Abstract
• Epidemic spreading. • Compartmental system. • Tridiagonal matrix. • Stability and spectral properties. • Disease dies out or disease remains. 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.
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