Nontrivial periodic solution for a stochastic brucellosis model with application to Xinjiang, China

Brucellosis is a kind of zoonotic disease caused by Gram-negative bacteria of the genus Brucella. In this paper, we propose a stochastic periodic brucellosis model by introducing the effect of environmental white noise on transmission dynamics of brucellosis. By Has'minskii theory of periodic solution and constructing a novel combination of Lyapunov functions, we establish the existence of nontrivial positive periodic solution if the condition R₀ ^S>1 holds. Based on the reported data of newly acute human brucellosis cases for each season from 2010 to 2014 in Xinjiang, numerical simulations have been performed to support our result and indicate that brucellosis in Xinjiang takes on the feature of long-term prevalence and cyclical fluctuation.