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The epidemic such as the bird flue is still a menace to mankind. Especially, rabies is a viral zoonotic disease that causes acute encephalitis in mammals: more than 50000 people a year have died from rabies. Analyses of the geographic spread of such epidemics are essential to control the infectious diseases. In this paper, noting that the infection rate of rabies contains the random fluctuations caused by the change of the environmental situation and considering the threshold from the biological reason, the stochastic model of rabies spreading with the infection rate of a saturation type is proposed. Using the proposed stochastic model, behaviors of rabies spreading and its spreading speed are studied by numerical simulations. The influence of the random fluctuations in the infection rate and the threshold on the rabies spreading is also analyzed.

Stochastic Modeling of Epidemic Spreading under Random Fluctuations and Simulation Analyses of Traveling Waves