-Pauli-Strasse 27
Zürich, 8093
Switzerland

Olivia Woolley-Meza (Contact Author)

ETH Zürich ( email )

Zürichbergstrasse 18
8092 Zurich, CH-1015
Switzerland

Nuno A.M. Araujo

ETH Zürich ( email )

Zürichbergstrasse 18
8092 Zurich, CH-1015
Switzerland

Hans J. Herrmann

ETH Zürich ( email )

Zürichbergstrasse 18
8092 Zurich, CH-1015
Switzerland

Dirk Helbing

ETH Zürich - Department of Humanities, Social and Political Sciences (GESS) ( email )

ETH Zurich - Swiss Federal Institute of Technology
Clausiusstrasse 50
Zurich, 8092
Switzerland

HOME PAGE: http://www.coss.ethz.ch

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