COLLABORATIVE RESEARCH: A MATHEMATICAL THEORY OF TRANSMISSIBLE VACCINES

病毒疫苗对人类健康产生了显著而持久的影响，在世界范围内消灭了天花，在许多发达国家消灭了小儿麻痹症，并有效控制了许多其他疾病。尽管自19世纪初爱德华·詹纳（Edward Jenner）首次接种牛痘疫苗以来，疫苗的开发和生产取得了巨大进步，但疫苗的交付方式几乎没有改变。即使在今天，几乎每种疫苗都必须直接给病人注射。分子生物学的最新进展表明，几个世纪以来以个体为基础的疫苗递送方法可能正处于一场重大革命的尖端。具体来说，基因工程带来了“传染性疫苗”的可能性。与直接为人群中的每个人接种疫苗不同，一种传染性疫苗将通过释放一种经过基因工程改造的传染性病原体，使大量人群毫不费力地接种疫苗。事实上，一些现有疫苗在有限程度上具有传染性，而且传染性疫苗已经开发出来并在野生动物种群中使用。然而，值得注意的是，没有任何理论可以指导安全有效地使用这种革命性的新型疫苗。我们将开发一个数学框架，以了解传染性疫苗的生态学和进化，并使用实验病毒系统测试新出现的数学结果。将通过计算传染性疫苗相对于传统疫苗在疾病保护方面的收益来评估流行病学效力。进化稳健性将通过预测基因工程疫苗失去效力或增加毒性的速度的模型来探索。在这两种情况下，将使用直接和渐近解、近似、数值解和基于个体的模拟的组合来分析模型。关键的数学结果将通过细菌和感染它们的病毒之间的相互作用进行实验测试。

Viral vaccines have had remarkable and long-lasting impacts on human health, resulting in the world wide eradication of smallpox, the elimination of polio within much of the developed world, and the effective control of many other diseases. Although great strides have been made in the development and production of vaccines since Edward Jenner's first vaccinations with cowpox in the early 1800's, little has changed in the way vaccines are delivered. Even today, virtually every vaccine must be given directly to the patient. Recent advances in molecular biology suggest that the centuries-old method of individual-based vaccine delivery could be on the cusp of a major revolution. Specifically, genetic engineering brings to life the possibility of a "transmissible vaccine." Rather than directly vaccinating every individual within a population, a transmissible vaccine would allow large swaths of the population to be vaccinated effortlessly by releasing an infectious agent that is genetically engineered to be benign yet infectious. In fact, some existing vaccines are transmissible to a limited extent, and transmissible vaccines have already been developed and deployed in wild animal populations. Remarkably enough, however, no theory exists to guide the safe and effective use of this revolutionary new type of vaccine. We will develop a mathematical framework for understanding the ecology and evolution of transmissible vaccines, and test the emerging mathematical results using an experimental viral system. Epidemiological efficacy will be assessed by calculating the gains in disease protection conferred by a transmissible vaccine relative to a traditional vaccine. Evolutionary robustness will be explored using models that predict the rate at which a genetically engineered vaccine will lose its efficacy or increase its virulence. In both cases, models will be analyzed using a combination of direct and asymptotic solutions, approximations, numerical solutions, and individual-based simulations. Key mathematical results will be tested experimentally using interactions between bacteria and viruses that infect them.