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Mathematical aspects of infectious disease dynamics : (doctoral thesis)
Boldin, Barbara, 1976-
The thesis "Mathematical aspects of infectious disease dynamics" is about model formulation, analysis and interpretation of four questions arising from biology or medicine. Suppose that a new ...population is introduced into a steady community. When the basic reproduction ratio ▫$R_0$▫ of the invading population exceeds 1, the invader is able to grow, while the invasion fails when ▫$R_0 < 1$▫. What happens when ▫$R_0$▫ passes the critical value 1? We provide the answer to this question, assuming that the populations are characterized by finitely many characteristics and that the dynamics is described as a deterministic process, either in a form of a parametrized system of differential equations or a parametrized map. We observe that population models, regardless of the biology that underlies them, take a specific form, which implies that the transition through ▫$R_0 = 1$▫ corresponds to a transcritical bifurcation. In a biological context we distinguish two cases of transcritical bifurcation, according to whether the positive branch of equilibria is subcritical or supercritical. We provide a formula that enables us to distinguish between the two scenarios. Another subject studied in the thesis is the evolution of virulence. Pathogens reproduce and are subject to natural selection at several different, but intertwined, levels. Viruses, for instance, compete for uninfected target cells within a single infected host, but also at the population level by competing for susceptible hosts. Increased reproduction inside a host may enhance transmission, but it may also increase host's mortality and consequently decrease transmission. Thus, the following question arises: how are these tendencies balanced in the course of evolution and to what extent do the two levels of reproduction influence the outcome? We study this question while relating the between-host dynamics to the dynamics inside a host. We couple the two levels of reproduction by incorporating the possibility of superinfection and study the evolution of the pathogen's within-host reproduction rate. The thesis also deals with the dynamics of pathogens found in intensive care units, such as Pseudomonas Aeruginosa and MRSA. Nosocomial infections are typically preceded by asymptomatic carriage at several body sites. Pathogen dynamics thus includes within-host transmission as well as transmission among patients. Different routes of transmission create a complex epidemiology, which is furthermore complicated by rapid patient turnover and small population sizes, typical for ICUs. We present a model that incorporates several colonization sites and evaluate the relative effects of barrier precautions and antibiotic prophylaxis on the prevalence of colonization. The last chapter of the thesis deals with the within-host dynamics of enterotoxigenic Escherichia coli (ETEC) in piglets. ETEC causes post-weaning diarrhoea, a disease that can lead to severe deterioration or even death in newly weaned piglets. We present a model describing the microbial dynamics in the intestine of a single piglet. We determine the Malthusian parameter for the case a piglet is infected with a single dose of ETEC. Since piglets come into contact with faeces containing the bacteria, we furthermore investigate the case a piglet is reinfected with a fraction of the shed bacteria.
Type of material - dissertation
Publication and manufacture - Enschede : [B. Boldin], 2007
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