The spread of infectious disease on complex networks with household-structure

Abstract

In this paper we study the household-structure SIS epidemic spreading on general complex networks. The household structure gives us the way to distinguish inner and the outer infection rate. Unlike household-structure models on homogenous networks, such as regular and random networks, here we consider heterogeneous networks with arbitrary degree distribution p(k). First we introduce the epidemic model. Then rate equations under mean field appropriation and computer simulations are used here to analyze our model. Some unique phenomena only existing in divergent network with household structure is found, while we also get some similar conclusions that some simple geometrical quantities of networks have important impression on infection property of infectous disease. It seems that in our model even when local cure rate is greater than inner infection rate in every household, disease still can spread on scale-free network. It implies that no disease is spreading in every single household, but for the whole network, disease is spreading. Since our society network seems like this structure, maybe this conclusion remind us that during disease spreading we should pay more attention on network structure than local cure condition.

Multi-state epidemic processes on complex networks

“…I. In many models, diverging second moments of the degree distribution extinguishes the epidemic thresholds, as reported previously for the percolation [2,9,10,33], the contact process [16,36,37], the SIR model [4,29,30,32], the SIRS model [25], and the household moodel [26]. On scale-free networks, which underly sexually transmitted diseases and computer viruses (see Sec.…”

“…1(C) [25]. They also studied the household model, in which each vertex has a graded state corresponding to the number of patients in a household [26]. They showed that the epidemic thresholds are proportional to k / k 2 also in these models.…”

Epidemic outbreaks in growing scale-free networks with local structure

“…But this network has been found to be disassortative mixing, which is a typical characteristic of nonsocial networks. Another shortcoming of most previous generative models is that they do not consider the local structures, especially the household structure, which has been found to be an important constituent for social contact networks, and has critical impact on the epidemic spreading process [18][19][20][21][22].…”

How demography-driven evolving networks impact epidemic transmission between communities

“…There are some network models that consider with demographics. For instance, Liu et al (2004) introduced an epidemic model with birth and death in networks, however, they also assumed that the size of the network was constant, and each site on the network was occupied by at most one individual and was otherwise empty. Jin et al (2014) initially proposed an epidemic model on networks with demographics and conducted various dynamic analyzes based on this model.…”