Applications of the stochastic Galerkin method to epidemic models with uncertainty in their parameters

Full Text
Thesis (PhD Doctorate)
Doctor of Philosophy (PhD)
School of Environment and Sc
Science, Environment, Engineering and Technology
Infectious diseases are a serious problem throughout the world and are responsible for a large number of deaths annually. It is estimated that tuberculosis was respon- sible for 1.3 million deaths in 2016 worldwide. Malaria, a vector-transmitted dis- ease (transmitted to humans by mosquitoes), is responsible for almost half a million deaths annually. There are also many sexually transmitted diseases, such as chlamy- dia, genital herpes and gonorrhea, as well as the much more serious HIV/AIDS. In order to help prevent the spread of an infectious disease, we rst need to understand how the disease is spreading through the population, as well as how fast it is spreading. To do this, we need to build mathematical models for the disease. These are referred to as epidemic models. These models can also help predict the e ectiveness of interventions, such as treatment and vaccines. One of the most widely used methods for constructing an epidemic model is the use of compartmental models. Each person within the population is assigned to a speci c compartment, based upon their current status with regard to the disease. As their status changes, for example, if they contract the disease, they are moved to the appropriate compartment. Using the compartment model, a system of ordinary di erential equations can be derived that models the disease. As the system of ordinary di erential equations is usually non-linear, numerical solvers often need to be used as an analytic solution is rarely obtainable. While it is usually a relatively easy process to derive a model for a particular dis- ease, the parameters within these compartment models are rarely known and usually have to be estimated. Even for well-studied or seasonal diseases, these parameter values are usually not known with certainty and are instead given as probability distributions or simply as a plausible range of values. Since the parameter values are not known with certainty, it is important for this uncertainty to be incl