WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 13, 2014
A Toxoplasmosis Spread Model between Cat and Oocyst Populations with Independent Stochastic Perturbations
Authors: ,
Abstract: A toxoplasmosis spread model between cat and oocyst populations with independent stochastic pertur- bations is proposed, the existence of global positive solution is derived. By the method of stochastic Lyapunov functions, we study their asymptotic behavior in terms of the intensity of the stochastic perturbations and the re- productive number. When the perturbations about the susceptible and infective cats are sufficiently small, as well as magnitude of the reproductive number is less than one, the infective cats, recovered cats and population oocysts decay to zero whilst the susceptible components converge to a class of explicit stationary distributions regardless of the perturbations on the recovered cats and population oocysts. When all the perturbations are small and the reproductive number is larger than one, we construct a new class of stochastic Lyapunov functions to show the positive recurrence, and our results reveal some cycling phenomena of recurrent diseases. These results mean that stochastic system has the similar property with the corresponding deterministic system when the white noise is small. Finally, numerical simulations are carried out to support our findings.
Search Articles
Pages: 790-799
WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 13, 2014, Art. #77