Thesis (PhD)--Stellenbosch University, 2013. / ENGLISH ABSTRACT: In Uganda, cattle are an important reservoir of Trypanosoma brucei rhodesiense, a parasite that causes human African trypanosomiasis or sleeping sickness. We developed mathematical models to examine the transmission of T. b. rhodesiense by tsetse vector species, Glossina fuscipes fuscipes in a host population that consists of humans, domestic and wild mammals, and reptiles. The models were developed and analysed based on the situation in Tororo district in Southeastern Uganda, where sleeping sickness is endemic and which has a cattle and human population of 40, 000 and 500, 000, respectively. Assuming populations of cattle and humans only, the impact of mass chemoprophylaxis and vector control through insecticide-treated cattle (ITC) is evaluated. Keeping 12% or 82% of the cattle population on insecticides that have an insecticidal killing effect of 100% at all times or trypanocides that have 100% efficacy, respectively, can lead to the control of T. b. rhodesiense in both humans and cattle. Optimal control of T. b. rhodesiense is shown to be achieved through ITC alone or a combination of chemoprophylaxis and ITC, the former being the cheapest control strategy. Allowing for the waning effect of insecticides and including wildhosts, T. b. rhodesiense control can be achieved by keeping 21% or 27% of the cattle population on insecticides through whole-body or restricted application, respectively. Restricting the treatment of insecticides to adult cattle only would require 24% or 33% of the adult cattle population to be kept on insecticides through whole-body or restricted application, respectively, to control T. b. rhodesiense. A cost-effectiveness and benefit-cost analysis of using ITC to control T. b. rhodesiense show that restricted application of insecticides is a cheaper and more beneficial strategy compared to whole-body treatment. The results of the study show that the restricted application of insecticides on cattle provides a cheap, safe and farmer-based strategy for controlling tsetse and trypanosomiasis. / AFRIKAANSE OPSOMMING: In Uganda is beeste ’n belangrike reservoir van Trypanosoma brucei rhodesiense, ’n parasiet wat tripanosomiase of slaapsiekte in mense veroorsaak. Ons het wiskundige modelle ontwikkel wat die oordrag van T. b. Rhodesiense deur tesetse vektor spesies, Glossina fuscipes fuscipes in ’n draer populasie wat bestaan uit mense, mak en wilde diere en reptiele, ondersoek. Die modelle was ontwikkel en geanaliseer gebaseer op die oordrag situasie in die Tororo distrik in Suidoostelike Uganda, ’n gebied waar slaapsiekte endemies is en wat ’n populasie van 40, 000 beeste en 500, 000 mense het. Die impak van massa chemoprofilakse en vektor beheer deur insekdoder-behandelde beeste is gevalueer onder die aanname van bees en mens populasies alleenlik. Beheer oor T. b. Rhodesiense in beide mense en beeste kan verkry word deur of 12% van die bees populasie te behandel met ’n insekdoder wat 100% effektief is ten alle tye of 82% van die bees populasie te behandel met tripanosiedes wat 100% effektief is. Daar is aangetoon dat optimale beheer van T. b. Rhodesiense bereik kan word deur die gebruik van insekdoders alleenlik of ’n kombinasie van insekdoders en chemoprofilakse, hoewel eersgenoemde die goedkoopste strategie is. Wanneer die kwynende effek van insekdoders asook wilde diere as draers in ag geneem word, kan T. b. Rhodesiense beheer verkry word deur 21% van beeste se hele liggaam met insekdoders te behandel of 27% gedeeltelik te behandel. As slegs volwasse beeste met insekdoders behandel word, moet 24% se hele liggaam of 33% gedeeltelik behandel word vir beheer van T. b. Rhodesiense. ’n Koste-effektiwiteit en voordeel-koste analise van insekdoders as beheermaatstaf vir T. b. Rhodesiense toon aan dat gedeeltelike behandeling van die bees se liggaam die goedkoper en meer voordelige strategie is in vergelyking met behandeling van die hele liggaam. Die resultate van die studie wys dat gedeeltelike behandeling van beeste met insekdoders ’n goedkoop, veilige en landbouer-gebaseerde strategie is om tsetse en tripanosomiase te beheer.