abstract: The 2009-10 influenza and the 2014-15 Ebola pandemics brought once again urgency to an old question: What are the limits on prediction and what can be proposed that is useful in the face of an epidemic outbreak? This thesis looks first at the impact that limited access to vaccine stockpiles may have on a single influenza outbreak. The purpose is to highlight the challenges faced by populations embedded in inadequate health systems and to identify and assess ways of ameliorating the impact of resource limitations on public health policy. Age-specific per capita constraint rates play an important role on the dynamics of communicable diseases and, influenza is, of course, no exception. Yet the challenges associated with estimating age-specific contact rates have not been decisively met. And so, this thesis attempts to connect contact theory with age-specific contact data in the context of influenza outbreaks in practical ways. In mathematical epidemiology, proportionate mixing is used as the preferred theoretical mixing structure and so, the frame of discussion of this dissertation follows this specific theoretical framework. The questions that drive this dissertation, in the context of influenza dynamics, proportionate mixing, and control, are: I. What is the role of age-aggregation on the dynamics of a single outbreak? Or simply speaking, does the number and length of the age-classes used to model a population make a significant difference on quantitative predictions? II. What would the age-specific optimal influenza vaccination policies be? Or, what are the age-specific vaccination policies needed to control an outbreak in the presence of limited or unlimited vaccine stockpiles? Intertwined with the above questions are issues of resilience and uncertainty including, whether or not data collected on mixing (by social scientists) can be used effectively to address both questions in the context of influenza and proportionate mixing. The objective is to provide answers to these questions by assessing the role of aggregation (number and length of age classes) and model robustness (does the aggregation scheme selected makes a difference on influenza dynamics and control) via comparisons between purely data-driven model and proportionate mixing models. / Dissertation/Thesis / Doctoral Dissertation Applied Mathematics for the Life and Social Sciences 2016

This paper presents a time-series model, analyzing the relationship between age structure and economic performance in developed countries, using age demographic growth rates as a measure of changes in age structure, and the growth rate of output per capita for economic growth. The results show the growth rate of output per capita has a positive relationship with the working age demographic, and negative relationships with the young and elderly population growth rates. The dataset used is retrieved from the databases of the OECD and the World Bank and includes 32 countries during the period of 1970-2020. The analysis includes a traditional time-series model, a country fixed effect model, a time-fixed effect model, with results for 1970-2020, and each decade separately. Based on the results, countries that have the highest working age population growth rate have the most economic growth, especially in periods where negative effects of the dependent age demographics are minimized.

Using Monte Carlo simulations and analytic methods, we examine the dynamics of inter-species competition using the Penna bit-string model. We begin with a study of the steady state with a single species, then proceed to the dynamics of competition between two species. When the species are not evenly matched in fitness, a simple differential equation provides a satisfactory model of the behavior of the system. However, when the species are equally fit, we show that a model, originally proposed to describe population genetics [Fisher,Wright], is required. When mutations are allowed between the competing species, the dynamics becomes more interesting. The mutation rate becomes a parameter that dictates the steady state behavior. If the two species are not equally fit, the value of the mutation rate determines whether the longer-lived or faster reproducing species is favored. With two species that are equally fit, the steady state varies with mutation rate from a single peaked to a double peaked distribution. This behavior is shown to be well described by an extension to the Fisher-Wright model mentioned above. Finally, we describe the preliminary results of a few new lines of investigation, and suggest ideas for further study of the dynamics of this model. / Ph. D.

Statistical age-structured models are widely used in fisheries stock assessment. These models have been become increasingly complex over recent decades, allowing them to incorporate a larger variety of fisheries data. These typically include information regarding annual fishery yields, indices of abundance and catch composition data, which reflect the distribution of ages in the harvested population each year. In some fisheries, age composition can be determined annually through the examination of annuli on hard parts, such as otoliths or scales. These methods are, however, costly, time consuming and require a relatively high level of expertise on the part of data collectors. Alternatively, length frequency distributions within the annual catch are relatively simple and inexpensive to acquire, and can be employed to extrapolate age structure given that some information regarding age length relationships in the population is known. This type of data is therefore critical for many age-structured fisheries models. Length frequency data are compiled from length measurements of a sub-sample of the commercial catch. Even when they derive from a relatively large sample size, however, these data depend on a number of biological, economic and logistical factors. In some fisheries, for example, larger, more valuable fish may be separated from the overall catch and sold quickly, before port samplers have chance to gather sub-samples (Burns et al. 1983). This can reduce the relative frequency of large individuals in length frequency data. Alternatively, fish may become stratified in holding bins or storage containers according to size, due to their slippery texture and body shape (Hilborn and Walters 1992). With smaller, shorter individuals falling to the bottom where they are less likely to be picked up and measured, length frequency data may contain a disproportionately high frequency of large fish. This study used simulations to examine the impact of these two types of bias in length frequency data on a statistical age-structured model. The model, which was similar to those used in stock assessments for black sea bass (Centropristis striata) and gag (Mycteroperca microlepis) in the southeastern United States, produced erroneous population estimates when given biased data. Length frequency data that contained too many small fish caused stock status estimates to became overly pessimistic, indicating that populations were more heavily depleted than was actually the case. This type of bias supported overly conservative management measures, which posed an unnecessary cost to fishermen. Conversely, when the data included too many large fish, estimates of stock status were overly optimistic, and supported management actions that did not effectively protect the stock from overfishing. These results indicate that the quantity of length frequency data alone does not protect against bias when using complex age-structured models. The likelihood and magnitude of bias in these must also be examined in order to determine whether results are likely to be biased. For a given fishery, it is therefore critical that potential sources of bias in length frequency data be thoroughly inspected, and that the modeling approach used to assess the stock be appropriate based on the availability and accuracy of the data. / Master of Science

