Modelling Tuberculosis notification data

This thesis describes the development of three different Tuberculosis epidemiological models. An age dependent parametric statistical model; a compartmental, age dependent, differential/difference model; and a Markov chain model that allows for location effects in the transmission of TB. Recently collected data from countries that have experienced a long-term decline in TB incidence and in the annual risk of TB infection has exhibited a slow down in the decline of the TB notification rate. This stagnation effect has implications for projected reductions in TB incidence made by the World Health Organisation. Parametric modelling was used to carry out a preliminary analysis of TB data sets that were considered to exhibit such stagnation effects. The aim was to examine the age and time dependent effects exhibited by each data set and to identify any shred trends. This analysis was a precursor to a more structural age dependent compartmental modelling of this data. The third model, a Markov chain model, is distinct from the previous two models described above. It is constructed to examine the relative significance of local and global effects in the transmission of TB. Examining/modelling ‘household’/local effects is a relatively new branch of TB modelling that is considered important in the planning of TB control strategies and has previously been tackled with compartmental modelling. The simple Markov chain local effects model is used to examine a time-spatial TB data set from the Nyanza province in western Kenya. It is also shown how this new local/global effects model can be used in the design of community/clustered randomised trials.