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Incorporating the host-pathogen kinetics of time-dose-response into epidemic outbreak models
Dissertation   Open access

Incorporating the host-pathogen kinetics of time-dose-response into epidemic outbreak models

Bidya Prasad
Doctor of Philosophy (Ph.D.), Drexel University
Mar 2017
DOI:
https://doi.org/10.17918/etd-7282
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Abstract

Environmental health--Research Environmental Engineering Public Health
Mathematical models charting disease outbreaks have been a central tenant of epidemiology since its inception. Pathogens responsible for these outbreaks replicate in the host, leading to adverse reactions over time. It may be concluded, therefore, that the incubation period is a function of pathogen reproduction, which is time-dependent. Yet no outbreak model has considered the effects of in-vivo kinetics to date. It is postulated that outbreak models which consider host-pathogen kinetics can provide better fits to outbreak data than models that do not consider this system. This dissertation demonstrates the relationship between the incubation function of a host-pathogen system and outbreak models. To examine this relationship, this work is divided into two categories: (1) derivations and model development, which includes (a) deriving time-dose-response (TDR) models, (b) deriving primary (common-source) and secondary (person-to-person spread) outbreak models that incorporate the TDR equations, and (c) developing a Matlab code which models a convolution of the exposure and incubation distributions; and (2) data modelling, which includes (a) mining the literature to find appropriate TDR and outbreak datasets for each respective pathogen, (b) generating dose-response model fits for each respective pathogen, (c) generating TDR model fits for each pathogen, and (d) generating fits for the TDR and non-time-dependent outbreak models. This methodology was partially verified using data from a Cryptosporidium parvum outbreak that occurred in Milwaukee. The pathogens modelled using this method are (1) Legionella spp.; (2) Giardia lamblia; (3) Salmonella spp.; (4) Shigella spp.; (5) Escherichia coli O157:H7; and (6) Campylobacter jejuni. The results of this work suggest good support for the TDR incorporation into the outbreak model. In several cases, the TDR outbreak had the lowest deviance values among time-dependent and non-time-dependent models, which was the metric that was used to determine the best-fit model. However, since the TDR contained extra parameters, it did not necessarily have the lowest Akaike information criterion (AIC) and Bayesian information criterion (BIC) values. Parameter estimates were generally consistent across different species. This work seeks to characterize the relationship between the time-dose-response functions, which reflect the in-vivo kinetics of the host-pathogen system, and the models that predict the number of ill persons per day of an outbreak, based on available data from epidemiological studies.

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