种群年龄/病程的异质性对传染病传播和控制的影响

The top priority of global public safety is to prevent and contain the spread of infectious diseases. However, the transmission of infectious diseases is greatly influenced by the heterogeneity of the population age and the infection age. Therefore, it is imperative and reliable to formulate the transmission of infectious diseases by using the age or infection-age structured epidemical models, and use the models to study their transmission dynamics, the effectiveness of control measures and some related issues. In the project, we will formulate the epidemic models by including the heterogeneity of the population age or the infection age based on the transmission mechanism of specific infectious diseases and their actual control background, then analyze the local and global dynamics of the epidemic models with a combination of mathematical theory and numerical simulations. One important purpose of the project is to use the age or infection age structured epidemic models to investigate the effect of the heterogeneity of population age and infection age on the transmisison dynamic of infectious diseases and control measures, and to evaluate the effectiveness of these measures on containging the spread of the diseases and related issues. We are also interesed in the optimal control issues: to find the optimal control strategy with given effect and minimal effort or to find the optimal control strategy with best effect and given effort. In addition, the benefit of pharmaceutical interventions can be compromised if mutated strains arise, thus in the project the potential risk of pharmaceutical interventions will further be evaluated in this circumstance. The project will make us to gain insights into the transmission and control of the disease. These insights can potentially help us to understand the effect of the heterogeneity of the population age and the infection age on transmission of infectious diseases and on the measures taken to control these diseases, to further assess the effectiveness and potential risk of various preventive and control strategies, and to provide important basis and guide on mitigating the spread of infectious diseases.

控制传染病的传播是全球公共安全最为优先考虑的问题，而种群年龄和疾病病程的异质性则是影响传染病传播的重要因素，因此利用年龄/病程结构传染病模型研究传染病的传播规律和控制措施的有效性及相关问题更加可靠和符合实际。本项目根据具体传染病的传播特点及其控制的实际背景建立具有年龄/病程结构的传染病模型；利用数学理论并结合实际数据的数值仿真分析系统的局部和整体动力学性态；研究种群年龄和疾病病程的异质性对传染病传播和控制措施的影响；从而评估控制措施的有效性及相关问题。并提供在一定控制代价前提下控制传染病传播的最佳方案或在一定的控制效果下寻求代价最小的控制方案。此外，变异菌株的出现是药物性防控传染病的潜在风险之一，本项目还将在此情形下评估药物性控制措施的潜在风险。本项目的研究将有助于人们了解年龄/病程的异质性对传染病传播和控制的影响，理解传染病控制措施的有效性和潜在风险，对传染病的防治提供重要的依据和指南。

理解传染病的传播规律和流行趋势，控制传染病的传播是全球公共安全最为优先考虑的问题，而种群年龄和疾病病程等异质性是影响传染病的重要因素。本项目就是根据传染病种群年龄和疾病病程等异质性建立具有年龄/病程等异质性结构的传染病数学模型，研究了年龄/病程等异质性对传染病传播和控制的影响。一方面，本项目根据具体传染病的实际背景建立了几类具有年龄/病程异质性的传染病模型，利用再生数的计算理论确定了传染病是否流行的基本再生数和相关控制再生数，进一步利用微分方程、算子半群和动力学系统的理论给出了模型动力学性态较为完整的分类，在探讨证明年龄/病程等异质性结构模型的全局性态的数学方法上取得了基础性的进展；另一方面本项目在模型的构建和分析的基础上，研究了年龄/病程等异质性因素对传染病传播和爆发以及其控制措施的影响，评估了一些控制手段的有效性，设计了相关的最优控制策略；同时本项目还考虑了具有多菌株竞争的年龄/病程等异质性结构传染病模型，确定敏感菌株和变异菌株的基本再生数和控制再生数，分析模型的动力学性态，研究了种群年龄/疾病病程的异质性和控制措施对相关传染病再生数和动力学性态的影响。

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