A Dissertation Submitted in Partial Fulfilment of the Requirements for the Degree of Doctor of Philosophy in Mathematical and Computer Sciences and Engineering of the Nelson Mandela African Institution of Science and TechnologyTaeniasis and cysticercosis are neglected food-borne diseases that pose challenges to food safety, human health and livelihood of rural livestock farmers. Cysticercosis reduces the market value for pigs and cattle by making pork and beef unsafe for consumption. In this research, deterministic and continuous time Markov chain (CTMC) models are formulated and analyzed to study the transmission dynamics of taeniasis and cysticercosis in humans, pigs and cattle. To study the dynamics of the diseases, we derived the basic reproduction numbers R01 for T. saginata and R0 for T. saginata and T. solium parasitic infections by next generation matrix method. Global stability for models’ equilibria are established by Lyapunov functions, Metzler matrix approach and cooperative systems theory whereas the normalized forward sensitivity index is employed to determine the sensitive parameters. The multitype branching process is adopted to compute the probability of diseases’ extinction or outbreak. The optimal control and cost-effectiveness analyses are used to determine the disease’s optimal strategy and most cost-effective strategy for disease’s control respectively. Analysis shows that both the disease free and endemic equilibria exist. The disease free equilibria are globally asymptotically stable when R01 < 1 and R0 < 1 whereas the endemic equilibria are globally asymptotically stable when R01 > 1 and R0 > 1. Sensitivity analysis for T. saginata bovine cysticercosis and human taeniasis model shows that T. saginata eggs to cattle transmission coefficient, human and cattle recruitment rates, the probability of humans to contract taeniasis, the open defecation rate by humans with taeniasis and the rate of eating raw or undercooked infected beef are the most pos itive sensitive parameters whereas the natural mortality rates for humans, cattle and T. saginata eggs, and the proportion of unconsumed infected beef are the most negative sensitive parame ters. Sensitivity results for taeniasis and cysticercosis transmission dynamics model due to T. solium and T. saginata tapeworms in humans, pigs and cattle show that human’s recruitment, the probability of humans to acquire taeniasis and the open defecation rate by humans with taeniasis are the most positive sensitive parameters whereas the T. saginata natural mortality rate is the most negative sensitive parameter. CTMC model results for T. saginata bovine cys ticercosis and human taeniasis show that the probability of diseases’ extinction is high when the diseases emerge from a small number of T. saginata eggs or from infected cattle and there is major diseases’ outbreak when the diseases emerge from infectious beef. On the other hand, CTMC model results for taeniasis and cysticercosis transmission dynamics due to T. solium and T. saginata tapeworms in humans, pigs and cattle indicate that the probability of disease’s ex tinction is high when the diseases emerge from humans with cysticercosis or a small number of taenia eggs in the environment. However, there is a major outbreak when the diseases emerge from humans with taeniasis or from infectious pork and beef. Basing on sensitivity analysis, various control strategies were designed. The T. saginata optimal control results indicate that i a strategy which targets improving meat cooking and treatment of infected humans is the opti mal strategy. The T. solium and T. saginata model results show that a strategy which combines meat inspection, treatment of humans with taeniasis and improving hygiene and sanitation is the most effective strategy for diseases’ control. Thus, to control the diseases at minimal cost, we recommend that more efforts be directed to treat humans with taeniasis and improve meat inspection, meat cooking, and hygiene and sanitation.