Dynamics and control of infectious disease epidemics: scaling from within-host to population-level models

正如西非2014-2016年埃博拉疫情所证明的那样，传染病疫情构成的威胁是一个巨大的持续关切。数学模型越来越多地被用于预测流行病的发展和规划干预措施。常用的流行病学模型通常假设每个感染宿主具有同等的传染性。在现实中，感染性和症状表现都会随着感染过程的不同而变化。在这个项目中，我们将开发在种群水平模型中嵌套宿主内病原体动态的方法。我们将调查在模型中包括宿主内的动态是否会影响对控制干预措施有效性的预测。不同模型的预测之间的差异可能会引起寻求准确预测的政策制定者的兴趣。这个项目将分为四个部分，总结如下。将不同的方法联系起来，以便在流行病模型中包括可变的传染性。通过包括多个感染室，依赖于时间的传染性可被合并到常微分方程式(ODE)室模型中，宿主通过这些感染室前进，并且它们的感染度在这些室之间变化。另一种方法是使用积分-微分方程(IDE)模型。我们的目标是首次将这两种方法严格地联系起来，考虑到ODE模型中感染间隔的数量趋于无穷大的限制。症状表达的变异性对监测的影响。传染病监测通常被建模为一个观察过程。换句话说，假设检测到一定比例的感染主机，并且假设每个主机的检测概率相同。然而，在现实中，检测概率在感染过程中会发生变化。我们将使用上面1中描述的ODE模型来研究这种可变性对观察到的流行病动态的模型预测的影响。我们还将开发新的模式，将监测建模为一个动态过程，不仅涉及对感染宿主的检测，而且还涉及对感染宿主的控制。将随机模型和确定性模型联系起来。虽然确定性的流行病模型在数值上求解速度很快，但现实世界的流行病系统本质上是随机的。确定性方程不仅描述了许多流行病的平均行为，而且还描述了变异性，它可以通过使用矩闭合技术从随机模型中推导出来。我们的目标是开发新的矩闭合技术，并将其应用于包含可变传染性的随机流行病学模型。通过这种方式，我们可以看到我们在上面1和2中开发的模型与那些包含随机性的模型相比是如何发展的。在控制埃博拉疫情方面的应用。在埃博拉病毒感染过程中，传染性水平和症状表现都有很大差异。此前，简单的Seir区隔模型被用来模拟埃博拉的传播和控制。然而，宿主内传染性和症状的变化将影响例如，何时可能检测到感染，以及在此之前可能产生多少继发感染。我们将进行文献搜索，以找到描述埃博拉感染期间传染性和症状表现的时间变化的数据，并使用这些数据来参数建立1中描述的ODE模型。然后，政策制定者可以使用该模型来测试不同的拟议控制干预措施。该项目属于EPSRC数学生物学研究领域，属于数学科学和医疗技术主题。可能的合作者1。Kit Yates博士，巴斯大学2.奥利弗·摩根博士，世界卫生组织乔纳森·波隆斯基，世界卫生组织

The threat posed by infectious disease epidemics, as evidenced by the 2014-2016 Ebola outbreak in West Africa, is a huge ongoing concern. Mathematical models are increasingly being used to predict the progression of epidemics and to plan interventions. Commonly used epidemiological models typically assume each infectious host is equally infectious. In reality, both infectiousness and symptom expression will vary over the course of an infection.In this project, we will develop methods for nesting within-host pathogen dynamics inside population-level models. We will investigate whether including within-host dynamics in models affects predictions as to the effectiveness of control interventions. Differences between the predictions of different models are likely to be of interest to policy-makers, who seek accurate forecasts.This project will be split into four parts, which are summarised below.1. Linking different approaches for including variable infectiousness in epidemic models. Time-dependent infectiousness may be incorporated into an ordinary differential equation (ODE) compartmental model by including multiple infectious compartments, through which a host progresses and between which their infectiousness varies. An alternative approach is to use an integro-differential equation (IDE) model. We aim to link rigorously these two approaches for the first time, by considering the limit in which the number of infectious compartments in the ODE model tends to infinity.2. The effect of variability in symptom expression on surveillance. Infectious disease surveillance is usually modelled as an observation process. In other words, some proportion of infectious hosts are assumed to be detected, with the detection probability of each host assumed to be the same. In reality, however, the detection probability changes over the course of an infection. We will use the ODE model described in 1 above to investigate the effect of this variability on model predictions of observed epidemic dynamics. We will also develop new models in which surveillance is modelled as a dynamic process, involving not only detection but also control of infectious hosts.3. Linking stochastic and deterministic models. Whilst deterministic epidemic models are fast to numerically solve, real-world epidemiological systems are inherently stochastic. Deterministic equations, which describe not only the mean behaviour over many epidemics but also the variability, may be derived from a stochastic model through the use of moment closure techniques. We aim to develop novel moment closure techniques and apply them to stochastic epidemiological models incorporating variable infectiousness. In this way, we can see how our models developed in 1 and 2 above compare to those that include stochasticity.4. Application to control of Ebola outbreaks. The level of infectiousness and symptom expression both vary significantly during the course of an Ebola infection. Previously, the simple SEIR compartmental model has been used to model Ebola spread and control. However, variations in infectiousness and symptoms within a host will affect, for example, when an infection is likely to be detected and how many secondary infections are likely to be generated before this time. We will perform a literature search to find data describing temporal variations in both infectiousness and symptom expression during an Ebola infection, and use this data to parametrise the ODE model described in 1. This model may then be used by policy-makers to test different proposed control interventions.This project falls within the EPSRC Mathematical Biology research area, within the Mathematical Sciences and Healthcare Technologies themes.Possible collaborators1. Dr Kit Yates, University of Bath2. Dr Oliver Morgan, World Health Organization3. Jonathan Polonsky, World Health Organization