Mathematical models in epidemiology

流行病学中的数学模型

• 批准号: RGPIN-2016-03706
• 负责人: Brauer, Fred
• 金额: $ 1.31万
• 依托单位: University of British Columbia
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2020
• 资助国家: 加拿大
• 起止时间: 2020-01-01 至 2021-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=708700
• 关键词: Mathematical; models; epidemiology

The age of infection epidemic model of Kermack and McKendrick (1927) was neglected for many years but has become a useful tool in studying epidemics. It allows a general compartmental structure including quarantine, isolation, and treatment and affords a way to compare effectiveness of different control strategies. However, it does not include such aspects as heterogeneity of mixing, indirect disease transmission through infection by contact with pathogens shed by infected individuals, and the development of drug resistant strains in populations including antiviral treatment of infected individuals. We plan to study extensions of the age of infection model to include these aspects. If the initial exponential growth rate of an epidemic can be estimated experimentally and the mean infectivity as a function of age of infection is known, it is possible to estimate the basic reproduction number. This estimate is valid whether the mixing in the model is homogeneous or heterogeneous. In the case of homogeneous mixing, the final size relation gives the final size of the epidemic. In the case of heterogeneous mixing, however, the final size of the epidemic depends on the mixing in the population. We will study the question of what additional information from observation in the early stages of an epidemic would suffice to estimate the epidemic final size. This should aid in choosing an optimal treatment strategy when treatment is included in the model. In models where treatment may lead to development of a drug-resistant strain of the disease, increasing the treatment rate may lead to more disease cases, an outcome that has been observed experimentally. Some compartmental models appear to predict this (from simulations, but not yet from theoretical analysis). We plan to develop a model of age of infection type giving conditions for such outcomes and leading to strategies that would avoid such behaviour. For example, a delay in the beginning of treatment might decrease the epidemic size by decreasing the development of resistance. In cholera, infection may be transmitted either through direct contact or through use of water contaminated by shedding of pathogens by infected individuals. In many airborne diseases, infection may be transmitted through contact with pathogens that have been deposited on counters or door knobs or other surfaces. This suggests a need for a deeper examination of the meaning of contact in disease transmission, leading to a rethinking of the form of the disease contact transmission terms in general epidemic models. Pandemics in the past have sometimes come in waves, possibly because contact rates may vary in time, depending on temperature and humidity, or may be seasonal with variations related to the school year. To understand such waves, it will be necessary to study models with time-dependent parameters, beginning with periodic models and extending to general non-autonomous models.

Kermack和McKendrick（1927）的传染年龄流行病模型多年来被忽视，但已成为研究流行病的有用工具。它允许一个一般的隔间结构，包括检疫，隔离和治疗，并提供了一种方法来比较不同的控制策略的有效性。然而，它不包括混合的异质性、通过与受感染个体散发的病原体接触而感染的间接疾病传播以及群体中耐药菌株的发展，包括受感染个体的抗病毒治疗。我们计划研究扩展的年龄感染模型，包括这些方面。 如果一种流行病的初始指数增长率可以通过实验来估计，并且作为感染年龄的函数的平均传染性是已知的，那么就有可能估计基本繁殖数。无论模型中的混合是均匀的还是非均匀的，该估计都是有效的。在均匀混合的情况下，最终的规模关系给出了流行病的最终规模。然而，在异质混合的情况下，流行病的最终规模取决于人口中的混合。我们将研究这样一个问题，即在流行病的早期阶段观察到的额外信息足以估计流行病的最终规模。当治疗包括在模型中时，这应该有助于选择最佳治疗策略。 在治疗可能导致疾病耐药菌株发展的模型中，增加治疗率可能导致更多的疾病病例，这是实验观察到的结果。一些房室模型似乎可以预测这一点（从模拟，但尚未从理论分析）。我们计划开发一个感染类型的年龄模型，为这种结果提供条件，并导致避免这种行为的战略。例如，治疗开始的延迟可能会通过减少耐药性的发展来减少流行规模。 在霍乱中，感染可以通过直接接触或通过使用受感染者释放病原体污染的水传播。在许多空气传播疾病中，感染可能通过接触沉积在柜台、门把手或其他表面上的病原体传播。这表明需要更深入地研究疾病传播中接触的意义，从而重新思考一般流行病模型中疾病接触传播术语的形式。 过去的大流行有时是一波一波的，可能是因为接触率可能随时间而变化，取决于温度和湿度，或者可能是季节性的，与学年有关。为了理解这种波，有必要研究具有时间依赖参数的模型，从周期模型开始，扩展到一般的非自治模型。