论文标题
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
论文作者
论文摘要
在本文中，我们首先提出了一个具有一般发病率的扩散病原体感染模型，该模型融合了细胞到细胞的传播。通过应用单调动力学系统的理论，我们证明该模型以基本复制数（$ \ MATHCAL {r} _ {0} $）的形式允许全局阈值动态，该模型由下一代操作员的光谱半径定义。然后，我们通过非标准有限差方案得出连续模型的离散对应物。结果表明，离散模型保留了解决方案的积极性和界限，以确保问题的适应性。此外，该方法保留了原始连续模型的所有均衡。通过为这两个模型构建适当的Lyapunov功能，我们表明全局阈值动力学完全由基本的再现数确定。此外，在灵敏度分析的帮助下，我们还确定了最敏感的参数，这些参数有效地有助于改变疾病动态。最后，我们以示例和数值模拟来结束论文，以改善和推广一些已知结果。
In this paper, we first propose a diffusive pathogen infection model with general incidence rate which incorporates cell-to-cell transmission. By applying the theory of monotone dynamical systems, we prove that the model admits the global threshold dynamics in terms of the basic reproduction number ($\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.
