Abstract In this paper, we present a discrete dynamic system which describes an epidemic spreading within a single farm, where animals are separated into batches. In this model, we consider an indirect transmission of the disease coming from the bacteria remaining in the reservoir and taking into account the transfer of bacteria between adjacent compartments. In our model, tridiagonal matrices of non-negative blocks are involved. The development of the matrix spectral properties allows us to improve our understanding of the epidemic spreading within a farm with the above mentioned characteristics. Based on the results obtained, we have determined some bounds to obtain the maximum number of batches and the maximum population in each batch to ensure that the disease dies out.

中文翻译：

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隔间农场间接传播的流行病

摘要在本文中，我们提出了一个离散动态系统，它描述了在单个农场内传播的流行病，其中动物被分成几批。在这个模型中，我们考虑了来自保留在水库中的细菌的疾病的间接传播，并考虑了相邻隔室之间的细菌转移。在我们的模型中，涉及非负块的三对角矩阵。矩阵光谱特性的发展使我们能够提高对具有上述特征的农场内流行病传播的理解。根据获得的结果，我们确定了一些界限，以获得最大批次数和每批次最大种群，以确保疾病消失。