A mathematical immuno-epidemiological framework for co-infection

随着疾病的细菌理论的出现，对病原体繁殖和生存机制的理解已经形成了自然科学的一个重要分支。数学免疫学（在宿主中）和流行病学（在人群中）对传染病的研究作出了贡献。最近，免疫流行病学领域已经发展起来，其中免疫学特征被纳入流行病学模型，以便更好地了解病原体和免疫系统相互作用对疾病在人群中的传播和持久性的影响。当两种病原体同时感染一个宿主和一个群体时，这一应用数学建议的重点是为共同感染建立一个数学免疫-流行病学框架。我们的首要目标是了解共同感染病原体之间的协同作用如何影响疾病的进展和繁殖。作为一个模型系统，我们将重点关注全球相关的人类免疫缺陷病毒-结核分枝杆菌（HIV-TB）合并感染。结核病和艾滋病毒都是困扰全球的疾病。这些疾病也有助于其他宿主内和群体中的传播。通过定义对HIV-TB合并感染至关重要的参数，这项工作将增强对协同作用在发病机制中的作用的理解，并最终为改善艾滋病毒/结核病患者的护理奠定基础。提出的工作的主要研究成果将是一个数学上易于处理和生物学相关的免疫流行病学模型框架的共同感染。新的数学和计算工具将在全局稳定性分析、分岔理论、矩闭和随机建模等领域产生。大型系统定性分析的理论和技术，以及稳健和高效的数值和随机工具的发展。这些方法可以很容易地转化为其他合并感染系统（即利什曼病-艾滋病毒、艾滋病毒-乙型肝炎病毒等），扩展到研究药物治疗和疫苗接种的局限性/有效性，并研究通过旅行联系在一起的人群网络中的感染传播。

With the advent of the germ theory of disease, understanding the mechanisms of pathogen propagation and survival has formed a major branch of the natural sciences. Mathematical immunology (in a host) and epidemiology (in a population) have contributed to the study of infectious diseases. Recently, the field of immuno-epidemiology, whereby immunological characteristics are incorporated into epidemiological models, has been developed so that a better understanding of effects of pathogen and immune system interactions on disease transmission and persistence in a population can be gained. This applied mathematics proposal focuses on the development of a mathematical immuno-epidemiological framework for co-infection, when two pathogens simultaneously infect a host, and a population. Our overriding objective is to understand how synergism between co-infecting pathogens influence disease progression and propagation. As a model system, we will focus on the globally relevant Human Immunodeficiency Virus- mycobacterium Tuberculosis (HIV-TB) co-infection. TB and HIV are both diseases which plague the globe. These diseases also contribute to the propagation of the other in-host and in a population. By defining the parameters critical to HIV-TB co-infection, this work will provide an enhanced understanding of the effects of synergy in pathogenesis and, ultimately, a basis for the improved care of HIV/TB patients. The primary research outcome of the proposed work will be a mathematically tractable and biologically relevant immuno-epidemiological modelling framework of co-infection. New mathematical and computational tools will result in the areas of global stability analysis, bifurcation theory, moment closure and stochastic modelling. Theory and techniques for qualitative analysis of the large systems are developed, as well as robust and efficient numerical and stochastic tools. These approaches can readily be translated to other co-infection systems (i.e. Leishmaniasis-HIV, HIV-HBV, etc), extended to study drug therapy and vaccination limitations/effectiveness, and to study infection spread in a network of populations linked by travel.