Lyapunov Functions for a Class of Discrete SIRS Epidemic Models with Nonlinear Incidence Rate and Varying Population Sizes

YingWang; ZhidongTeng; MehbubaRehim

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Lyapunov Functions for a Class of Discrete SIRS Epidemic Models with Nonlinear Incidence Rate and Varying Population Sizes

机译：一类具有非线性发生率和种群大小变化的离散SIRS传染病模型的Lyapunov函数

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We investigate the dynamical behaviors of a class of discrete SIRS epidemic models with nonlinear incidence rate and varying population sizes. The model is required to possess different death rates for the susceptible, infectious, recovered, and constant recruitment into the susceptible class, infectious class, and recovered class, respectively. By using the inductive method, the positivity and boundedness of all solutions are obtained. Furthermore, by constructing new discrete type Lyapunov functions, the sufficient and necessary conditions on the global asymptotic stability of the disease-free equilibrium and endemic equilibrium are established.

机译：我们研究了一类具有非线性发生率和不同人口规模的离散SIRS流行病模型的动力学行为。要求模型分别针对易感人群，感染人群，恢复的人群和不断招募到易感人群，传染人群和恢复人群的死亡率。通过归纳法，可以得到所有溶液的正性和有界性。此外，通过构造新的离散型Lyapunov函数，建立了无病平衡和地方平衡的全局渐近稳定性的充要条件。

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《Discrete dynamics in nature and society》 |2014年第4期|共10页
作者
YingWang; ZhidongTeng; MehbubaRehim;
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中图分类数学模拟、近似计算;
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1. Asymptotic properties of a stochastic SIRS epidemic model with nonlinear incidence and varying population sizes [J] . Ramziya Rifhat, Ahmadjan Muhammadhaji, Zhidong Teng Dynamical Systems . 2020,第1期

机译：具有非线性发生率和种群数量变化的随机SIRS传染模型的渐近性质
2. Global Behaviors of a Class of Discrete SIRS Epidemic Models with Nonlinear Incidence Rate [J] . LeiWang, ZhidongTeng, LongZhang Abstract and applied analysis . 2014,第15期

机译：一类离散SIRS流行模式具有非线性发病率的全球行为
3. On the Lyapunov stability for SIRS epidemic models with general nonlinear incidence rate [J] . Buonomo B., Rionero S. Applied mathematics and computation . 2010,第8期

机译：具有一般非线性发生率的SIRS传染病模型的Lyapunov稳定性。
4. Stability analysis for a delayed SIRS epidemic model with vaccination and nonlinear incidence rate [C] . Zhixing Hu, Xiaofan Huang, Wanbiao Ma International congress on mathematical biology;ICMB2011 . 2011

机译：具有接种和非线性发生率的时滞SIRS传染病模型的稳定性分析。
5. Disease transmission models with varying population sizes. [D] . Zhou, Jinshi. 1995

机译：不同人口规模的疾病传播模型。
6. Global dynamics for a class of discrete SEIRS epidemic models with general nonlinear incidence [O] . Xiaolin Fan, Lei Wang, Zhidong Teng -1

机译：一类具有一般非线性事件的离散SEIRS流行病模型的全局动力学
7. Global dynamics of a delayed SIRS epidemic model with a wide class of nonlinear incidence rates [O] . Yoichi Enatsu, Eleonora Messina, Yukihiko Nakata, 2011

机译：具有广泛非线性发病率的延迟SIRS疫情模型的全球动态

Lyapunov Functions for a Class of Discrete SIRS Epidemic Models with Nonlinear Incidence Rate and Varying Population Sizes

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