Dietz K, Hadeler K P
Institut für Medizinische Biometrie, Universität Tübingen, Federal Republic of Germany.
J Math Biol. 1988;26(1):1-25. doi: 10.1007/BF00280169.
The classical models for sexually transmitted infections assume homogeneous mixing either between all males and females or between certain subgroups of males and females with heterogeneous contact rates. This implies that everybody is all the time at risk of acquiring an infection. These models ignore the fact that the formation of a pair of two susceptibles renders them in a sense temporarily immune to infection as long as the partners do not separate and have no contacts with other partners. The present paper takes into account the phenomenon of pair formation by introducing explicitly a pairing rate and a separation rate. The infection transmission dynamics depends on the contact rate within a pair and the duration of a partnership. It turns out that endemic equilibria can only exist if the separation rate is sufficiently large in order to ensure the necessary number of sexual partners. The classical models are recovered if one lets the separation rate tend to infinity.
性传播感染的经典模型假定所有男性和女性之间或者具有不同接触率的某些男性和女性亚组之间存在均匀混合。这意味着每个人始终都有感染的风险。这些模型忽略了这样一个事实，即一对易感个体的形成在某种意义上使他们暂时对感染具有免疫力，只要伴侣不分开且不与其他伴侣接触。本文通过明确引入配对率和分离率来考虑配对现象。感染传播动态取决于配对内的接触率和伴侣关系的持续时间。结果表明，只有当分离率足够大以确保有必要数量的性伴侣时，地方病平衡点才可能存在。如果让分离率趋于无穷大，就会恢复到经典模型。
