Modelling Infectious Diseases with discontinuities

对具有不连续性的传染病进行建模

• 批准号: RGPIN-2015-05414
• 负责人: Smith, Robert
• 金额: $ 1.24万
• 依托单位: University of Ottawa
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2016
• 资助国家: 加拿大
• 起止时间: 2016-01-01 至 2017-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=613538
• 关键词: Modelling; Infectious; Diseases; discontinuities

With the recent Ebola outbreak, the need for mathematical models to understand transmission between and within countries worldwide is critical. Although we have had some success in reducing disease prevalence in the Western world, many diseases continue to threaten developing nations, with over 50% of the world’s population at risk for one or more transmissable infections. Emerging infections such as West Nile Virus, SARS and swine flu have threatened the West in recent years, with potential pandemics from avian influenza, MERS and others looming. Tools at our disposal include vaccines, drugs, quarantine and education. Many of the effects of such interventions occur in short bursts or shocks. For example, National Immunization Days (NIDs) for measles, polio etc occur in many developing countries over 1–2 days, twice a year. During this time, millions of children are vaccinated at once. India vaccinates 174,000,000 children in a single NID. On a smaller scale, antiretroviral treatment for HIV involves taking pills, whose duration of action is about 20 minutes long, significantly shorter than the period of hours between pills. Quarantine often involves relocation of infected individuals occuring on a short timescale, whereas education can involve bursts of media information happening quickly. To analyse these effects, we will develop mathematical models using impulsive differential equations, impulse extension equations and Filippov systems. These methods are used to analyse short, sharp shocks, either in the state variables or their derivatives. By harnessing the power of short-burst modelling, a great many problems can be analysed using novel mathematical techniques. This will be useful in an applied context when dealing with biological, physical or other real-word models where precision of the results are important.

随着最近的埃博拉病毒爆发，需要数学模型来了解全球国家之间和国家之间的传播至关重要。尽管我们在降低西方世界的疾病患病率方面取得了一些成功，但许多疾病仍在威胁发展国家，世界上有50％以上人口有一种或多种可传播感染的风险。近年来，西尼罗河病毒，SARS和猪流感等新兴感染威胁着西方，并可能来自鸟类影响力，MERS和其他人迫在眉睫。我们可以使用的工具包括疫苗，药物，隔离和教育。 这种干预措施的许多影响发生在短爆发或冲击中。例如，在许多发展中国家，每年两次，许多发展中国家发生了麻疹，小儿麻痹症等的全国免疫日（NID）。在此期间，数以百万计的儿童立即接种疫苗。印度在一个NID中接种174,000,000名儿童。在较小的规模上，对HIV的抗逆转录病毒治疗涉及服用药丸，其作用持续时间约为20分钟，比药丸之间的小时时间短得多。检疫通常涉及在短时间内发生的感染者搬迁，而教育可能涉及迅速发生的媒体信息爆发。 为了分析这些效果，我们将使用冲动的微分方程，冲动扩展方程和Filippov系统开发数学模型。这些方法用于分析状态变量或其衍生物中的短而尖锐的冲击。通过利用短期建模的力量，可以使用新颖的数学技术来分析许多问题。在处理结果很重要的情况下，在处理生物，物理或其他现实词模型时，这将在应用的环境中有用。