Transmission Dynamics of a High Dimensional Rabies Epidemic Model in a Markovian Random Environment.

This paper develops the spread dynamics of a 11-dimensional stochastic multi-host zoonotic model for the dog-CFB-human transmission of rabies, which is formulated as a piecewise deterministic Markov process. We firstly prove the existence of the global unique positive solution. Then we obtain sufficient conditions for the extinction and persistence of disease. One of the distinct features of this paper is that we prove the positive recurrence of the solution to the model by constructing a series of appropriate Lyapunov functions. Finally, numerical simulations are carried out to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]