No description available.

This thesis presents mathematical models for the dynamics of vaccine preventable diseases, specifically looking at the New Zealand situation. Through the use of integral and differential equations, we develop models and compare the results of these to known data. Using game theory analysis we determine and compare the proportion of the population that needs to be vaccinated in order to minimise the expected costs to the individuals in the population and to the community. Two different scenarios and methods are considered, where the effects of vaccination last only one epidemic cycle (using an integral equation method) and where vaccination is effective over an entire lifetime (using a differential equation method). For both scenarios, we find that the minimum cost for the individuals is reached when a lower proportion of the population is vaccinated than needed for the minimum cost to the community. We then elaborate on the integral equation method to produce a model for repeated epidemics of measles in a population, where a discrete mapping is used to include the year to year demographics of the population. The results of this model show a different epidemic pattern then that produced from a differential equation model, with numerical problems encountered. From here on, we use differential equation models in our analysis. A critique and extension to an existing model for the dynamics of the hepatitis B virus is presented, with discussion on the appropriateness of the model’s construct for predicting the incidence of infection. Alternative differential equation models for hepatitis B virus and immunisation that include splitting the population into age groups with nonhomogeneous mixing are presented. The results of these models are compared with the known data on incidence of infection and carriage in New Zealand, showing how affective different immunisation schedules may have been. Differential equation models are then presented for meningococcal B virus epidemiology in New Zealand, with the models incorporating different features of the virus until the best model is found that fits the New Zealand data. Each model is compared with the known incidence of infection, with the population being either treated as a whole or split into age groups with non-homogeneous mixing. The effect of vaccination is included in this model so that we can explore the future of the infection in the population, and how best to tackle any future epidemics. The model shows that the current vaccination campaign was the best solution for controlling the epidemic, but there will be epidemics in the future that will need subsequent vaccination campaigns to limit the number of infections.

A indústria de seguros é uma atividade econômica relativamente jovem, possuindo raízes na revolução industrial. O desenvolvimento dessa indústria ocorreu de forma bastante intensa durante o século passado, quando a atividade passou a ser inserida na área de gestão de riscos. As Companhias de Seguros que trabalham nesse ambiente de negócio fundamentam todo o processo de precificação dos seus produtos em rígidas bases técnicas e atuariais. O presente trabalho dedica-se ao estudo dessas questões, abordando especificamente os seguros de vida, com ênfase à cobertura de morte. A pesquisa tem por objetivo comparar duas modalidades distintas de seguros que são ofertadas ao mercado: o seguro de vida individual e o seguro de vida em grupo. Embora ofereçam aos consumidores coberturas bastante similares, ambas as modalidades devem obedecer a requisitos e princípios técnicos diferenciados por parte das instituições que fazem a sua gestão. / The insurance industry is a relatively young economic activity; its bases are found in the industrial revolution. The development of such industry occurred in a very intense way in the last century, when the activity started being placed in the area of management of risks. The insurance companies that work in this business environment base the whole pricing process of their products on rigid technical and actuarial bases. The present work aims at studying these questions, focusing on the life insurance, with emphasis on the death coverage. The research intends to explore and compare two distinct modalities of insurance that are offered to the market: the individual life insurance and the group life insurance. Even though they offer similar coverage, they must fulfill requirements and different technical principles ruled by the institutions which are responsible for their management.

A indústria de seguros é uma atividade econômica relativamente jovem, possuindo raízes na revolução industrial. O desenvolvimento dessa indústria ocorreu de forma bastante intensa durante o século passado, quando a atividade passou a ser inserida na área de gestão de riscos. As Companhias de Seguros que trabalham nesse ambiente de negócio fundamentam todo o processo de precificação dos seus produtos em rígidas bases técnicas e atuariais. O presente trabalho dedica-se ao estudo dessas questões, abordando especificamente os seguros de vida, com ênfase à cobertura de morte. A pesquisa tem por objetivo comparar duas modalidades distintas de seguros que são ofertadas ao mercado: o seguro de vida individual e o seguro de vida em grupo. Embora ofereçam aos consumidores coberturas bastante similares, ambas as modalidades devem obedecer a requisitos e princípios técnicos diferenciados por parte das instituições que fazem a sua gestão. / The insurance industry is a relatively young economic activity; its bases are found in the industrial revolution. The development of such industry occurred in a very intense way in the last century, when the activity started being placed in the area of management of risks. The insurance companies that work in this business environment base the whole pricing process of their products on rigid technical and actuarial bases. The present work aims at studying these questions, focusing on the life insurance, with emphasis on the death coverage. The research intends to explore and compare two distinct modalities of insurance that are offered to the market: the individual life insurance and the group life insurance. Even though they offer similar coverage, they must fulfill requirements and different technical principles ruled by the institutions which are responsible for their management.

A indústria de seguros é uma atividade econômica relativamente jovem, possuindo raízes na revolução industrial. O desenvolvimento dessa indústria ocorreu de forma bastante intensa durante o século passado, quando a atividade passou a ser inserida na área de gestão de riscos. As Companhias de Seguros que trabalham nesse ambiente de negócio fundamentam todo o processo de precificação dos seus produtos em rígidas bases técnicas e atuariais. O presente trabalho dedica-se ao estudo dessas questões, abordando especificamente os seguros de vida, com ênfase à cobertura de morte. A pesquisa tem por objetivo comparar duas modalidades distintas de seguros que são ofertadas ao mercado: o seguro de vida individual e o seguro de vida em grupo. Embora ofereçam aos consumidores coberturas bastante similares, ambas as modalidades devem obedecer a requisitos e princípios técnicos diferenciados por parte das instituições que fazem a sua gestão. / The insurance industry is a relatively young economic activity; its bases are found in the industrial revolution. The development of such industry occurred in a very intense way in the last century, when the activity started being placed in the area of management of risks. The insurance companies that work in this business environment base the whole pricing process of their products on rigid technical and actuarial bases. The present work aims at studying these questions, focusing on the life insurance, with emphasis on the death coverage. The research intends to explore and compare two distinct modalities of insurance that are offered to the market: the individual life insurance and the group life insurance. Even though they offer similar coverage, they must fulfill requirements and different technical principles ruled by the institutions which are responsible for their management.

In this work we describe the basic facts of non-life insurance and then explain risk processes. In particular, we will explain in detail the asymptotic behavior of the probability that an insurance product may end up in ruin during its lifetime. As expected, the behavior of such asymptotic probability will be highly dependent on the tail distribution of each claim. / En este artículo describimos los conceptos básicos relacionados a seguros que no sean de vida y luego explicamos procesos de riesgo. En particular, tratamos al detalle el comportamiento asintótico de la probabilidad de que un producto sea declarado en ruina. Como es suponible, el comportamiento en el horizonte depende de la cola de la distribución de las primas.