Influenza viral dynamics models to explore the roles of innate and adaptive immunity
AuthorYan, Ada W. C.
AffiliationMathematics and Statistics
Document TypePhD thesis
Access StatusOpen Access
© 2017 Dr. Ada Wing Chi Yan
A mathematical model which captures how the immune response controls influenza infection is essential for predicting the effects of pharmaceutical interventions, and alleviating the public health burden of the disease. However, current models do not agree on how immune response components work together to control infection. Hence, the predicted effects of existing treatments differ between models, implying that predictions of the effects of novel treatments may be unreliable. The discrepancies between models arise because many models are only fit to viral load data from a single infection, from which it is difficult to distinguish between competing models. This study focuses on the construction of a viral dynamics model which reproduces experimental observations of the protection conferred by a primary infection against a subsequent infection. Incorporating observations from multiple experimental conditions enables more accurate extraction of the timing and strength of cross-immunity, and thus quantification of the roles of each component of the immune response. Following a literature review and mathematical preliminaries (Chapters 1-4), Chapter 5 details the analysis of data from experiments where ferrets are sequentially infected with two different influenza strains. The analysis shows that the protection conferred by a primary infection against a subsequent infection depends on the time between exposures as well as the strains used. Chapters 6 and 7 then present the construction of a viral dynamics model to show that the innate immune response can explain the delay of a secondary infection by a primary infection, and that both cross-reactivity and memory in the cellular adaptive immune response are required to explain the shortening of a secondary infection by a primary infection. The model also reproduces qualitative observations from a range of knockout experiments. To quantify the roles of each immune component, the model must be fitted to experimental data. However, because of the large number of model parameters, a simulation estimation study is first conducted in Chapters 8 and 9. The study shows that rather than examining marginal posterior distributions, using a fitted model to make predictions more clearly elucidates the role of each immune component in controlling infection. Moreover, a model fitted to sequential infection data accurately recovers the timing and extent of cross-protection between strains, whereas insufficient information is available from single infection data to enable inference of these quantities. This represents significant progress in ensuring that results of data fitting are interpreted appropriately, such that the fitted model provides a sound foundation upon which to explore the effects of interventions. Lastly, Chapter 10 addresses the observation that under identical experimental conditions, some ferrets become infected when exposed to a second virus and some do not. Equations are derived for the extinction probability of the second virus for a stochastic version of one of the models in the study. The numerical solutions to these equations show that the dependence of the extinction probability on the inter-exposure interval is consistent with experimental observations. Thus, stochasticity in viral dynamics alone is a viable hypothesis for the difference in observed infection outcomes.
Keywordsinfluenza; viral dynamics; mathematical model; stochastic process; simulation estimation; Markov chain Monte Carlo; immunology; within-host; cross-immunity
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