一类具有离散时滞与不同传染性的霍乱模型研究
Research on a Class of Cholera Model with Discrete Delay and Different Infectious
张育茹 1桑媛 1宋冰 1张龙1
作者信息
- 1. 新疆大学 数学与系统科学学院,新疆 乌鲁木齐 830046;新疆维吾尔自治区应用数学重点实验室,新疆 乌鲁木齐 830046
- 折叠
摘要
本文研究了一类具有疫苗接种策略的时滞霍乱模型,考虑了高低传染性霍乱弧菌混合感染以及直接传播和间接传播.通过计算,得到了系统的基本再生数R0,证明了当R0<1时,无病平衡点局部及全局渐近稳定,当R0>1时,地方病平衡点全局渐近稳定.通过数值模拟演示了理论结果,发现时滞对于霍乱传播具有重要影响,其动力学可以与无时滞系统相同,不同甚至相反,忽略时滞会高估霍乱的传播,付出更多控制成本.
Abstract
In this paper,a delayed cholera model with vaccination strategy,mixed infection of hyperinfectious and hypoinfectious cholera vibrios,direct and indirect transmission pathways is established.The basic reproduction number R0 is obtained,by which the local and global asymptotic stability of the disease-free equilibrium is obtained if R0<1,while the endemic equilibrium is globally asymptotically stable if R0>1.In addition,the theoretical results are illustrated by numerical simulations.It is found that time delay has important effect on cholera propagation,the dynamics of system with delay can be the same,different or even opposite to that of system without delay.Ignoring the influence of delay could overestimate the spread of cholera and cost more to control it.
关键词
时滞/高低传染性霍乱弧菌/疫苗接种/基本再生数/全局渐近稳定性Key words
time delay/hyperinfectious and hypoinfectious cholera vibrios/vaccination/basic reproduction number/globally asymp-totic stability引用本文复制引用
基金项目
新疆应用数学重点实验室开放课题(2021D04014)
国家自然科学基金(12261087)
国家自然科学基金(11861065)
新疆维吾尔自治区高校科研重点项目(XJEDU2021I002)
新疆维吾尔自治区自然科学基金(2022D01E41)
出版年
2024
国家科技期刊平台
NSTL
万方数据