Limits...
Large epidemic thresholds emerge in heterogeneous networks of heterogeneous nodes.

Yang H, Tang M, Gross T - Sci Rep (2015)

Bottom Line: One of the famous results of network science states that networks with heterogeneous connectivity are more susceptible to epidemic spreading than their more homogeneous counterparts.We show that the resilience of networks with heterogeneous connectivity can surpass those of networks with homogeneous connectivity.For epidemiology, this implies that network heterogeneity should not be studied in isolation, it is instead the heterogeneity of infection risk that determines the likelihood of outbreaks.

View Article: PubMed Central - PubMed

Affiliation: Web Sciences Center, University of Electronic Science and Technology of China, Chengdu 610054, China.

ABSTRACT
One of the famous results of network science states that networks with heterogeneous connectivity are more susceptible to epidemic spreading than their more homogeneous counterparts. In particular, in networks of identical nodes it has been shown that network heterogeneity, i.e. a broad degree distribution, can lower the epidemic threshold at which epidemics can invade the system. Network heterogeneity can thus allow diseases with lower transmission probabilities to persist and spread. However, it has been pointed out that networks in which the properties of nodes are intrinsically heterogeneous can be very resilient to disease spreading. Heterogeneity in structure can enhance or diminish the resilience of networks with heterogeneous nodes, depending on the correlations between the topological and intrinsic properties. Here, we consider a plausible scenario where people have intrinsic differences in susceptibility and adapt their social network structure to the presence of the disease. We show that the resilience of networks with heterogeneous connectivity can surpass those of networks with homogeneous connectivity. For epidemiology, this implies that network heterogeneity should not be studied in isolation, it is instead the heterogeneity of infection risk that determines the likelihood of outbreaks.

No MeSH data available.


Related in: MedlinePlus

Bifurcation diagram of the adaptive heterogeneous SIS model.Show is the stationary level of disease prevalence I* as a function of infectivity β. When the infectivitiy is decreased the endemic state vanishes in a saddle node bifurcation (‘Persistence threshold’). The disease free state can be invaded by the epidemic, if the infectivity surpasses a point where a transcritical bifurcation occurs (‘Invasion threshold’). Agent-based simulation (circles) and equation-based continuation (lines) provide consistent results on the persistence threshold, but predict different invasion thresholds. This discrepancy appears due to a projection effect, because the state where the disease is extinct is not uniquely defined (see text). In addition to stable solution branches (solid) the continuation also reveals an unstable solution branch (dotted). Parameters: ψa = 0.65, ψb = 0.05, pa = 0.75, ω = 0.2, μ = 0.002, N = 105, K = 106.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4543971&req=5

f1: Bifurcation diagram of the adaptive heterogeneous SIS model.Show is the stationary level of disease prevalence I* as a function of infectivity β. When the infectivitiy is decreased the endemic state vanishes in a saddle node bifurcation (‘Persistence threshold’). The disease free state can be invaded by the epidemic, if the infectivity surpasses a point where a transcritical bifurcation occurs (‘Invasion threshold’). Agent-based simulation (circles) and equation-based continuation (lines) provide consistent results on the persistence threshold, but predict different invasion thresholds. This discrepancy appears due to a projection effect, because the state where the disease is extinct is not uniquely defined (see text). In addition to stable solution branches (solid) the continuation also reveals an unstable solution branch (dotted). Parameters: ψa = 0.65, ψb = 0.05, pa = 0.75, ω = 0.2, μ = 0.002, N = 105, K = 106.

Mentions: To gain some basic intuition, let us first investigate the system by explicit agent-based simulation of the network model49. For this purpose we evolve the system in time, according to the stochastic rules, until a stationary level of epidemic prevalence is approached. Repeating this procedure for different values of infectivity β reveals the diagram shown in Fig. 1. The Figure is qualitatively similar to results from the homogeneous adaptive SIS model: Epidemics starting from a small proportion of initially infected agents go extinct deterministically if the infectivity is below a certain threshold, βinv, which we identify as the invasion threshold. By contrast, established epidemics, i.e. simulation runs starting with a higher initial proportion of infected, can persist if the infectivity surpasses a different persistence threshold βper.


