宿主内扩散病原体感染模型的动力学
Dynamics of an Intra-host Diffusive Pathogen Infection Model
AI总结：
本文提出一个考虑细胞间传播的扩散病原体感染模型，通过单调动力系统理论证明其全局阈值动力学由基本再生数决定，并利用非标准有限差分方法保持模型的正性和平衡点，同时通过敏感性分析识别关键参数。
摘要：
在本文中，我们首先提出一个具有通用发病率的扩散病原体感染模型，该模型纳入了细胞间传播。通过应用单调动力系统理论，我们证明该模型在基本再生数（R0）方面具有全局阈值动力学，R0由下一世代算子的谱半径定义。然后，我们通过非标准有限差分方案推导出连续模型的离散对应物。结果表明，离散模型保持了解的正性和有界性，以确保问题的良态性。此外，该方法保留了原始连续模型的所有平衡点。通过为两种模型构造适当的Lyapunov函数，我们证明全局阈值动力学完全由基本再生数决定。进一步地，借助敏感性分析，我们还确定了最敏感的参数，这些参数有效影响疾病动力学。最后，我们通过一个例子和数值模拟来改进和推广一些已知的结果。
英文摘要：
In this paper, we first propose a diffusive pathogen infection model with general incidence rate which incorporates cell-to-cell transmission. By applying the theory of monotone dynamical systems, we prove that the model admits the global threshold dynamics in terms of the basic reproduction number ($\mathcal{R}_{0}$), which is defined by the spectral radius of the next generation operator. Then, we derive a discrete counterpart of the continuous model by nonstandard finite difference scheme. The results show that the discrete model preserves the positivity and boundedness of solutions in order to ensure the well-posedness of the problem. Moreover, this method preserves all equilibria of the original continuous model. By constructing appropriate Lyapunov functionals for both models, we show that the global threshold dynamics is completely determined by the basic reproduction number. Further, with the help of sensitivity analysis we also have identified the most sensitive parameters which effectively contribute to change the disease dynamics. Finally, we conclude the paper by an example and numerical simulations to improve and generalize some known results.
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