School of Science, Jiangnan University, Wuxi, Jiangsu 214122, P.R. China.
School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, P.R. China.
Math Biosci Eng. 2019 Jun 24;16(5):5897-5922. doi: 10.3934/mbe.2019295.
In this paper by adding the factors of disease relapse and vaccination in the space hetero-geneous environment, we establish and discuss a class of reaction-diffusion SVIR model with relapse and a varying external source in spatial heterogeneous environment. By applying a different method than the Lyapunov function, we study the long-term dynamic behavior of this model by means of global exponential attractor theory and gradient flow method. The global asymptotic stability and the persistence of epidemic are proved. To test the validity of our theoretical results, we choose some specific epidemic disease with some more practical and more definitive official data to simulate the global stability and exponential attraction of the model. The simulation results showed that the factors of disease relapse, vaccination and spatial heterogeneity had a great influence on the persists uniformly of the disease.
在本文中，我们通过在空间异质环境中加入疾病复发和疫苗接种的因素，建立并讨论了一类具有复发和时变外部源的反应扩散 SVIR 模型。我们应用不同于 Lyapunov 函数的方法，利用全局指数吸引子理论和梯度流方法研究了该模型的长期动力学行为。证明了全局渐近稳定性和传染病的持久性。为了检验我们理论结果的有效性，我们选择了一些具有更实际和更明确官方数据的特定传染病来模拟模型的全局稳定性和指数吸引。模拟结果表明，疾病复发、疫苗接种和空间异质性等因素对疾病的持久性有很大影响。
