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- W2466704842 abstract "We consider a contact system that describes the behavior of a process which has been used to model the spread of a disease or a biological population. The collection of individuals that may be infected at any given time is taken to be the set of vertices of a connected, undirected graph S. For such a graph, the degree of a vertex x is the number of vertices y that are connected to x by an edge. In the present paper, we consider the contact model on the dimensional integer lattice {0,1}Zd (in which the degree of each vertex is 2d). In d-dimensional space, one point is stood by one individual. The virus infects one proximate individual at a rate equal to λ, where λ is an intensity of the contact model. And the individual infected recovers at rate one. Speaking concretely, contact model is a continuous time Markov process ηs in the configuration {0,1}Zd. At some random time, one individual at the point x is deemed to be infected when ηs(x) = 1 and the infected individual recovers at rate one; if ηs(x) = 0, the individual at the point x is healthy and will be infected at a rate equal to λ times the number of the infected neighbors. In this paper, applying the theory of the contact system, one kind of spread of infection model (which defined from the contact model) is analyzed and estimated by the theory of stochastic analysis. Further, we show the asymptotic behavior of probability distributions which describe the fluctuations for the spread of infection." @default.
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- W2466704842 date "2009-05-20" @default.
- W2466704842 modified "2023-09-24" @default.
- W2466704842 title "The statistical behavior of the spread of infection by the contact systems" @default.
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