Host vector dynamics of a nonlinear pine wilt disease model in deterministic and stochastic environments.

• A vector-host transmission model with general incidence rates in deterministic and stochastic environments is developed. • For the deterministic model, the equilibrium points and their local asymptotic stability are obtained. • Sufficient conditions for the existence of ergodic stationary distribution and extinction of stochastic system are obtained. • The exact expression of the density function around a quasi-equilibrium is derived. • Numerical results are carried out to illustrate the theoretical results. In this study, we develop a vector-host transmission model with general incidence rates for the dynamics of pine wilt disease in deterministic and stochastic environments. The existence and local asymptotic stability of equilibria are investigated in the deterministic case. We show the required conditions for the ergodic stationary distribution and extinction of the model in the stochastic case by constructing appropriate Lyapunov functions. Furthermore, by solving the corresponding Fokker-Planck equation, we obtain exact expressions of probability density function around the quasi-equilibrium of the stochastic model. Finally, we employ comprehensive numerical simulations to support our results and compare deterministic and stochastic situations. [ABSTRACT FROM AUTHOR]