The Effect of Ongoing Exposure Dynamics in Dose Response Relationships

Abstract

Characterizing infectivity as a function of pathogen dose is integral to microbial risk assessment. Dose-response experiments usually administer doses to subjects at one time. Phenomenological models of the resulting data, such as the exponential and the Beta-Poisson models, ignore dose timing and assume independent risks from each pathogen. Real world exposure to pathogens, however, is a sequence of discrete events where concurrent or prior pathogen arrival affects the capacity of immune effectors to engage and kill newly arriving pathogens. We model immune effector and pathogen interactions during the period before infection becomes established in order to capture the dynamics generating dose timing effects. Model analysis reveals an inverse relationship between the time over which exposures accumulate and the risk of infection. Data from one time dose experiments will thus overestimate per pathogen infection risks of real world exposures. For instance, fitting our model to one time dosing data reveals a risk of 0.66 from 313 Cryptosporidium parvum pathogens. When the temporal exposure window is increased 100-fold using the same parameters fitted by our model to the one time dose data, the risk of infection is reduced to 0.09. Confirmation of this risk prediction requires data from experiments administering doses with different timings. Our model demonstrates that dose timing could markedly alter the risks generated by airborne versus fomite transmitted pathogens. We model the relationship between the temporal patterns of pathogen exposure and infection take off within people. Since different routes of transmission (e.g., airborne versus surface transfer routes) may result in different temporal patterns of exposure, this model helps to better compare the risks of transmission from one person to another through these different routes. Previous models assumed that the risk of infection is the same whether pathogens are inoculated all at once or over one day. Our model, in contrast, captures how one pathogen affects the potential of immunity to keep concurrently or subsequently arriving particles from initiating an infection. Since the pattern of timing of airborne and surface spread pathogen arrivals differ, our model shows that each airborne pathogen could carry less risk than each surface transmitted pathogen. Unfortunately, data to fully fit our model are not currently available. Therefore new experiments will have to be conducted where doses are given across different temporal windows.