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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

Network heterogeneity in the adapted state, indicated by the degree ratio kb/ka.The dependence of the degree ratio in agent-based simulations (black circles) closely follows the prediction from integration of the ODE model (solid red line), a very good approximation is also provided by the relationship  (blue dashed line), whereas the naive expectation kb/ka = ψa/ψb (pink dotted line) overestimates the network heterogeneity significantly. Contrary to expectations the networks following the naive solution (the most heterogeneous case), would be maximally stable against disease invasion. Parameters: ψb = 0.05, ω = 0.2, μ = 0.002, N = 105, K = 106. Inset: the magnification of the superimposed part of the main figure.
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f3: Network heterogeneity in the adapted state, indicated by the degree ratio kb/ka.The dependence of the degree ratio in agent-based simulations (black circles) closely follows the prediction from integration of the ODE model (solid red line), a very good approximation is also provided by the relationship (blue dashed line), whereas the naive expectation kb/ka = ψa/ψb (pink dotted line) overestimates the network heterogeneity significantly. Contrary to expectations the networks following the naive solution (the most heterogeneous case), would be maximally stable against disease invasion. Parameters: ψb = 0.05, ω = 0.2, μ = 0.002, N = 105, K = 106. Inset: the magnification of the superimposed part of the main figure.

Mentions: The numerical value of the degree ration kb/ka is shown in Fig. 3. To gain also an analytical understanding we resort to a description of the system that is coarser-grained than the full moment expansion. First, note that, on a population level ki, the mean degree of nodes of type i ∈ {a, b}, obeys a differential equation of the form


Large epidemic thresholds emerge in heterogeneous networks of heterogeneous nodes.

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

Network heterogeneity in the adapted state, indicated by the degree ratio kb/ka.The dependence of the degree ratio in agent-based simulations (black circles) closely follows the prediction from integration of the ODE model (solid red line), a very good approximation is also provided by the relationship  (blue dashed line), whereas the naive expectation kb/ka = ψa/ψb (pink dotted line) overestimates the network heterogeneity significantly. Contrary to expectations the networks following the naive solution (the most heterogeneous case), would be maximally stable against disease invasion. Parameters: ψb = 0.05, ω = 0.2, μ = 0.002, N = 105, K = 106. Inset: the magnification of the superimposed part of the main figure.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f3: Network heterogeneity in the adapted state, indicated by the degree ratio kb/ka.The dependence of the degree ratio in agent-based simulations (black circles) closely follows the prediction from integration of the ODE model (solid red line), a very good approximation is also provided by the relationship (blue dashed line), whereas the naive expectation kb/ka = ψa/ψb (pink dotted line) overestimates the network heterogeneity significantly. Contrary to expectations the networks following the naive solution (the most heterogeneous case), would be maximally stable against disease invasion. Parameters: ψb = 0.05, ω = 0.2, μ = 0.002, N = 105, K = 106. Inset: the magnification of the superimposed part of the main figure.
Mentions: The numerical value of the degree ration kb/ka is shown in Fig. 3. To gain also an analytical understanding we resort to a description of the system that is coarser-grained than the full moment expansion. First, note that, on a population level ki, the mean degree of nodes of type i ∈ {a, b}, obeys a differential equation of the form

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