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        Mathematical models for the spread of multiple pathogens with cross-reactivity and waning of immunity

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        NieuwenhuizenJaap_MastersThesis_MathematicalSciences_MathModelsMultiStrain_FINAL.pdf (3.756Mb)
        Publication date
        2023
        Author
        Nieuwenhuizen, Jaap
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        Summary
        Using several mathematical models for multi-strain epidemics, we study both theoretically and with stochastic simulations, how waning of overall immunity and cross-immunity impact the coexistence of multiple pathogen strains. The focus lies on one specific multi-strain model with individual-based continuous waning (cross-)immunity. For that model, we observe and study three immunity regimes: (1) short-term immunity, (2) long-term immunity and short-term cross immunity, and (3) long-term immunity and long-term cross-immunity, which differ in the observed number of coexisting strains. Equilibria densities are derived using a compartmentalised model. The short-term immunity coexistence regime is also studied through compartmental models, with analysis being conducted to: (i) influence of cross-immunity on strain density, and (ii) the densities of total infecteds and susceptibles, in addition to the chance of invasion of a new strain into an existing equilibrium. For the long-term immunity non-coexistence parameter regime, we obtain explicit approximations for the expected time between outbreaks.
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        https://studenttheses.uu.nl/handle/20.500.12932/45451
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