A dose and time response Markov model for the in-host dynamics of infection with intracellular bacteria following inhalation: with application toFrancisella tularensis

Abstract

In a novel approach, the standard birth–death process is extended to incorporate a fundamental mechanism undergone by intracellular bacteria, phagocytosis. The model accounts for stochastic interaction between bacteria and cells of the immune system and heterogeneity in susceptibility to infection of individual hosts within a population. Model output is the dose–response relation and the dose-dependent distribution of time until response, where response is the onset of symptoms. The model is thereafter parametrized with respect to the highly virulent Schu S4 strain of Francisella tularensis, in the first such study to consider a biologically plausible mathematical model for early human infection with this bacterium. Results indicate a median infectious dose of about 23 organisms, which is higher than previously thought, and an average incubation period of between 3 and 7 days depending on dose. The distribution of incubation periods is right-skewed up to about 100 organisms and symmetric for larger doses. Moreover, there are some interesting parallels to the hypotheses of some of the classical dose–response models, such as independent action (single-hit model) and individual effective dose (probit model). The findings of this study support experimental evidence and postulations from other investigations that response is, in fact, influenced by both in-host and between-host variability.

Human Dose–Response Data for Francisella tularensis and a Dose‐ and Time‐Dependent Mathematical Model of Early‐Phase Fever Associated with Tularemia After Inhalation Exposure

“…The statistical characterization of the complete data set from 118 volunteers (112 febrile with measured IP, fever rise time, and near‐maximum fever) fills gaps in knowledge about early‐phase human tularemia unappreciated in previously published studies from portions of these data (Egan, Hall, & Leach, ; Jones, Nicas, Hubbard, Sylvester, & Reingold, ; Wood, Egan, & Hall, ). The statistical characterization of three parameters defining human fever profile are useful for comparisons to outputs of theoretical models of tularemia mechanisms, particularly IPs in animal models (Gillard, Laws, Lythe, & Molina‐París, ; Huang & Haas, ; Wood et al., ) and from human epidemiologic investigation (Egan et al., ). All of these studies considered F. tularensis strain Schu S4.…”

A review of back-calculation techniques and their potential to inform mitigation strategies with application to non-transmissible acute infectious diseases

“…Within-host modelling can potentially unify dose-dependent incubation periods with infection probabilities and can further allow the consideration of mitigation strategies. To date, this has really only been possible for inhalational anthrax, but it is hoped that further research in this area will benefit the planning and response to potential outbreaks of other pertinent diseases, such as tularaemia [104], Q fever and pneumonic plague.…”

Microbiota and Dose Response: Evolving Paradigm of Health Triangle

“…Scientific evidence that contradicts the common simplifying assumptions of microbial dose–response assessment is accumulating (Aderem et al., ; Cornforth, Matthews, Brown, & Raymond, ; Muthukumar, Alexander, Thangam, & Ahmed, ; Van Leeuwen, O'Neill, Matthews, & Raymond, ; Wood, Egan, & Hall, ), pointing to a need for microbial risk assessors to consider ecological and systems biology approaches (Aderem et al., ; Muthukumar et al., ), with less reliance on historical “germophobia” and oversimplifications based on the Disease Triangle that excludes the protective effects of the microbiota in healthy and more susceptible hosts. Some might argue that nonthreshold, low‐dose linear models have been validated with outbreak observations.…”