Year: 2011
Type: dissertation
Abstract: The evolution of drug resistance in human immunodeficiency virus (HIV) infection has \nbeen a focus of research in many fields, as it continues to pose a problem to disease \nprevention and HIV patient management. In addition to techniques of molecular \nbiology, studies in mathematical modelling have contributed to the knowledge here, \nbut many questions remain unanswered. This thesis explores the application of a \nnumber of hybrid stochastic/deterministic models of viral replication to scenarios \nwhere viral evolution may be clinically or epidemiologically important. The choice of \nappropriate measures of viral evolution/diversity is non-trivial, and this impacts on \nthe choice of mathematical techniques deployed. The use of probability generating \nfunctions to describe mutations occurring during early infection scenarios suggest \nthat very early interventions such as pre-exposure prophylaxis (PrEP) or vaccines \nmay substantially reduce viral diversity in cases of breakthrough infection. A modified \nsurvival analysis coupled to a deterministic model of viral replication during transient \nand chronic treatment helps identify clinically measurable indicators of the time it \ntakes for deleterious rare mutations to appear. Lastly, persistence of problematic \nmutations is studied through the use of deterministic models with stochastic averaging \nover initial conditions.
Author: Tinevimbo Shiri
Language: French
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2140262231