AI 中文总结
该研究针对时空异质环境下的非局部扩散SIS流行病模型，定义了依赖于扩散率、总种群规模和饱和参数的基本再生数，分析了平衡点性质，揭示了饱和效应对疾病动态的影响并通过数值模拟验证结论。
AI 中文摘要
本文研究时空异质环境下具有饱和发生率和Neumann边界条件的时间周期非局部扩散易感-感染-易感（SIS）流行病模型。首先，定义该模型的基本再生数，其依赖于扩散率、总种群规模和饱和参数，与采用标准或双线性发生率的模型存在显著差异；接着，建立其变分特征并分析上述参数对基本再生数的影响；随后，探究平衡点的存在性、唯一性和全局吸引性，还分析了地方病稳态在小饱和参数、小扩散率及大扩散率下的渐近行为。结果表明，饱和效应使总种群规模对疾病动态产生显著影响；当饱和参数趋于0时，基本再生数和地方病平衡点分别退化为标准发生率模型对应的结果。最后，通过数值模拟验证所得结论。
英文摘要
In this paper, we consider a time-periodic nonlocal dispersal susceptible-infected-susceptible (SIS) epidemic model with saturated incidence and Neumann boundary conditions in a spatiotemporally heterogeneous environment. First, we define the basic reproduction number for the model, which depends on dispersal rates, total population size and saturation parameters, and is quite different from those of models incorporating standard or bilinear incidence. Then, we establish its variational characterization and investigate the impacts of those parameters on it. Next, we explore the existence, uniqueness and global attractivity of the equilibria. We also analyze the asymptotic behaviors of endemic steady states for small saturation parameters, and for both small and large diffusion rates. Our results show that the saturation effect enables the total population size to have a significant impact on the disease dynamics. Furthermore, as the saturation parameter tends to zero, the basic reproduction number and the endemic equilibrium reduce to those of the standard-incidence model, respectively. Finally, we support our findings by numerical simulations.
Comments46 pages, 8 figures, 3 tables
