Dynamic Modelling of Communicable and Non-Communicable Diseases

Abstract: This thesis consists of two papers dealing with the stochastic dynamic modelling of one communicable and one non-communicable disease respectively. In the first paper we derive a patient- and organ-specific measure for the estimated negative side effects of radiotherapy using a stochastic logistic birth-death process. We find that the region of a maximum tolerable radiation dose can be approximated by an asymptotic simplification  and illustrate our findings on brachytherapy for prostate cancer. The second paper is concerned with the stochastic dynamic modelling of infectious disease spread in a large population to explain routine rotavirus surveillance data.  More specifically, we show that a partially observed dynamical system which includes structural variability in the transmission rates but which is simple with respect to disease progression is able to explain the available incidence data. A careful mathematical analysis addresses parameter identifiability and a model-based estimate for the basic reproduction number $R_0$ is given. As inference method we use iterated filtering which is implemented in the \texttt{R} package \texttt{pomp}, available from the comprehensive R archive network (CRAN)