Wang Jianpeng, Teng Zhidong, Dai Binxiang
School of Mathematics and Statis, Central South University, Changsha, Hunan, 410075, People's Republic of China.
College of Medical Engineering and Technology, Xinjiang Medical University, Urumqi, Xinjiang, 830011, People's Republic of China.
Infect Dis Model. 2023 Jul 17;8(3):881-911. doi: 10.1016/j.idm.2023.07.006. eCollection 2023 Sep.
In this paper, a reaction-diffusion SIRS epidemic model with nonlinear incidence rate and partial immunity in a spatially heterogeneous environment is proposed. The well-posedness of the solution is firstly established. Then the basic reproduction number is defined and a threshold dynamics is obtained. That is, when < 1, the disease-free steady state is locally stable, which implies that the disease is extinct, when > 1, the disease is permanent, and there exists at least one positive steady state solution. Finally, the asymptotic profiles of the positive steady state solution as individuals disperse at small and large rates are investigated. Furthermore, as an application of theoretical analysis, a numerical example involving the spread of influenza is discussed. Based on the numerical simulations, we find that the increase of transmission rate and spatial heterogeneity can enhance the risk of influenza propagation, and the increase of diffusion rate, saturation incidence for susceptible and recovery rate can reduce the risk of influenza propagation. Therefore, we propose to reduce the flow of people to lower the effect of spatial heterogeneity, increase the transfer of infected individuals to hospitals in surrounding areas to increase the diffusion rate, and increase the construction of public medical resources to increase the recovery rate for controlling influenza propagation.
本文提出了一个在空间异质环境中具有非线性发病率和部分免疫的反应扩散SIRS流行病模型。首先建立了解的适定性。然后定义了基本再生数并得到了一个阈值动力学。即，当(< 1)时，无病稳态局部稳定，这意味着疾病灭绝；当(> 1)时，疾病持续存在，并且至少存在一个正稳态解。最后，研究了个体以小速率和大速率扩散时正稳态解的渐近分布。此外，作为理论分析的应用，讨论了一个涉及流感传播的数值例子。基于数值模拟，我们发现传播率和空间异质性的增加会增强流感传播的风险，扩散率、易感者的饱和发病率和恢复率的增加会降低流感传播的风险。因此，我们建议减少人员流动以降低空间异质性的影响，增加感染个体向周边地区医院的转移以提高扩散率，增加公共医疗资源建设以提高恢复率来控制流感传播。
