School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu, 730000, People's Republic of China.
J Math Biol. 2021 Nov 13;83(6-7):62. doi: 10.1007/s00285-021-01688-x.
In this paper, a stochastic eco-epidemiological system with patchy structure and transport-related infection is proposed and the stochastic dynamical behaviors are investigated. Firstly, by constructing suitable Lyapunov functions, it is revealed that there is a unique globally positive solution starting from the positive initial value. Secondly, it is proved that the presented system is stochastically ultimately bounded and the average in time of the second moment of solution is bounded. Thirdly, we prove that the large enough stochastic perturbations may lead the predator population and the diseases in the predator to be extinct while it is persistent in the deterministic system. Finally, some numerical simulations are given to test our theoretical results.
本文提出了一个具有斑块结构和与传输相关感染的随机生态流行病学系统，并研究了其随机动力学行为。首先，通过构建合适的李雅普诺夫函数，揭示了从正初始值开始存在唯一全局正解。其次，证明了所提出的系统是随机最终有界的，并且解的二次矩的时间平均值是有界的。第三，我们证明了足够大的随机扰动可能导致捕食者种群和捕食者中的疾病灭绝，而在确定性系统中则是持久的。最后，给出了一些数值模拟来验证我们的理论结果。
