Towards an immuno-epidemiological framework: The trade-off between biological detail and mathematical complexity

传染病模型领域最终源于两个子领域。数学流行病学的重点是疾病在宿主群体中的传播，目的是追踪有助于病原体传播的因素。相反，数学免疫学(宿主内模型)研究受感染宿主内的疾病动态，以揭示推动疾病进展的潜在机制(病原体/免疫系统相互作用)。近年来，免疫流行病学领域兴起。在这里，宿主内模型被结合到种群水平模型中，从而可以研究传染病在个体和群体感染水平之间的内在反馈回路。 在疾病建模中，在模型中包含的生物学细节水平和数学模型本身的复杂性之间存在权衡。我们的目标是开发一种模型，以一种数学上易于处理的方式充分地代表生物系统。然而，考虑到相同的生物系统和简化的假设，可以开发不同的模型。因此，模型结果/结果可能不同。在数学流行病学和数学免疫学中，这意味着对公共卫生和医学很重要的感染和疾病的关键指标和衡量标准将有所不同。此外，根据所研究的模型，结果甚至可能是相互矛盾的。当然，在这些情况下，疾病模型在产生关于不同病原体动态的新知识方面是有限的。在免疫流行病学中，在每个感染级别上发现的不同结果也可能被放大，从而无助于(个人和人群之间)传染病反馈回路的研究。因此，我们必须研究简化假设对每个感染级别的影响。 在拟议的工作中，我们将详细说明数学免疫学和数学流行病学中常用的简化假设的影响，并研究它们对感染的关键衡量标准的影响。我们将开发、比较和对比确定性和随机性模型。还将开发简单的免疫流行病学模型，以研究在每个感染水平上一个或两个简化假设对反馈回路的影响。我们的工作重点是传染病，这使得我们能够研究免疫(免疫系统记忆细胞)的发展和衰退。 最终，我们的工作将为传染病建模领域提供信息，这反过来将为公共卫生决策者提供信息，并使加拿大人的健康受益。

The field of infectious disease modelling ultimately stems from two sub-fields. Mathematical epidemiology focuses on the spread of disease in a population of hosts with the aim of tracing factors that contribute to pathogen propagation. Mathematical immunology (in-host models), in contrast, investigates disease dynamics within an infected host, to uncover the underlying mechanisms (pathogen/immune system interactions) driving disease progression. Recently, the field of immuno-epidemiology (IE) has arisen. Here, in-host models are combined into population level models so that the inherent feedback loop of infectious disease, between individual and population levels of infection, can be studied. In disease modelling a tradeoff exists between the level of biological detail included in a model and the complexity of the mathematical model itself. The goal is to develop a model that sufficiently' represents the biological system in a mathematically tractable way. However, given the same biological system and simplifying assumptions, different models can be developed. Thus, model outcomes/results can differ. In mathematical epidemiology and mathematical immunology this means that key indicators and measurements of infection and disease that are important to public health and medicine will vary. Also, depending on the models studied, the results may even be contradictory. Certainly, in these cases, disease models are limited in producing new knowledge about the dynamics of different pathogens. In immuno-epidemiology, the differing results found at each scale of infection can also be magnified, and thus will not aid in the study of the feedback loop of infectious diseases (between individuals and populations). It is therefore imperative that we study the effects of simplifying assumptions on each scale of infection. In the proposed work, we will detail the effects of commonly used simplifying assumptions in mathematical immunology and mathematical epidemiology, and we will study their effects on key measurements of infection. Deterministic and stochastic models will be developed, compared, and contrasted. Simple immuno-epidemiological models will also be developed to study the effects of one or two simplifying assumptions at each level of infection on the feedback loop. We focus our work on infectious diseases that enable the study of the development and waning of immunity (immune system memory cells). Ultimately, our work will inform the field of infectious disease modelling, which, in turn, will inform public health decision makers, and benefit the health of Canadians.