Time-varying human mobility patterns with metapopulation epidemic dynamics

Abstract

h i g h l i g h t s• We propose a time-varying human mobility pattern. • The pattern does not alter the epidemic threshold.• The pattern can lower the final density of infected individuals as a whole.• We derive a critical node degree leading to the presence of a transition. a b s t r a c tIn this paper, explicitly considering the influences of an epidemic outbreak on human travel, a time-varying human mobility pattern is introduced to model the time variation of global human travel. The impacts of the pattern on epidemic dynamics in heterogeneous metapopulation networks, wherein each node represents a subpopulation with any number of individuals, are investigated by using a mean-field approach. The results show that the pattern does not alter the epidemic threshold, but can slightly lower the final average density of infected individuals as a whole. More importantly, we also find that the pattern produces different impacts on nodes with different degree, and that there exists a critical degree k c . For nodes with degree smaller than k c , the pattern produces a positive impact on epidemic mitigation; conversely, for nodes with degree larger than k c , the pattern produces a negative impact on epidemic mitigation.

Suppression of epidemic spreading in complex networks by local information based behavioral responses

“…15 For example, news obtained from the social neighborhood of an individual is local, but information from the mass media or from the public health authorities can be regarded as global. The influences of local [16][17][18][19][20] or global [21][22][23] information based behavioral responses, or awareness, on the epidemic dynamics can in general be quite different, and there is also recent work on a)…”

Epidemic spreading in metapopulation networks with heterogeneous infection rates

“…We assume statistical equivalence for subpopulations of the same degree, which has been successfully applied to many dynamical processes on complex networks [25,26,30,31]; thus it is reasonable for us to provide a same local infection rate to the same degree nodes (i.e., β i = β j if k i = k j ). We assume statistical equivalence for subpopulations of the same degree, which has been successfully applied to many dynamical processes on complex networks [25,26,30,31]; thus it is reasonable for us to provide a same local infection rate to the same degree nodes (i.e., β i = β j if k i = k j ).…”

“…(2): negative-correlation infection regime (NIR) (i.e., the case of α < 0) and positive-correlation infection regime (PIR) (i.e., the case of α > 0). In the special case of α = 0, we have a homogeneous infection rate β k = β that has been considered in the previous studies [25][26][27][28][29][30][31][32][33]. That is to say, the infection rate in nodes with higher degree is smaller than that in nodes with lower degree.…”

“…[25,30,32], we formulate the dynamical reaction rate equations for ρ I,k (t) and ρ S,k (t) at the MF level where P(k ′ /k) is the conditional probability that a node with degree k connects to another node with degree k ′ , and Γ k (t) is the reaction kernel given by [25,30,32], we formulate the dynamical reaction rate equations for ρ I,k (t) and ρ S,k (t) at the MF level where P(k ′ /k) is the conditional probability that a node with degree k connects to another node with degree k ′ , and Γ k (t) is the reaction kernel given by…”

“…Recently, the metapopulation epidemic models based on the reaction-diffusion (RD) process have been introduced to investigate epidemic spreading in a spatially structured social network [25][26][27][28][29][30]. In these models, the social network is characterized by the metapopulation network where each node represents a city (subpopulation) consisting of any number of individuals and links denote transportation routes among cities.…”