Magpantay F M G
Department of Mathematics, University of Manitoba, Winnipeg, MB, R3T 2N2, Canada.
J Math Biol. 2017 Dec;75(6-7):1591-1617. doi: 10.1007/s00285-017-1126-5. Epub 2017 Apr 17.
A general model of an imperfect vaccine for a childhood disease is presented and the effects of different types of vaccine failure on transmission were investigated using models that consider both homogeneous and age-specific mixing. The models are extensions of the standard SEIR equations with an additional vaccinated component that allows for five different vaccine parameters: three types of vaccine failure in decreasing susceptibility to infection via failure in degree ("leakiness"), take ("all-or-nothingness") and duration (waning of vaccine-derived immunity); one parameter reflecting the relative reduction in infectiousness of vaccinated individuals who get infected; and one parameter that reflects the relative reduction in reporting probability of vaccinated individuals due to a possible reduction in severity of symptoms. Only the first four parameters affect disease transmission (as measured by the basic reproduction number). The reduction in transmission due to vaccination is different for age-structured models than for homogeneous models. Notably, if the vaccine exhibits waning protection this could be larger for an age-structured model with high contact rates between young children who are still protected by the vaccine and lower contact rates between adults for whom protection might have already waned. Analytic expressions for age-specific "vaccine impacts" were also derived. The overall vaccine impact is bounded between the age-specific impact for the oldest age class and that of the youngest age class.
提出了一种针对儿童疾病的不完善疫苗的通用模型，并使用考虑了均匀混合和年龄特异性混合的模型，研究了不同类型的疫苗失效对传播的影响。这些模型是标准SEIR方程的扩展，带有一个额外的接种成分，允许有五个不同的疫苗参数：三种因程度（“渗漏”）、接种成功（“全或无”）和持续时间（疫苗衍生免疫力减弱）导致感染易感性降低的疫苗失效类型；一个参数反映感染的接种个体传染性的相对降低；以及一个参数反映由于症状严重程度可能降低导致接种个体报告概率的相对降低。只有前四个参数影响疾病传播（以基本再生数衡量）。与均匀模型相比，年龄结构模型中疫苗接种导致的传播减少情况有所不同。值得注意的是，如果疫苗表现出保护作用减弱，对于年龄结构模型而言，在仍受疫苗保护的幼儿之间接触率高而保护作用可能已经减弱的成年人之间接触率低的情况下，这种减弱可能更大。还推导了年龄特异性“疫苗影响”的解析表达式。总体疫苗影响介于最年长者年龄组和最年幼者年龄组的年龄特异性影响之间。
