Despite advances m understanding the basic biology of HIV the aetiological agent of AIDS, medica1, public health and health education planning is plagued by uncertainties Mathematical models of the dynamics of HIV transmission and its progression to AIDS can clarify what data must be collected in order to predict future prevalence, make predictions about the likely effect of future intervention pobcies and provide predictions for several decades ahead. The motivation of this research is to provide reliable estimates of the incidence of HIV infection and AIDS in the Irish population.ududIn Chapters 1 and 2 we discuss the background to the disease in Ireland and theudrole of mathematical modelling in the spread AIDS. From this we show where key epidemiological data is lacking and how models to date have concentrated on the spread of the disease within the homosexual population. In Chapter 3 we describe the adjustment of the number of AIDS cases to allow for reporting delays Subsequently we consider the solution of the integral equation models generated by the back-projection method for the adjusted AIDS cases. In Chapter 4 we improve upon the estimates of the incidence of HIV infection found in Chapter 3 by evaluating the integral arising in back-projection, in terms of a gamma function plus a remainder in the form of a series in t. We also provide error bounds for the remainder. This new solution allows us to predict new and more reliable estimates of the level of HIV infection m Ireland.ududIn Chapter 5 we provide estimates of the minimum number of deaths from AIDS, based on the number of AIDS cases known to the Department of Health and the distribution of the length of survival times after the onset of AIDS.ududThe results of a HIV transmission survey are presented in Chapter 6 These provide detailed information on the habits and behaviour of those at risk of HIV infection and allow us to derive preliminary model parameters. Finally in Chapter 7 we develop and implement a nonlinear deterministic differential equation model for the spread of HIV and its progression to AIDS m the Irish IVDU and homosexual populations. We examine the effects of likely intervention policies on the extent and spread of the disease and we make recommendations based on our thesis findings.
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机译：尽管在了解艾滋病毒的基本生物学，艾滋病，医学，公共卫生和健康教育计划的认识上取得了进步，但不确定性困扰着艾滋病毒传播及其演变为艾滋病的动力学的数学模型可以阐明必须收集哪些数据才能预测未来的患病率，对未来的干预措施可能产生的影响进行预测，并提供未来几十年的预测。这项研究的目的是提供有关爱尔兰人群中HIV感染和AIDS发生率的可靠估计。 ud ud在第1章和第2章中，我们讨论了爱尔兰疾病的背景以及传播过程中的数学建模方法艾滋病。由此可见，缺乏主要的流行病学数据以及迄今为止的模型如何集中于该疾病在同性恋人群中的传播。在第三章中，我们描述了艾滋病病例数量的调整以允许报告延误。随后，我们考虑了反投影方法为调整后的艾滋病病例生成的积分方程模型的解。在第4章中，我们通过评估反投影中产生的积分（以伽马函数加上t序列中的余数形式）来改进在第3章中发现的HIV感染率的估计。我们还为其余部分提供误差范围。这种新的解决方案使我们能够预测爱尔兰的HIV感染水平的新的和更可靠的估计。 ud ud在第5章中，我们将根据该部门已知的AIDS病例数来估计艾滋病最小死亡人数。艾滋病发作后的健康状况和生存时间长度的分布。 ud ud第6章介绍了艾滋病毒传播调查的结果。这些报告提供了有关易感染艾滋病毒的人的习惯和行为的详细信息，并允许我们得出初步模型参数。最后，在第7章中，我们为爱尔兰IVDU和同性恋人群中HIV的传播及其向AIDS的发展建立并实施了非线性确定性微分方程模型。我们研究了可能的干预政策对疾病的程度和传播的影响，并根据我们的论文发现提出了建议。
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