Large epidemic thresholds emerge in heterogeneous networks of heterogeneous nodes.

Yang H, Tang M, Gross T - Sci Rep (2015)

Bifurcation diagram of the adaptive heterogeneous SIS model.Show is the stationary level of disease prevalence I* as a function of infectivity β. When the infectivitiy is decreased the endemic state vanishes in a saddle node bifurcation (‘Persistence threshold’). The disease free state can be invaded by the epidemic, if the infectivity surpasses a point where a transcritical bifurcation occurs (‘Invasion threshold’). Agent-based simulation (circles) and equation-based continuation (lines) provide consistent results on the persistence threshold, but predict different invasion thresholds. This discrepancy appears due to a projection effect, because the state where the disease is extinct is not uniquely defined (see text). In addition to stable solution branches (solid) the continuation also reveals an unstable solution branch (dotted). Parameters: ψa = 0.65, ψb = 0.05, pa = 0.75, ω = 0.2, μ = 0.002, N = 105, K = 106.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4543971&req=5

f1: Bifurcation diagram of the adaptive heterogeneous SIS model.Show is the stationary level of disease prevalence I* as a function of infectivity β. When the infectivitiy is decreased the endemic state vanishes in a saddle node bifurcation (‘Persistence threshold’). The disease free state can be invaded by the epidemic, if the infectivity surpasses a point where a transcritical bifurcation occurs (‘Invasion threshold’). Agent-based simulation (circles) and equation-based continuation (lines) provide consistent results on the persistence threshold, but predict different invasion thresholds. This discrepancy appears due to a projection effect, because the state where the disease is extinct is not uniquely defined (see text). In addition to stable solution branches (solid) the continuation also reveals an unstable solution branch (dotted). Parameters: ψa = 0.65, ψb = 0.05, pa = 0.75, ω = 0.2, μ = 0.002, N = 105, K = 106.
Mentions: To gain some basic intuition, let us first investigate the system by explicit agent-based simulation of the network model49. For this purpose we evolve the system in time, according to the stochastic rules, until a stationary level of epidemic prevalence is approached. Repeating this procedure for different values of infectivity β reveals the diagram shown in Fig. 1. The Figure is qualitatively similar to results from the homogeneous adaptive SIS model: Epidemics starting from a small proportion of initially infected agents go extinct deterministically if the infectivity is below a certain threshold, βinv, which we identify as the invasion threshold. By contrast, established epidemics, i.e. simulation runs starting with a higher initial proportion of infected, can persist if the infectivity surpasses a different persistence threshold βper.

Bottom Line: One of the famous results of network science states that networks with heterogeneous connectivity are more susceptible to epidemic spreading than their more homogeneous counterparts.We show that the resilience of networks with heterogeneous connectivity can surpass those of networks with homogeneous connectivity.For epidemiology, this implies that network heterogeneity should not be studied in isolation, it is instead the heterogeneity of infection risk that determines the likelihood of outbreaks.

View Article: PubMed Central - PubMed

Affiliation: Web Sciences Center, University of Electronic Science and Technology of China, Chengdu 610054, China.

ABSTRACT
One of the famous results of network science states that networks with heterogeneous connectivity are more susceptible to epidemic spreading than their more homogeneous counterparts. In particular, in networks of identical nodes it has been shown that network heterogeneity, i.e. a broad degree distribution, can lower the epidemic threshold at which epidemics can invade the system. Network heterogeneity can thus allow diseases with lower transmission probabilities to persist and spread. However, it has been pointed out that networks in which the properties of nodes are intrinsically heterogeneous can be very resilient to disease spreading. Heterogeneity in structure can enhance or diminish the resilience of networks with heterogeneous nodes, depending on the correlations between the topological and intrinsic properties. Here, we consider a plausible scenario where people have intrinsic differences in susceptibility and adapt their social network structure to the presence of the disease. We show that the resilience of networks with heterogeneous connectivity can surpass those of networks with homogeneous connectivity. For epidemiology, this implies that network heterogeneity should not be studied in isolation, it is instead the heterogeneity of infection risk that determines the likelihood of outbreaks.

No MeSH data available.


Related in: MedlinePlus