Population dynamics of infectious disease and pathogen evolution: modelling vaccine escape

Abstract

This thesis investigates how the risk that an infectious pathogen evolves antigenically (leading to pathogen strains that evade existing immunity) depends on the vaccination coverage of its host population. Deterministic compartmental models are coupled with a parsimonious approach to pathogen evolution, focussing on the selection pressure for immune escape. We study the qualitative patterns of this escape pressure — as a function of the vaccination coverage — and the epidemiological impact thereof, taking analytical approaches wherever possible. Chapter 2 varies the balance of the contributions to the escape pressure from infections in unvaccinated and vaccinated hosts. We use SIR-type models, for endemic disease and a transient epidemic wave. If within-host adaptation is substantially stronger in vaccinees, we find that the escape pressure follows a unimodal pattern: intermediate vaccination levels pose the greatest risk of escape. Otherwise, vaccination reduces the escape pressure. Chapter 3 extends the approach of Chapter 2 to heterogeneous populations. We account for differences in the pathogen adaptation rate within host types, such as immunocompromised individuals. We find that this novel form of heterogeneity may qualitatively change how the escape pressure depends on the vaccination coverage. In particular, for some parameters, the escape pressure has a bimodal pattern. We also analyse strategies for vaccine prioritisation. Chapter 4 extends the approach of Chapter 2 to account for a different pathogen adaptation rate during reinfections. We derive the final size of an epidemic in which infections induce partial protection against reinfection. If vaccines induce stronger protection than past infections, we find a new pattern: vaccination always reduces the escape pressure, regardless of the adaptation rate in hosts with prior immunity (acquired from infection, vaccination, or both). Chapter 5 extends the deterministic escape pressure of Chapter 2 to consider the stochastic establishment of emerging immune escape strains. Using a time-inhomogeneous branching process, we find that interference with the wildtype strain may substantially hinder the establishment probability of new strains, especially those emerging at late times. As a result, new patterns appear in the escape pressure. Depending on the cross-reactivity of existing immunity, intermediate vaccination coverages may lead to the lowest escape pressure. Bringing together the preceding chapters, Chapter 6 balances the risks of vaccine escape with the epidemiological benefits of vaccination. Here the escape pressure of Chapter 2 determines the cross-reactivity of existing immunity to an emerging strain, which may cause a new, non-overlapping, epidemic wave. For this second epidemic, we again use a deterministic model. We find that it is theoretically possible for the overall public health burden to be highest at intermediate vaccination coverages, but only if the relative adaptation rate in vaccinees is very high. Otherwise, vaccination reduces the overall public health burden.