A Framework for Model Development and Mathematical Evaluation of Vaccination

数学建模对疫苗接种计划的设计和分析做出了重要贡献。然而，我们对疫苗接种动态的理解仍然存在重大差距，这需要发展新的理论和计算方法，以了解生物、流行病学和高危人群的特点。这项研究计划将开发一个数学框架，以评估疫苗接种的影响，基于适当的模型结构。目前缺乏这样一个框架，妨碍对不同建模技术产生的结果进行验证和比较。*目前的疫苗接种模式通常假设人群中的疾病风险随着时间的推移是稳定的。然而，具有重要社会和经济影响的传染病(如流感、百日咳)情况并非如此。此外，间歇性或特定时间的事件(例如，环境因素或季节性)可能会极大地增加或降低疾病风险。此外，疫苗接种的效果取决于两个明显的疫苗特性：效力(在个人层面上的保护)和效力(减少人群中的发病率)。在动态模型中，通常使用相同的参数来量化这些属性。因此，考虑到这些因素，必须制定一个通用的数学框架来研究疫苗接种动态中新出现的问题，并更好地了解疫苗接种的短暂和持久影响。*我们建议根据两大类病毒和细菌疾病的特征构建一个数学框架。对于每一门课程，我们将研究基本参数、模型结构和理论方法。疫苗接种的效果将根据不仅影响疾病动态而且影响政策和计划交付的属性进行调查。这些因素包括要接种疫苗的人口百分比、疫苗失败的可能性、接种疫苗的时间表和疫苗剂量。我们将对疫苗接种模式进行比较分析，以确定评估框架的关键要素。*这项计划将带来重大成果。首先，它创建了一个数学和计算框架，将指导今后在疾病建模和干预措施评估方面的努力。此外，随着疫苗生产的新技术出现，重要的参数和潜在的假设可能会改变，因此在评估疫苗接种计划时需要考虑这些因素。除了其科学贡献外，这项研究还将直接解决最终用户在决策中的需求。该计划将为高素质人员提供特殊的培训机会，以获得关键的专业知识和领导技能，并为加拿大的社会经济地位做出贡献。

Mathematical modelling has made key contributions to the design and analysis of vaccination programs. However, major gaps in our understanding of vaccination dynamics still remain, which require the development of new theoretical and computational methods that are informed by biological, epidemiological, and at-risk population characteristics. This research program will develop a mathematical framework to evaluate the impact of vaccination based on appropriate model structures. Such a framework is currently lacking, hindering the validation and comparison of outcomes produced by different modelling techniques. ***Current models of vaccination often assume that the risk of disease in a population is stable over time. However, this is not the case with communicable diseases (e.g., influenza, pertussis), which has important social and economic implications. Furthermore, intermittent or time specific events (e.g., environmental factors or seasonality) could acutely increase or decrease the risk of disease. Moreover, the effect of vaccination depends on two distinguishable vaccine properties of efficacy (protection at the individual level) and effectiveness (reduction of disease incidence in the population). These properties are often quantified in dynamic models using the same parameter. Considering these factors, it is therefore imperative to develop a general mathematical framework to study emerging issues in vaccination dynamics, and provide a better understanding of the transient and lasting effects of vaccination. ***We propose to construct a mathematical framework based on characteristics of two major classes of viral and bacterial diseases. For each class, essential parameters, model structures, and theoretical methods will be studied. The effect of vaccination will be investigated based on attributes that affect not only disease dynamics but also policy and program delivery. These include the percentage of the population to be vaccinated, the possibility of vaccine failure, timelines of vaccination, and number of vaccine doses. We will conduct comparative analyses of vaccination models to identify key elements of the evaluation framework. ***This program will lead to significant outcomes. First and foremost, it creates a mathematical and computational framework that will guide future efforts in disease modelling and evaluation of interventions. Furthermore, as new technologies for vaccine production emerge, important parameters and underlying assumptions may be altered, and will therefore need to be considered in assessing vaccination programs. Beyond its scientific contributions, this research will directly address the needs of end-users in decision-making. This program will offer exceptional training opportunities for highly qualified personnel to acquire critical expertise and leadership skills, and contribute to the socioeconomic status of Canada.