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Title: Mathematical evolutionary epidemiology : limited epitopes, evolution of strain structures and age-specificity
Author: Cherif, Alhaji
ISNI:       0000 0004 5915 7336
Awarding Body: University of Oxford
Current Institution: University of Oxford
Date of Award: 2015
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We investigate the biological constraints determined by the complex relationships between ecological and immunological processes of host-pathogen interactions, with emphasis on influenza viruses in human, which are responsible for a number of pandemics in the last 150 years. We begin by discussing prolegomenous reviews of historical perspectives on the use of theoretical modelling as a complementary tool in public health and epidemiology, current biological background motivating the objective of the thesis, and derivations of mathematical models of multi-locus-allele systems for infectious diseases with co-circulating serotypes. We provide detailed analysis of the multi-locus-allele model and its age-specific extension. In particular, we establish the necessary conditions for the local asymptotic stability of the steady states and the existence of oscillatory behaviours. For the age-structured model, results on the existence of a mild solution and stability conditions are presented. Numerical studies of various strain spaces show that the dynamic features are preserved. Specifically, we demonstrate that discrete antigenic forms of pathogens can exhibit three distinct dynamic features, where antigenic variants (i) fully self-organize and co-exist with no strain structure (NSS), (ii) sort themselves into discrete strain structure (DSS) with non-overlapping or minimally overlapping clusters under the principle of competitive exclusion, or (iii) exhibit cyclical strain structure (CSS) where dominant antigenic types are cyclically replaced with sharp epidemics dominated by (1) a single strain dominance with irregular emergence and re-emergence of certain pathogenic forms, (2) ordered alternating appearance of a single antigenic type in periodic or quasi-periodic form similar to periodic travelling waves, (3) erratic appearance and disappearance of synchrony between discrete antigenic types, and (4) phase-synchronization with uncorrelated amplitudes. These analyses allow us to gain insight into the age-specific immunological profile in order to untangle the effects of strain structures as captured by the clustering behaviours, and to provide public health implications. The age-structured model can be used to investigate the effect of age-specific targeting for public health purposes.
Supervisor: Maini, Philip K. ; Gupta, Sunetra ; Dyson, Janet Sponsor: National Science Foundation (US)
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Mathematics ; Biology ; Disease (zoology) ; Ecology (zoology) ; Evolution (zoology) ; Biology and other natural sciences (mathematics) ; Dynamical systems and ergodic theory (mathematics) ; Functional analysis (mathematics) ; Mathematical biology ; Ordinary differential equations ; Partial differential equations ; Infectious diseases ; Epidemiology ; antigenic variation ; strain structure ; influenza ; age-structured model ; age-specificity