Models of infectious disease transmission to explore the effects of immune boosting
AuthorLeung, Ngo Nam
AffiliationSchool of Mathematics and Statistics
Document TypePhD thesis
Access StatusOpen Access
© 2019 Ngo Nam Leung
Despite advances in prevention and control, infectious diseases continue to be a burden to human health. Many factors, including the waning and boosting of immunity, are involved in the spread of disease. The link between immunological processes at an individual level and population-level immunity is complex and subtle. Mathematical models are a useful tool to understand the biological mechanisms behind the observed epidemiological patterns of an infectious disease. Here I construct deterministic, compartment models of infectious disease transmission to study the effects of waning and boosting of immunity on infectious disease dynamics. While waning immunity has been studied in many models, incorporation of immune boosting in models of transmission has largely been neglected. In my study, I look at three different aspects of immune boosting: (i) the influence of immune boosting on the critical vaccination thresholds required for disease control; (ii) the effect of immune boosting and cross-immunity on infectious disease dynamics; and (iii) the influence of differentiating vaccine-acquired immunity from natural (infection-acquired) immunity and different mechanisms of immune boosting on infection prevalence. Models can provide support for public health control measures in terms of critical vaccination thresholds. There is a direct relationship, from mathematical theory, between the critical vaccination threshold and the basic reproduction number, R0. Key epidemiological quantities, such as R0, are measured from data, but the selection of the model used to infer these quantities matters. I show how the inferred values of R0---and thus, critical vaccination thresholds---can vary when immune boosting is taken into account. I also investigate the effects of interactions between immune boosting and cross-immunity on infectious disease dynamics, using a two-pathogen transmission model. Immunity to one pathogen that confers immunity to another pathogen, or to another strain of a given pathogen, is known as cross-immunity. Varying levels of susceptibility to infection conferred by cross-immunity are included in the model. Using a combination of numerical simulations and bifurcation analyses, I show that immune boosting at strong levels can lead to recurrent epidemics (or periodic solutions) independent of cross-immunity. Where immune boosting is weak, cross-immunity allows the model to generate periodic solutions. For some diseases, there are differences in infection-acquired immunity and vaccine-acquired immunity. I explore the effect of vaccination and immune boosting on epidemiological patterns of infectious disease. I construct and analyse a model that differentiates vaccine-acquired immunity from infection-acquired immunity in the form of duration of protection. The model also distinguishes between primary and secondary infections. I show that vaccination is effective at reducing primary infections but not necessarily secondary infections, which can maintain overall transmission. Two different mechanisms through which immune boosting provides protection are also explored. Whether immune boosting delays or bypasses a primary infection can determine whether primary or secondary infections contribute most to transmission.
Keywordsmathematical modelling; compartmental models; waning immunity; immune boosting; bifurcation analysis
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