Lin Jia Zhe, Xu Rui, Tian Xiao Hong
Institute of Applied Mathematics, Army Engineering University, Shijiazhuang 050003, Hebei, P.R. China.
Complex Systems Research Center, Shanxi University, Taiyuan 030006, Shanxi, P.R. China.
Math Biosci Eng. 2019 May 16;16(5):4339-4358. doi: 10.3934/mbe.2019216.
Cholera is a common infectious disease caused by Vibrio cholerae, which has different infectivity. In this paper, we propose a cholera model with hyperinfectious and hypoinfectious vibrios, in which both human-to-human and environment-to-human transmissions are considered. By analyzing the characteristic equations, the local stability of disease-free and endemic equilibria is established. By using Lyapunov functionals and LaSalle's invariance principle, it is verified that the global threshold dynamics of the model can be completely determined by the basic reproduction number. Numerical simulations are carried out to illustrate the corresponding theoretical results and describe the cholera outbreak in Haiti. The study of optimal control helps us seek cost-effective solutions of time-dependent control strategies against cholera outbreaks, which shows that control strategies, such as vaccination and sanitation, should be taken at the very beginning of the outbreak and become less necessary after a certain period.
霍乱是由霍乱弧菌引起的一种常见传染病，霍乱弧菌具有不同的传染性。在本文中，我们提出了一个包含高传染性和低传染性弧菌的霍乱模型，其中考虑了人际传播和环境-人传播。通过分析特征方程，建立了无病平衡点和地方病平衡点的局部稳定性。利用Lyapunov泛函和LaSalle不变性原理，验证了模型的全局阈值动态可以完全由基本再生数决定。进行了数值模拟以说明相应的理论结果，并描述海地的霍乱疫情。最优控制研究有助于我们寻求针对霍乱疫情的时间依赖控制策略的经济有效解决方案，这表明应在疫情爆发之初采取疫苗接种和环境卫生等控制策略，经过一段时间后这些策略的必要性会降低。
