Host vector dynamics of a nonlinear pine wilt disease model in deterministic and stochastic environments |
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| Institution: | 1. School of Mathematics and Statistics, Key Laboratory of Applied Statistics of MOE, Northeast Normal University, Changchun 130024, Jilin Province, China;2. College of Science, China University of Petroleum, Qingdao 266580, Shandong Province, China;3. Logistics Industry Economy and Intelligent Logistics Laboratory, Jilin University of Finance and Economics, Changchun 130117, Jilin Province, China |
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| Abstract: | 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. |
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