View Record

TitleMathematical modeling of TB disease dynamics in a crowded population.
AuthorMaku Vyambwera, Sibaliwe
SubjectCross effect
SubjectAwaiting trial
SubjectSentenced convict
SubjectTwo-group TB model
SubjectAlmost sure exponential stability
SubjectStochastic TB model
SubjectRemoval rate
SubjectInflow of infecteds
SubjectPrison TB model
SubjectCrowded environment
SubjectMulti-drug resistant TB
SubjectBasic reproduction number
SubjectOptimal control
SubjectLyapunov function
SubjectLocal and global stability of disease free
SubjectEndemic equilibrium
SubjectDisease-free equilibrium
AbstractPhilosophiae Doctor - PhD
AbstractTuberculosis is a bacterial infection which is a major cause of death worldwide. TB is a curable disease, however the bacterium can become resistant to the first line treatment against the disease. This leads to a disease called drug resistant TB that is difficult and expensive to treat. It is well-known that TB disease thrives in communities in overcrowded environments with poor ventilation, weak nutrition, inadequate or inaccessible medical care, etc, such as in some prisons or some refugee camps. In particular, the World Health Organization discovered that a number of prisoners come from socio-economic disadvantaged population where the burden of TB disease may be already high and access to medical care may be limited. In this dissertation we propose compartmental models of systems of differential equations to describe the population dynamics of TB disease under conditions of crowding. Such models can be used to make quantitative projections of TB prevalence and to measure the effect of interventions. Indeed we apply these models to specific regions and for specific purposes. The models are more widely applicable, however in this dissertation we calibrate and apply the models to prison populations.
PublisherUniversity of the Western Cape