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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

Epidemics self-accelerate when resources are endogenously constrained.(a) The school friendship network, which exhibits long-range connections, clustering and community structure (colors denote communities found through modularity maximization). (b) Evolution of the fraction of infected individuals i(t) (red circles) and the budget b(t) (blue crosses), for healing costs above the critical cost (c = 2 > c* ≈ 0.833), on the friendship network. Recovery requires a budget: q0 = 0 and qb = 0.8, and p = 0.285. In the pure SIS model the fraction of infected individuals reaches a stationary regime. The bSIS model also initially converges to the same stationary regime until the budget is exhausted at a critical time t = t* ≈ 7.3. For t > t* recovery is not possible anymore, and the infection spreads to all of the population (i.e. i(∞) = 1). The difference in the steady state infection in both models, which is also the size of the jump in the bSIS model due to the budget constraints, is denoted Δi∞.
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f2: Epidemics self-accelerate when resources are endogenously constrained.(a) The school friendship network, which exhibits long-range connections, clustering and community structure (colors denote communities found through modularity maximization). (b) Evolution of the fraction of infected individuals i(t) (red circles) and the budget b(t) (blue crosses), for healing costs above the critical cost (c = 2 > c* ≈ 0.833), on the friendship network. Recovery requires a budget: q0 = 0 and qb = 0.8, and p = 0.285. In the pure SIS model the fraction of infected individuals reaches a stationary regime. The bSIS model also initially converges to the same stationary regime until the budget is exhausted at a critical time t = t* ≈ 7.3. For t > t* recovery is not possible anymore, and the infection spreads to all of the population (i.e. i(∞) = 1). The difference in the steady state infection in both models, which is also the size of the jump in the bSIS model due to the budget constraints, is denoted Δi∞.

Mentions: In real systems disease transmission occurs through non-random interactions, in contrast to the assumptions of the mean-field approximation. The interactions can be modeled as networks generated through the interplay between multiple social mechanisms3334. These generating mechanisms together lead to complex structural features that are not generically found in random networks, most importantly: high clustering coefficients35, community structure3637, and the small-world property33. Because the dynamics of disease spread can be highly sensitive to the interaction structure, we study the limited resource case on a real social network alongside the mean-field approximation. Specifically, we consider a school friendship network shown in Fig. 2a, which exhibits the features characteristic of real social networks: clustering, community structure and the small-world property. This network was constructed based on the answers of school students in the United States to an Add-Health questionnaire38. From the full set of networks obtained from this data set, we consider the largest connected component, which consists of 2539 nodes and 20910 edges. (See Supplementary Information for a more detailed characterization of the network.) We will show that, surprisingly, the simple mean-field approximation captures the behavior on this more realistic interaction structure.


Disease-induced resource constraints can trigger explosive epidemics.

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

Epidemics self-accelerate when resources are endogenously constrained.(a) The school friendship network, which exhibits long-range connections, clustering and community structure (colors denote communities found through modularity maximization). (b) Evolution of the fraction of infected individuals i(t) (red circles) and the budget b(t) (blue crosses), for healing costs above the critical cost (c = 2 > c* ≈ 0.833), on the friendship network. Recovery requires a budget: q0 = 0 and qb = 0.8, and p = 0.285. In the pure SIS model the fraction of infected individuals reaches a stationary regime. The bSIS model also initially converges to the same stationary regime until the budget is exhausted at a critical time t = t* ≈ 7.3. For t > t* recovery is not possible anymore, and the infection spreads to all of the population (i.e. i(∞) = 1). The difference in the steady state infection in both models, which is also the size of the jump in the bSIS model due to the budget constraints, is denoted Δi∞.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f2: Epidemics self-accelerate when resources are endogenously constrained.(a) The school friendship network, which exhibits long-range connections, clustering and community structure (colors denote communities found through modularity maximization). (b) Evolution of the fraction of infected individuals i(t) (red circles) and the budget b(t) (blue crosses), for healing costs above the critical cost (c = 2 > c* ≈ 0.833), on the friendship network. Recovery requires a budget: q0 = 0 and qb = 0.8, and p = 0.285. In the pure SIS model the fraction of infected individuals reaches a stationary regime. The bSIS model also initially converges to the same stationary regime until the budget is exhausted at a critical time t = t* ≈ 7.3. For t > t* recovery is not possible anymore, and the infection spreads to all of the population (i.e. i(∞) = 1). The difference in the steady state infection in both models, which is also the size of the jump in the bSIS model due to the budget constraints, is denoted Δi∞.
Mentions: In real systems disease transmission occurs through non-random interactions, in contrast to the assumptions of the mean-field approximation. The interactions can be modeled as networks generated through the interplay between multiple social mechanisms3334. These generating mechanisms together lead to complex structural features that are not generically found in random networks, most importantly: high clustering coefficients35, community structure3637, and the small-world property33. Because the dynamics of disease spread can be highly sensitive to the interaction structure, we study the limited resource case on a real social network alongside the mean-field approximation. Specifically, we consider a school friendship network shown in Fig. 2a, which exhibits the features characteristic of real social networks: clustering, community structure and the small-world property. This network was constructed based on the answers of school students in the United States to an Add-Health questionnaire38. From the full set of networks obtained from this data set, we consider the largest connected component, which consists of 2539 nodes and 20910 edges. (See Supplementary Information for a more detailed characterization of the network.) We will show that, surprisingly, the simple mean-field approximation captures the behavior on this more realistic interaction structure.

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