Study Of Epidemic Dynamics On Coupled Networks

Infectious diseases can not only harm human beings, but also bring disaster to communities, countries and even the whole world, so it is significant to study the mechanism of epidemic transmission and corresponding preventive measures. The rise of complex networks injects new vitality into dynamics of infectious diseases. Many real-world networks interact with and depend on each other, so we have to take into account the interaction among networks instead of only single network, when we study the epidemic spreading on these networks. Coupled networks can reflect such kind of interaction among networks. In this paper, we study the epidemic dynamics on several new types of coupled networks. The main research results are as follows:Firstly, we consider the epidemic dynamics on one-way-coupled networks with two subnetworks. Many zoonotic diseases have the characteristic that animals can infect human beings but not the reverse. In response to this characteristic, we propose a new type of coupled network—one-way-coupled network. By proposing a mathematical model through mean-field approximation approach, we prove the global stability of the disease-free and endemic equilibria of this model. Through next-generation matrix approach, we obtain the accurate expression of the basic reproduction number R0. We find the basic reproduction number R0 of the whole network is the maximum of the basic reproduction numbers of the two subnetworks, and R0 is independent of the cross-infection rate and cross contact pattern. This shows the cross-infection rate between subnetworks does not has any effect on the transmission threshold. This is a very meaningful conclusion because previous studies on coupled network have indicated that the transmission threshold is relevant to all infection rates. Through numerical analysis, we also find: R0 increases rapidly with the growth of inner infection rate if the inner contact pattern is scale-free; in order to eradicate zoonotic diseases from human beings, we must simultaneously eradicate them from animals; bird-to-bird infection rate has bigger impact on the human's average infected density than bird-to-human infection rate. This conclusion contradicts people's intuition that bird-to-human infection rate has bigger impact on the human beings.Secondly, we study the epidemic dynamics on tripartite networks. Many vector-borne diseases spread among three populations(human beings, vectors and animals). In response to such diseases, we propose tripartite networks. Through theoretical analysis,we find the basic reproduction number of tripartite networks is not only relevant to the ratio?k2??k?, but also to the average degree ?k?. There are substantial distinction between this result and previous results that the basic reproduction number of bipartite networks is only relevant to the ratio?k2??k?. This illustrates that the diseases on the tripartite networks are more easy to propagate than that on the bipartite networks. Through numerical analysis,we also find: under the same contact patterns, four infection rates have the same effect on the basic reproduction number; the diseases exist or disappear on three subnetworks at the same time.Finally, we study the epidemic dynamics on two typical three-layer interdependent networks including string-coupled networks and circular-coupled networks. Three-layer interdependent networks can manifest the disease transmission of three communities.Researches show that: the increase of each inner infection rate affects effectively only on its own subnetwork and neighbors; in a string-coupled network, the middle subnetwork has bigger impact on the basic reproduction number than the end subnetworks with the growth of network size or infection rates; the basic reproduction number on a circular-coupled network is larger than that on a string-coupled network with the growth of network size; but the basic reproduction number and the average infection densities are almost the same on both string-coupled and circular-coupled networks with the increasing of infection rate.