Immunity following natural infection or immunization may wane, increasing susceptibility to infection with time since infection or vaccination. Symptoms, and concomitantly infectiousness, depend on residual immunity. We quantify these phenomena in a model population composed of individuals whose susceptibility, infectiousness, and symptoms all vary with immune status. We also model age, which affects contact, vaccination and possibly waning rates. The resurgences of pertussis that have been observed wherever effective vaccination programs have reduced typical disease among young children follow from these processes. As one example, we compare simulations with the experience of Sweden following resumption of pertussis vaccination after the hiatus from 1979 to 1996, reproducing the observations leading health authorities to introduce booster doses among school-aged children and adolescents in 2007 and 2014, respectively. Because pertussis comprises a spectrum of symptoms, only the most severe of which are medically attended, accurate models are needed to design optimal vaccination programs where surveillance is less effective.

中文翻译：

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模拟感染或疫苗接种的免疫力的减弱和增强。

自然感染或免疫接种后的免疫力可能会减弱，从而随着感染或接种疫苗后的时间增加对感染的易感性。症状和随之而来的传染性取决于残余免疫力。我们在由易感性、传染性和症状都随免疫状态变化的个体组成的模型人群中量化这些现象。我们还模拟年龄，这会影响接触、疫苗接种和可能的下降率。在有效的疫苗接种计划减少了幼儿的典型疾病的任何地方都观察到了百日咳的死灰复燃，这些都源于这些过程。作为一个例子，我们将模拟与瑞典在 1979 年至 1996 年中断后恢复百日咳疫苗接种后的经验进行比较，重现导致卫生当局分别在 2007 年和 2014 年在学龄儿童和青少年中引入加强剂量的观察结果。由于百日咳包含一系列症状，其中只有最严重的症状需要就医，因此需要准确的模型来设计最佳的疫苗接种计划，而监测效果较差。