Mwambi, Henry Godwell.Owino, Ngesa Oscar.Okango, Elphas Luchemo.2018-04-052018-04-0520172017http://hdl.handle.net/10413/15130Doctor of Philosophy in Statistics. University of KwaZulu-Natal, Pietermaritzburg 2017.In this thesis we develop and extend existing statistical models for spatial disease modeling and apply them to HIV, HSV-2 and malaria data. The availability of geo-referenced data and free software has seen many disease mapping models developed and applied in epidemiology, public health, agriculture and ecology among other areas. In chapter 1 we provide a background and developments in the field of disease mapping. We present in brief some limiting assumptions and how recent developments have tried to relax them. Chapter 2 introduces a model; the semi-parametric joint model to model HIV and HSV-2. The semi-parametric joint model performed better than the single models in terms of DIC. The limiting linearity assumption was relaxed by using the penalized regression splines for the continuous covariate age. The main focus of chapter 3 was to develop a model that relaxes the stationarity assumption. This was achieved by allowing the e ects of the covariates to vary spatially by using the conditional autoregressive model. This new model performed better than the stationary models. In chapter 4 we introduce a spatial temporal spatially varying covariate model. In this model, the covariates were allowed to vary both spatially and temporally. We fit this model to the Angolan malaria data. The fifth chapter presents a review of various assumptions in spatial disease modeling and improvements for some limiting assumptions such as the normality assumption on random effects and linearity assumption on the covariates. We use the non-parametric spatial model approach to relax the limiting normality assumption. The last part of chapter 5 involves developing a joint spatially varying model (an extension of the spatially varying coefficient model in chapter 3) and fitting it to the HIV and HSV-2 data. Chapter six of the study provides the overview of the thesis, the conclusion and presents areas of further studies.en-ZATheses - Statistics.Conditional autoregressive model.Disease mapping.Spatial temporal modeling.Dirichlet prior.Polya trees.HIV.Thesis