Classic Hodgkin Lymphoma (cHL) has an annual incidence of 2.4 cases per 100 000 population in the UK, and is one of the most common malignancies diagnosed in young adults aged 15 to 34. The majority of younger patients have a good long-term outcome with between 80 and 90% disease-specific survival but cHL also affects older adults in whom the prognosis is significantly poorer. The role of tumour-associated macrophages (TAM) in cHL has gained much interest, with several studies reporting an association between high numbers of CD68-positive TAM and poor prognosis. There is also a question over the prognostic significance of Epstein-Barr Virus (EBV) infection which is implicated in up to 50% of cHL cases in developed countries. Published data suggests that EBV positivity in elderly patients may be associated with a poorer outcome, whereas in younger adults may be of prognostic benefit. Differences related to age are of interest particularly as an age-related decline in immunity has been linked with the development of certain subtypes of Non-Hodgkin Lymphoma in older patients. In a retrospective study, two separate cohorts of patients with cHL were examined with the aim of identifying: • Differences in the cellular composition of the tumour microenvironment in cHL which has arisen in young and elderly adult patients; • Differences in the cellular composition of the tumour microenvironment in cHL associated with or without EBV infection; • Factors within the tumour microenvironment which may influence prognosis and may be targeted for novel treatments. One group consisted of patients aged between 15 and 34 years at diagnosis and the other, of those aged 60 or over at presentation. Tissue obtained at the time of diagnosis was examined with regard to a number of factors related to the malignant cells and the surrounding microenvironment, including the number and phenotype of macrophages, the number of plasmacytoid dendritic cells and the number of malignant Hodgkin Reed-Sternberg (HRS) cells and non-malignant ‘background’ cells undergoing apoptosis. Comparisons were made between the two age groups, also taking into account the EBV-status of tumours, cHL subtype and gender. Results confirmed the current understanding that EBV-positive cHL is more common in older patients and has a strong, but not exclusive, association with the MCHL subtype. In addition, a strong link between young males and EBV-positive disease was shown. Macrophages were found to vary between the two age groups, in number and phenotype and there were clear differences associated with the presence or absence of EBV infection. While no definite link with outcome and macrophages was identified it was apparent that the implications of macrophages in the tumour microenvironment may differ between the two age groups. The number of apoptotic cells correlated closely with the number of macrophages and in the young the number of HRS cells was associated with prognosis. Investigation of the tumour microenvironment is complex and caution is needed in interpreting studies which do not differentiate between patients according to age, as tumour characteristics may have variable implications in different age groups. In this thesis a number of clinicopathological differences were identified between the two age groups. These point to the need for further larger studies to delineate how such age-related differences may or may not be associated with immune function and how this information could be translated into treatments to improve outcomes.

Significant progress has been made in understanding different scenarios for disease transmissions and behavior of epidemics in recent years. A considerable amount of work has been done in modeling the dynamics of diseases by systems of ordinary differential equations. But there are very few mathematical models that deal with the genetic mutations of a pathogen. In-fact, not much has been done to model the dynamics of mutations of pathogen explaining its effort to escape the host's immune defense system after it has infected the host. In this dissertation we develop an SIR model with variable infection age for the transmission of a pathogen that can mutate in the host to produce a second infectious mutant strain. We assume that there is a period of temporary immunity in the model. A temporary immunity period along with variable infection age leads to an integro-differential-difference model. Previous efforts on incorporating delays in epidemic models have mainly concentrated on inclusion of latency periods (this assumes that the force of infection at a present time is determined by the number of infectives in the past). We begin with reviewing some basic models. These basic models are the building blocks for the later, more detailed models. Next we consider the model for mutation of pathogen and discuss its implications. Finally, we improve this model for mutation of pathogen by incorporating delay induced by temporary immunity. We examine the influence of delay as we establish the existence, and derive the explicit forms of disease-free, boundary and endemic equilibriums. We will also investigate the local stability of each of these equilibriums. The possibility of Hopf bifurcation using delay as the bifurcation parameter is studied using both analytical and numerical solutions.

abstract: Rabies disease remains enzootic among raccoons, skunks, foxes and bats in the United States. It is of primary concern for public-health agencies to control spatial spread of rabies in wildlife and its potential spillover infection of domestic animals and humans. Rabies is invariably fatal in wildlife if untreated, with a non-negligible incubation period. Understanding how this latency affects spatial spread of rabies in wildlife is the concern of chapter 2 and 3. Chapter 1 deals with the background of mathematical models for rabies and lists main objectives. In chapter 2, a reaction-diffusion susceptible-exposed-infected (SEI) model and a delayed diffusive susceptible-infected (SI) model are constructed to describe the same epidemic process -- rabies spread in foxes. For the delayed diffusive model a non-local infection term with delay is resulted from modeling the dispersal during incubation stage. Comparison is made regarding minimum traveling wave speeds of the two models, which are verified using numerical experiments. In chapter 3, starting with two Kermack and McKendrick's models where infectivity, death rate and diffusion rate of infected individuals can depend on the age of infection, the asymptotic speed of spread $c^\ast$ for the cumulated force of infection can be analyzed. For the special case of fixed incubation period, the asymptotic speed of spread is governed by the same integral equation for both models. Although explicit solutions for $c^\ast$ are difficult to obtain, assuming that diffusion coefficient of incubating animals is small, $c^\ast$ can be estimated in terms of model parameter values. Chapter 4 considers the implementation of realistic landscape in simulation of rabies spread in skunks and bats in northeast Texas. The Finite Element Method (FEM) is adopted because the irregular shapes of realistic landscape naturally lead to unstructured grids in the spatial domain. This implementation leads to a more accurate description of skunk rabies cases distributions. / Dissertation/Thesis / Ph.D. Mathematics 2013