While kinetic models are widely used to describe viral infection at various levels, most of them are focused on temporal aspects and understanding of corresponding spatio-temporal aspects remains limited. In this work, our attention is focused on the initial stage of infection of immobile cells by virus particles (“virions”) under flow conditions with diffusion. A practical example of this scenario occurs when humans or animals consume food from virion-containing sources. Mathematically, such situations can be described by using a model constructed in analogy with those employed in chemical engineering for analysis of the function of a plug-flow reactor with dispersion. As in the temporal case, the corresponding spatio-temporal model predicts either the transition to a steady state or exponential growth of the populations of virions and infected cells. The spatial distributions of these species are similar in both of these regimes. In particular, the maximums of the populations are shifted to the upper boundary of the infected region. The results illustrating these conclusions were obtained analytically and by employing numerical calculations without and with the dependence of the kinetic parameters on the coordinate. The model proposed has also been used in order to illustrate the effect of antiviral feed additives on feedborne infection towards curbing disease transmission.

虽然动力学模型被广泛用于描述各个层面的病毒感染，但大多数模型都集中在时间方面，而对相应时空方面的理解仍然有限。在这项工作中，我们的注意力集中在扩散流动条件下病毒颗粒（“病毒粒子”）感染固定细胞的初始阶段。当人类或动物食用含有病毒粒子的食物时，就会发生这种情况的一个实际例子。从数学上讲，这种情况可以通过使用与化学工程中用于分析具有分散的活塞流反应器的功能的模型类似地构建的模型来描述。与时间情况一样，相应的时空模型预测病毒粒子和受感染细胞群的过渡到稳定状态或指数增长。这些物种的空间分布在这两个区域中是相似的。特别是，人口的最大值转移到感染区域的上边界。说明这些结论的结果是通过分析和采用数值计算获得的，不依赖于或依赖于坐标的动力学参数。所提出的模型也被用来说明抗病毒饲料添加剂对饲料传播感染的作用，从而遏制疾病传播。