Global analysis of a vector-host epidemic model in stochastic environments

In this paper, a vector-host epidemic model is formulated from a classical deterministic framework to a stochastic differential equation. The model incorporates the potential impact of the free pathogens as well as the random environment on disease dynamics. The dynamics of the vector-host epidemic model is analyzed for the deterministic and stochastic cases, respectively. In the deterministic case, the global dynamics of the system is determined by the criteria R-0, i.e., if R-0 <= 1 the disease-free equilibrium is globally asymptotically stable; if R-0 > 1 the unique endemic equilibrium is globally asymptotically stable. In the stochastic case, the stochastic system admits a unique ergodic stationary distribution if (R) over tilde (0 )> 1, which indicates that the disease can be persistent in vivo. Finally, numerical simulations are conducted to verify these analytical results. (C) 2019 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.