Impact of heterogeneity on infection probability: Insights from single-hit dose-response models

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.