College of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang, People's Republic of China.
J Biol Dyn. 2022 Dec;16(1):373-396. doi: 10.1080/17513758.2021.1900428. Epub 2021 Mar 16.
In this paper, a reaction-diffusion SIR epidemic model via environmental driven infection in heterogeneous space is proposed. To reflect the prevention and control measures of disease in allusion to the susceptible in the model, the nonlinear incidence function is applied to describe the protective measures of susceptible. In the general spatially heterogeneous case of the model, the well-posedness of solutions is obtained. The basic reproduction number is calculated. When the global asymptotical stability of the disease-free equilibrium is obtained, while when the model is uniformly persistent. Furthermore, in the spatially homogeneous case of the model, when the global asymptotic stability of the endemic equilibrium is obtained. Lastly, the numerical examples are enrolled to verify the open problems.
本文提出了一个通过环境驱动感染的异质空间反应扩散 SIR 传染病模型。为了反映模型中易感人群的疾病防控措施，应用非线性感染率函数来描述易感人群的保护措施。在模型的一般空间异质情况下，得到了解的适定性。计算了基本再生数 。当 时，得到了无病平衡点的全局渐近稳定性，而当 时，模型是一致持续的。此外，在模型的空间均匀情况下，当 时，得到了地方病平衡点的全局渐近稳定性。最后，通过数值例子验证了所提出的开放性问题。
