Leng Xiaona, Feng Tao, Meng Xinzhu
College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, 266590 P.R. China.
State Key Laboratory of Mining Disaster Prevention and Control Co-founded by Shandong Province and the Ministry of Science and Technology, Shandong University of Science and Technology, Qingdao, 266590 P.R. China.
J Inequal Appl. 2017;2017(1):138. doi: 10.1186/s13660-017-1418-8. Epub 2017 Jun 15.
This paper proposes a new nonlinear stochastic SIVS epidemic model with double epidemic hypothesis and Lévy jumps. The main purpose of this paper is to investigate the threshold dynamics of the stochastic SIVS epidemic model. By using the technique of a series of stochastic inequalities, we obtain sufficient conditions for the persistence in mean and extinction of the stochastic system and the threshold which governs the extinction and the spread of the epidemic diseases. Finally, this paper describes the results of numerical simulations investigating the dynamical effects of stochastic disturbance. Our results significantly improve and generalize the corresponding results in recent literatures. The developed theoretical methods and stochastic inequalities technique can be used to investigate the high-dimensional nonlinear stochastic differential systems.
本文提出了一种具有双重流行假设和 Lévy 跳跃的新型非线性随机 SIVS 流行病模型。本文的主要目的是研究随机 SIVS 流行病模型的阈值动力学。通过使用一系列随机不等式技术，我们获得了随机系统均值持续存在和灭绝的充分条件以及控制流行病灭绝和传播的阈值。最后，本文描述了研究随机扰动动力学效应的数值模拟结果。我们的结果显著改进并推广了近期文献中的相应结果。所发展的理论方法和随机不等式技术可用于研究高维非线性随机微分系统。
