title: Disease-induced resource constraints can trigger explosive epidemics.
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.
authors.affiliation: ETH Zurich, Computational Physics for Engineering Materials, CH-8093 Zurich, Switzerland.
authors.forename: L
authors.initials: L
authors.lastname: Böttcher
authors.affiliation: ETH Zurich, Computational Social Science, CH-8092 Zurich, Switzerland.
authors.forename: O
authors.initials: O
authors.lastname: Woolley-Meza
authors.affiliation: ETH Zurich, Computational Physics for Engineering Materials, CH-8093 Zurich, Switzerland.|Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, P-1749-016 Lisboa, Portugal.|Centro de Física Teórica e Computacional, Universidade de Lisboa, P-1649-003 Lisboa, Portugal.
authors.forename: N A M
authors.initials: NA
authors.lastname: Araújo
authors.affiliation: ETH Zurich, Computational Physics for Engineering Materials, CH-8093 Zurich, Switzerland.|Departamento de Física, Universidade Federal do Ceará, 60451-970 Fortaleza, Ceará, Brazil.
authors.forename: H J
authors.initials: HJ
authors.lastname: Herrmann
authors.affiliation: ETH Zurich, Computational Social Science, CH-8092 Zurich, Switzerland.
authors.forename: D
authors.initials: D
authors.lastname: Helbing
mesh_terms: D003140:Communicable Disease Control; D003141:Communicable Diseases / Q000191:economics / Q000453:epidemiology; D058872:Epidemics / Q000191:economics / Q000517:prevention & control / Q000706:statistics & numerical data*; D017048:Health Care Costs; D006801:Humans; D015233:Models, Statistical