La Modélisation spatio-temporelle permet la prédiction d’une variable régionalisée à des sites non observés du domaine d’étude, basée sur l’observation de cette variable en quelques sites du domaine à différents temps t donnés. Dans cette thèse, l’approche que nous avons proposé consiste à coupler des modèles numériques et statistiques. En effet en privilégiant l’approche bayésienne nous avons combiné les différentes sources d’information : l’information spatiale apportée par les observations, l’information temporelle apportée par la boîte noire ainsi que l’information a priori connue du phénomène. Ce qui permet une meilleure prédiction et une bonne quantification de l’incertitude sur la prédiction. Nous avons aussi proposé un nouveau critère d’optimalité de plans d’expérience incorporant d’une part le contrôle de l’incertitude en chaque point du domaine et d’autre part la valeur espérée du phénomène. / Spatio-temporal modeling allows to make the prediction of a regionalized variable at unobserved points of a given field, based on the observations of this variable at some points of field at different times. In this thesis, we proposed a approach which combine numerical and statistical models. Indeed by using the Bayesian methods we combined the different sources of information : spatial information provided by the observations, temporal information provided by the black-box and the prior information on the phenomenon of interest. This approach allowed us to have a good prediction of the variable of interest and a good quantification of incertitude on this prediction. We also proposed a new method to construct experimental design by establishing a optimality criterion based on the uncertainty and the expected value of the phenomenon.

Since the earliest reported cases of HIV/AIDS probably in 1959 in Africa, there has been a consistent progression in the new HIV/AIDS infection cases. In South Africa, Gauteng, records one of the highest HIV/AIDS prevalence rates in the country. The Department of Health (DOH) South Africa conducts ongoing studies on HIV/AIDS at provincial levels; these studies monitor the prevalence of HIV/AIDS amongst pregnant women attending antenatal clinics, as a tool for determining and monitoring the prevalence, trends, patterns and spread of the disease in the general population. This study analyses sentinel and spatial data collected from the (DOH) and Statistics South Africa (StatsSA) respectively, and depicts them in the form of spatial maps, and then critically analyses the spatial patterns that occur. The research findings would hopefully contribute to the overall knowledge of HIV/AIDS and provide framework and relevant literature for further investigation. / Geography / M.Sc. (Geography)

Since the earliest reported cases of HIV/AIDS probably in 1959 in Africa, there has been a consistent progression in the new HIV/AIDS infection cases. In South Africa, Gauteng, records one of the highest HIV/AIDS prevalence rates in the country. The Department of Health (DOH) South Africa conducts ongoing studies on HIV/AIDS at provincial levels; these studies monitor the prevalence of HIV/AIDS amongst pregnant women attending antenatal clinics, as a tool for determining and monitoring the prevalence, trends, patterns and spread of the disease in the general population. This study analyses sentinel and spatial data collected from the (DOH) and Statistics South Africa (StatsSA) respectively, and depicts them in the form of spatial maps, and then critically analyses the spatial patterns that occur. The research findings would hopefully contribute to the overall knowledge of HIV/AIDS and provide framework and relevant literature for further investigation. / Geography / M.Sc. (Geography)