发表机构
Lomonosov Moscow State University; Texas Tech University; Oil and Gas Research Institute of the Russian Academy of Sciences (OGRI RAS)（莫斯科国立大学; 德克萨斯理工大学; 俄罗斯科学院石油天然气研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文建立一维模型研究病毒在空间分布易感群体中的传播，证明行波存在性，并通过数值方法验证了分析解。核心贡献是提出保守离散格式，准确捕捉病毒传播机制。
AI 中文摘要
本文针对可移动病毒组分在空间分布的易感群体中传播的问题，建立了一个一维模型。病毒的随机运动产生扩散，而对易感密度相对梯度的响应则产生定向输运。当定向输运占主导地位时，证明了正整体行波的存在性，并单独构造了输运与扩散系数相等的极限情形。随后，通过无量纲变换将剩余方程转化为逻辑斯蒂方程，并提供了闭式解。这些公式确定了唯一的病毒最大值和远场行为。一种保守的隐式-显式有限差分方法提供了独立的数值验证。扩散项在新时间层上评估，梯度驱动的通量在单元界面处显式处理，易感群体的消耗则逐点计算。精确的行波值设定了初始数据和两个端点处随时间变化的狄利克雷条件。因此，该计算检验了分析解的保持与平移。使用八百个空间子区间的计算再现了局部化的病毒带和单调的易感前沿。病毒密度的最大均匀误差约为$1.70\cdot10^{-2}$，易感密度的最大均匀误差约为$2.22\cdot10^{-3}$。数值结果证实了分析构造，并表明保守离散格式捕捉了所提出的传播机制。
英文摘要
This paper develops a one-dimensional model for a mobile viral component propagating through a spatially distributed susceptible population. Random viral motion produces diffusion, whereas a response to the relative gradient of susceptible density generates directed transport. The existence of a positive entire traveling wave is proved when directed transport dominates diffusion, and the limiting case of equal transport and diffusion coefficients is constructed separately. A dimensionless transformation then converts the remaining equation into a logistic equation and supplies closed-form profiles. These formulas identify the unique viral maximum and the far-field behavior. A conservative implicit-explicit finite-difference method provides an independent numerical check. Diffusion is evaluated at the new time level, the gradient-driven flux explicitly at cell interfaces, and susceptible depletion pointwise. Exact traveling-wave values specify the initial data and time-dependent Dirichlet conditions at both endpoints. Thus, the computation tests preservation and translation of the analytical profiles. A calculation with eight hundred spatial subintervals reproduces the localized viral band and the monotone susceptible front. The largest uniform errors are approximately $1.70\cdot10^{-2}$ for viral density and $2.22\cdot10^{-3}$ for susceptible density. The numerical results corroborate the analytical construction and show that the conservative discretization captures the proposed propagation mechanism.
Comments14 pages, 4 figures
