An additional compartment of vaccinated individuals is considered in a SIS stochastic epidemic model with infection reintroduction. The quantification of the spread of the disease is modeled by a continuous time Markov chain. A well-known measure of the initial transmission potential is the basic reproduction number $$R_0$$ R 0 , which determines the herd immunity threshold or the critical proportion of immune individuals required to stop the spread of a disease when a vaccine offers a complete protection. Due to repeated contacts between the typical infective and previously infected individuals, $$R_0$$ R 0 overestimates the average number of secondary infections and leads to, perhaps unnecessary, high immunization coverage. Assuming that the vaccine is imperfect, alternative measures to $$R_0$$ R 0 are defined in order to study the influence of the initial coverage and vaccine efficacy on the transmission of the epidemic.

中文翻译：

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在具有重新引入感染和不完善疫苗的随机 SIV 模型中测量感染传播

在重新引入感染的 SIS 随机流行模型中考虑了额外的接种个体隔间。疾病传播的量化由连续时间马尔可夫链建模。初始传播潜力的一个众所周知的衡量标准是基本繁殖数 $$R_0$$R 0 ，它决定了群体免疫阈值或当疫苗提供完整的疫苗时阻止疾病传播所需的免疫个体的临界比例。保护。由于典型感染者和先前感染者之间的反复接触，$$R_0$$R 0 高估了继发感染的平均数量，并导致可能不必要的高免疫覆盖率。假设疫苗不完善，