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: 2018
• 资助国家: 加拿大
• 起止时间: 2018-01-01 至 2019-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=646183
• 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)的传染病年龄模型多年来一直被忽视，但它已成为研究流行病的有用工具。它允许一个包括隔离、隔离和处理在内的一般分区结构，并提供了一种比较不同控制策略的有效性的方法。然而，它不包括混合的异质性、通过接触感染者排出的病原体而感染的间接疾病传播、以及人群中耐药菌株的发展，包括对感染者的抗病毒治疗。我们计划研究感染年龄模型的扩展，以包括这些方面。*如果流行病的初始指数增长率能够通过实验估计，并且作为感染年龄的函数的平均传染性已知，那么估计基本繁殖数是可能的。无论模型中的混合是均匀的还是非均匀的，这一估计都是有效的。在均匀混合的情况下，最终大小关系给出了流行病的最终大小。然而，在异质混合的情况下，疫情的最终规模取决于人口中的混合。我们将研究在疫情初期观察到的额外信息足以估计疫情最终规模的问题。当治疗包括在模型中时，这应该有助于选择最佳的治疗策略。*在治疗可能导致疾病耐药株发展的模型中，提高治疗率可能会导致更多的疾病病例，这一结果已经在实验中观察到。一些隔间模型似乎预测到了这一点(来自模拟，但还不是来自理论分析)。我们计划开发一个感染年龄类型的模型，为这种结果提供条件，并导致避免这种行为的策略。例如，推迟开始治疗可能会减少抗药性的发展，从而缩小流行病的规模。*在霍乱中，感染可以通过直接接触或通过使用受感染者脱落的病原体污染的水来传播。在许多空气传播的疾病中，感染可能通过接触沉积在柜台或门把手或其他表面上的病原体而传播。这表明有必要对疾病传播中接触的含义进行更深入的研究，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。过去的大流行有时会出现波动，可能是因为接触率可能会随时间而变化，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相关参数的模型，从周期模型开始，扩展到一般的非自治模型。