Abstract
In this paper, we construct a microscopic mechanism for the epidemic processes in heterogeneous populations, which contains two basic assumptions: all edges of the network are broken and reconnected at every time step among the epidemic process; the probability of randomly chosen two half-edges to make a pair is identical. We define the stochastic epidemic process and get the epidemic distributions numerically according to the transmission probability λ. Two different phases are observed, which means the onset of phase transition, and the threshold value is very small. Under the thermodynamic limit, the process can be approximated by a deterministic dynamical system. About this deterministic system, we get the analytical threshold value, which is consistent with the numerical results of the epidemic distributions.
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Wang, JZ., Qian, M. Discrete Stochastic Modeling for Epidemics in Networks. J Stat Phys 140, 1157–1166 (2010). https://doi.org/10.1007/s10955-010-0034-5
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DOI: https://doi.org/10.1007/s10955-010-0034-5