Global Analysis of a Novel Nonlinear Stochastic SIVS Epidemic System with Vaccination Control

Leng Xiaona; Feng Tao; Meng Xinzhu

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Global Analysis of a Novel Nonlinear Stochastic SIVS Epidemic System with Vaccination Control

机译：具有疫苗接种控制的新型非线性随机SIVS流行病系统的全局分析

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This paper proposes a stochastic SIVS epidemic system with nonlinear saturated infection rate under vaccination and investigates the dynamics predicted by the model. By using It (o) over cap 's formula and Lyapunov methods, we first study the existence and uniqueness of global positive solution. Then we investigate the stochastic dynamics of the system and obtain the thresholds which govern the extinction and the spread of the epidemic disease. Results show that large stochastic noises can lead to the extinction of epidemic diseases; that is, stochastic disturbances can suppress the outbreak of epidemic diseases. Finally, we carry out a series of numerical simulations to demonstrate the performance of our theoretical findings.

机译：本文提出了一种带有非线性饱和疫苗接种率的随机SIVS流行病系统，并研究了该模型预测的动力学。通过在cap的公式上使用It（o）和Lyapunov方法，我们首先研究了整体正解的存在性和唯一性。然后，我们研究了系统的随机动力学，并获得了控制流行病的灭绝和传播的阈值。结果表明，较大的随机噪声可导致流行病的灭绝。也就是说，随机干扰可以抑制流行病的爆发。最后，我们进行了一系列数值模拟，以证明我们的理论发现的性能。

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《Mathematical Problems in Engineering》 |2017年第6期|8098475.1-8098475.11|共11页
作者
Leng Xiaona; Feng Tao; Meng Xinzhu;
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Shandong Univ Sci & Technol, Coll Math & Syst Sci, Qingdao 266590, Peoples R China;

Shandong Univ Sci & Technol, Coll Math & Syst Sci, Qingdao 266590, Peoples R China;

Shandong Univ Sci & Technol, Coll Math & Syst Sci, Qingdao 266590, Peoples R China|Shandong Univ Sci & Technol, State Key Lab Min Disaster Prevent & Control Cofo, Qingdao 266590, Peoples R China|Shandong Univ Sci & Technol, Minist Sci & Technol, Qingdao 266590, Peoples R China;

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1. Global analysis of a delayed epidemic dynamical system with pulse vaccination and nonlinear incidence rate [J] . Yu Jiang, Liquan Mei, Xinyu Song Applied Mathematical Modelling . 2011,第10期

机译：具有脉冲接种和非线性发生率的时滞流行病动力学系统的全局分析
2. Application of stochastic inequalities to global analysis of a nonlinear stochastic SIRS epidemic model with saturated treatment function [J] . Shengqiang Zhang, Xinzhu Meng, Xinzeng Wang Advances in Difference Equations . 2018,第1期

机译：随机不等式在具有饱和处理函数的非线性随机SIRS流行病模型的全局分析中的应用
3. Controlling global stochasticity of Hamiltonian systems by nonlinear perturbation [J] . Ying Zhang, Gang Hu, Shigang Chen, The European physical journal, B. Condensed matter physics . 2002,第3期

机译：通过非线性摄动控制哈密顿系统的整体随机性
4. GLOBAL ANALYSIS FOR AN EPIDEMIC MODEL WITH NONLINEAR VACCINATION RATE [C] . YA-LI YANG, JIAN-QUAN LI, JI-GUANG ZHANG 2009 International Conference on Machine Learning and Cybernetics（2009机器学习与控制论国际会议）论文集 . 2009

机译：带有非线性接种率的传染病模型的全局分析
5. Non-intrusive methods for probabilistic uncertainty quantification and global sensitivity analysis in nonlinear stochastic phenomena. [D] . Liu, Yaning. 2013

机译：非线性随机现象中概率不确定性量化和全局灵敏度分析的非侵入性方法。
6. Dynamics Analysis of a Nonlinear Stochastic SEIR Epidemic System with Varying Population Size [O] . Xiaofeng Han, Fei Li, Xinzhu Meng 2018

机译：不同群体大小的非线性随机SEIR流行病系统的动力学分析
7. Application of stochastic inequalities to global analysis of a nonlinear stochastic SIRS epidemic model with saturated treatment function [O] . Shengqiang Zhang, Xinzhu Meng, Xinzeng Wang 2018

机译：随机不等式在饱和治疗功能中对非线性随机SIRS流行病模型的全局分析

Global Analysis of a Novel Nonlinear Stochastic SIVS Epidemic System with Vaccination Control

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