Abstract
Foodborne diseases remain a major public health concern because of their high incidence and the substantial number of deaths they cause worldwide. Consequently, there is a need to develop multiscale mathematical models that improve our understanding of the biological mechanisms driving disease transmission and identify key factors influencing disease persistence. Traditional mathematical models typically investigate within-host and between-host dynamics separately, overlooking the interactions between processes occurring at these two scales. This study develops and analyses a nested multiscale mathematical model for Escherichia coli O157:H7 that integrates within-host bacterial replication with between-host environmental transmission. The two scales are explicitly coupled through pathogen shedding, allowing the influence of within-host bacterial dynamics on environmental contamination and disease transmission to be quantified. A nonstandard finite difference (NSFD) scheme is constructed to preserve the essential dynamical properties of the continuous model, and the resulting discrete model is analysed mathematically. Numerical simulations demonstrate that once E. coli O157:H7 becomes established within infected cattle, continued bacterial replication and pathogen shedding sustain environmental contamination, thereby promoting the persistence of disease transmission within the cattle population. These findings highlight the important role of within-host bacterial dynamics in driving environmental transmission and provide a quantitative framework for evaluating intervention strategies targeting both within-host bacterial replication and between-host disease transmission.