论文标题
均匀准确的有效方程，用于通过成对形成动力学介导的疾病传播
Uniformly accurate effective equations for disease transmission mediated by pair formation dynamics
论文作者
论文摘要
我们得出并渐近地分析了疾病扩散的质量表演模型，包括瞬态对形成和解离。未配对的易感和感染者的种群与三种个人对的种群区分开来；两者都敏感，一种易感性和一种感染，均为感染。疾病传播只能发生在一个由一个易感人群和一个受感染的人组成的一对中。通过考虑快速对的形成和快速对分解极限，我们使用扰动扩展来正式得出均匀有效的近似，以概述全部感染和易感人群的动力学。在不同的参数制度下，我们为全受感染人群提供了均匀的有效方程，并将其结果与完整的质量分歧模型的结果进行了比较。我们的结果源自基本的质量行动系统，而没有隐式施加传输机制，例如在频率依赖模型中使用的传输机制。它们为有效的配对模型提供了一种新的配方，并与以前的模型进行了比较。
We derive and asymptotically analyze mass-action models for disease spread that include transient pair formation and dissociation. Populations of unpaired susceptibles and infecteds are distinguished from the population of three types of pairs of individuals; both susceptible, one susceptible and one infected, and both infected. Disease transmission can occur only within a pair consisting of one susceptible individual and one infected individual. By considering the fast pair formation and fast pair dissociation limits, we use a perturbation expansion to formally derive a uniformly valid approximation for the dynamics of the total infected and susceptible populations. Under different parameter regimes, we derive uniformly valid effective equations for the total infected population and compare their results to those of the full mass-action model. Our results are derived from the fundamental mass-action system without implicitly imposing transmission mechanisms such as that used in frequency-dependent models. They provide a new formulation for effective pairing models and are compared with previous models.
