  The process of infection of a host is complex, influenced by factors such as
microbial variation within and between hosts as well as differences in dose
across hosts. This study uses dose-response and microbial growth models to
delve into the impact of these factors on infection probability. It is
rigorously demonstrated that within-host heterogeneity in microbial infectivity
enhances the probability of infection. The effect of infectivity and dose
variation between hosts is studied in terms of the expected value of the
probability of infection. General analytical findings, derived under the
assumption of small infectivity, reveal that both types of heterogeneity reduce
the expected infection probability. Interestingly, this trend appears
consistent across specific dose-response models, suggesting a limited role for
the small infectivity condition. Additionally, the vital dynamics behind
heterogeneous infectivity are investigated with a microbial growth model which
enhances the biological significance of single-hit dose-response models.
Testing these mathematical predictions inspire new and challenging laboratory
experiments that could deepen our understanding of infections.
