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Disease-induced resource constraints can trigger explosive epidemics.

Böttcher L, Woolley-Meza O, Araújo NA, Herrmann HJ, Helbing D - Sci Rep (2015)

Bottom Line: 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.

View Article: PubMed Central - PubMed

Affiliation: ETH Zurich, Computational Physics for Engineering Materials, CH-8093 Zurich, Switzerland.

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.

No MeSH data available.


Related in: MedlinePlus

The explosive epidemic transition to a high epidemic state occurs generically in the bSIS model.(a) The phase space of Eq. (8) and the corresponding stationary states. In this plot the parameters are the same as in Fig. 5b,d. The black dots indicate the stationary states of Eq. (9) and the arrows illustrate the stability of i(∞)+. In general one can rewrite Eq. (8) to get an equation of a parabola. The equilibrium infection level without the budget restriction is denoted , and it is always the case that . (b) The general behavior of the bSIS system can be illustrated by a phase diagram of the different regimes depending on healing costs and basic reproduction number. Three different regimes are found: the healthy regime with a zero fraction of infected individuals (i(∞) = 0); the low epidemic regime; and the higher infection high epidemic regime. As discussed in the text, transitions between the healthy and low epidemic regimes are always continuous, while transitions to the high epidemic regime are discontinuous.
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f6: The explosive epidemic transition to a high epidemic state occurs generically in the bSIS model.(a) The phase space of Eq. (8) and the corresponding stationary states. In this plot the parameters are the same as in Fig. 5b,d. The black dots indicate the stationary states of Eq. (9) and the arrows illustrate the stability of i(∞)+. In general one can rewrite Eq. (8) to get an equation of a parabola. The equilibrium infection level without the budget restriction is denoted , and it is always the case that . (b) The general behavior of the bSIS system can be illustrated by a phase diagram of the different regimes depending on healing costs and basic reproduction number. Three different regimes are found: the healthy regime with a zero fraction of infected individuals (i(∞) = 0); the low epidemic regime; and the higher infection high epidemic regime. As discussed in the text, transitions between the healthy and low epidemic regimes are always continuous, while transitions to the high epidemic regime are discontinuous.

Mentions: (In the Supplementary Information we present a more detailed characterization of the critical cost c* that guarantees convergence to the higher infection fixed point.) Furthermore, it is in fact the case that i(∞)+ is stable while i(∞)− is unstable. To characterize the stability we note that Eq. (8) can in general be written as the expression of a parabola with a maximum at [i(∞)+ + i(∞)−]/2, as shown in the phase plot in Fig. 6a.


Disease-induced resource constraints can trigger explosive epidemics.

Böttcher L, Woolley-Meza O, Araújo NA, Herrmann HJ, Helbing D - Sci Rep (2015)

The explosive epidemic transition to a high epidemic state occurs generically in the bSIS model.(a) The phase space of Eq. (8) and the corresponding stationary states. In this plot the parameters are the same as in Fig. 5b,d. The black dots indicate the stationary states of Eq. (9) and the arrows illustrate the stability of i(∞)+. In general one can rewrite Eq. (8) to get an equation of a parabola. The equilibrium infection level without the budget restriction is denoted , and it is always the case that . (b) The general behavior of the bSIS system can be illustrated by a phase diagram of the different regimes depending on healing costs and basic reproduction number. Three different regimes are found: the healthy regime with a zero fraction of infected individuals (i(∞) = 0); the low epidemic regime; and the higher infection high epidemic regime. As discussed in the text, transitions between the healthy and low epidemic regimes are always continuous, while transitions to the high epidemic regime are discontinuous.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4644972&req=5

f6: The explosive epidemic transition to a high epidemic state occurs generically in the bSIS model.(a) The phase space of Eq. (8) and the corresponding stationary states. In this plot the parameters are the same as in Fig. 5b,d. The black dots indicate the stationary states of Eq. (9) and the arrows illustrate the stability of i(∞)+. In general one can rewrite Eq. (8) to get an equation of a parabola. The equilibrium infection level without the budget restriction is denoted , and it is always the case that . (b) The general behavior of the bSIS system can be illustrated by a phase diagram of the different regimes depending on healing costs and basic reproduction number. Three different regimes are found: the healthy regime with a zero fraction of infected individuals (i(∞) = 0); the low epidemic regime; and the higher infection high epidemic regime. As discussed in the text, transitions between the healthy and low epidemic regimes are always continuous, while transitions to the high epidemic regime are discontinuous.
Mentions: (In the Supplementary Information we present a more detailed characterization of the critical cost c* that guarantees convergence to the higher infection fixed point.) Furthermore, it is in fact the case that i(∞)+ is stable while i(∞)− is unstable. To characterize the stability we note that Eq. (8) can in general be written as the expression of a parabola with a maximum at [i(∞)+ + i(∞)−]/2, as shown in the phase plot in Fig. 6a.

Bottom Line: 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.

View Article: PubMed Central - PubMed

Affiliation: ETH Zurich, Computational Physics for Engineering Materials, CH-8093 Zurich, Switzerland.

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.

No MeSH data available.


Related in: MedlinePlus