Human activity and other events can cause environmental changes to the habitat of organisms. The environmental changes effect the vital rates for a population. In order to predict the impact of these environmental changes on populations, we use two different models for population dynamics. One simpler linear model that ignores environmental competition between individuals and another model that does not. Our population models take into consideration the age distribution of the population and thus takes into consideration the impact of demographics. This thesis generalize two theorems, one for each model, developed by Sonja Radosavljevic regarding long term upper and lower bounds of a population with periodic birth rate ; see [6] and [5]. The generalisation consist in including the case where the periodic part of the birth rate can be expressed with a finite Fourier series and also infinite Fourier series under some constraints. The old theorems only considers the case when the periodic part of the birth rate can be expressed with one cosine term. From the theorems we discover a connection between the frequency of oscillation and the effect on population growth. From this derived connection we conclude that periodical changing environments can have both positive and negative effects on the population.

This study deals with the development of the number and the age and sex structure of Czech physicians according their medical specialty in the period 2000-2010. The aim of the study is to identify which medical specialties are already problematic or could face the lack of physicians and demographic ageing in the future and on the other hand which medical specialties are popular among young physicians. Firstly, the Czech health system and particular groups of health workforce are introduced. After that follows the analysis of the number and the sex and age structure according their medical specialty. The cluster analysis which produces groups of medical specialties with similar characteristics of development of the number and the structure was used for schematic overview. The second part of the study is focused on the most numerous fourteen medical specialties. The number of medical school graduates, the number of attestations and the development of workload of physicians regarding the number of ambulant treatment and hospitalization is taken into account.

Analysis and forecast of the number and demographic structure of dentists in the Czech Republic Abstract Demographic aging and the associated fear of shortage of dentists in the near future is currently frequent topic. This problem is caused in the late seventies and early eighties, when unusually large number of graduates of dental disciplines finished studium and became dentists. In the next few years, the number of graduates declined significantly, and then held for decades at a constant level. This dominant age category of dentists has currently reached retirement age. A large number of old dentists provoked a reaction in the form of re-increase university capacity and current number of graduates is comparable with numbers in the period before 35-40 years ago. The purpose of this paper is to examine this changes and decide, if this changes were sufficient to keep current situation in the field of dental health care. Keywords: dentists, aging of dentists, forecast, age structure, Czech republic

This paper applies the methods of multi-dimensional mathematical demography to project national populations based on alternative assumptions on future, fertility, mortality, migration and educational transitions that correspond to the five shared socioeconomic pathways (SSP) storylines. In doing so it goes a significant step beyond past population scenarios in the IPCC context which considered only total population size. By differentiating the human population not only by age and sex - as is conventionally done in demographic projections - but also by different levels of educational attainment the most fundamental aspects of human development and social change are being explicitly addressed through modeling the changing composition of populations by these three important individual characteristics. The scenarios have been defined in a collaborative effort of the international Integrated Assessment Modeling community with themedium scenario following that of a major new effort by the Wittgenstein Centre for Demography and Global Human Capital (IIASA, OEAW, WU) involving over 550 experts from around the world. As a result, in terms of total world population size the trajectories resulting from the five SSPs stay very close to each other until around 2030 and by the middle of the century already a visible differentiation appears with the range between the highest (SSP3) and the lowest (SSP1) trajectories spanning 1.5 billion. The range opens up much more with the SSP3 reaching 12.6 billion in 2100 and SSP1 falling to 6.9 billion which is lower than today's world population.

Student Number: 9811822T - MSc Dissertation - School of Computational and Applied Mathematics - Faculty of Science / This dissertation reviews population dynamic type models of viral infection and introduces some new models to describe strain competition and the infected cell lifecycle. Laboratory data from a recent clinical trial, tracking drug resistant virus in patients given a short course of monotherapy is comprehensively analysed, paying particular attention to reproducibility. A Bayesian framework is introduced, which facilitates the inference of model parameters from the clinical data. It appears that the rapid emergence of resistance is a challenge to popular unstructured models of viral infection, and this challenge is partly addressed. In particular, it appears that minimal ordinary differential equations, with their implicit exponential lifetime (constant hazard) distributions in all compartments, lack the short transient timescales observed clinically. Directions for future work, both in terms of obtaining more informative data, and developing more systematic approaches to model building, are identified.

We construct a new dataset of inequality in educational attainment by age and sex at the global level. The comparison of education inequality measures across age groups allows us to assess the effect of inter-generational education attainment trends on economic growth. Our results indicate that countries which are able to reduce the inequality of educational attainment of young cohorts over time tend to have higher growth rates of income per capita. This effect is additional to that implied by the accumulation of human capital and implies that policies aiming at providing broad-based access to schooling have returns in terms of economic growth that go beyond those achieved by increasing average educational attainment. / Series: WWWforEurope