Stochastic dynamic modelling and statistical analysis of infectious disease spread and cancer treatment

Sammanfattning: Mathematical models have proven valuable for public health decision makers as they can provide insights into the understanding, control and, ultimately, the prevention of diseases. This thesis contains four manuscripts dealing with stochastic dynamic modelling and statistical analysis of infectious disease spread and optimization of cancer treatment.Paper I is concerned with deriving a patient- and organ-specific measure for the estimated negative side effects of radiotherapy using a stochastic logistic birth-death process. Our analysis shows that the region of a maximum tolerable radiation dose can be related to the solution of a logistic differential equation; we illustrate our results for brachytherapy for prostate cancer.Paper II and III deal with inference for stochastic epidemic models. Parameter estimation for this model class can be challenging as disease spread is usually only partially observed, e.g. in the form of accumulated reported incidences within specified time periods. To perform inference for these types of models, a useful method for maximum likelihood estimation is iterated filtering which takes advantage of the fact that it is relatively easy to generate samples from the underlying transmission process while the likelihood function for the given data is intractable.Paper II is an application-oriented introduction to iterated filtering via the R package pomp (King et al., 2016) which contains a wide collection of simulation-based inference methods for partially observed Markov processes. We review the theoretical background of the method and discuss by two examples its performance and some associated practical difficulties.Paper III is concerned with model selection for partially observed epidemic models that differ with respect to the amount of variability they allow for and parameter estimation of those models from routinely collected surveillance data. We illustrate the model selection and inference framework via the R package pomp for rotavirus transmission in Germany, however, the method can be easily adapted to other diseases.In Paper IV we develop a transmission model for hepatitis C virus (HCV) infection among people who inject drugs (PWIDs) to enable countries to monitor their progress towards HCV elimination. In the scope of the WHO’s commitment to viral hepatitis elimination, this topic is highly relevant to public health since injection drug use is the main route of transmission in many countries. From the model and using surveillance data, we derive estimates of four key HCV-indicators. Furthermore, the model can be used to investigate the impact of two interventions, direct-acting antiviral drug treatment and needle exchange programs, on the disease dynamics. In order to make the model and its output accessible to relevant users, it is made available through a Shiny app.