The Markovian approach, which assumes exponentially distributed interinfection times, is dominant in epidemic modeling. However, this assumption is unrealistic as an individual's infectiousness depends on its viral load and varies over time. In this paper, we present a Susceptible-Infected-Recovered-Vaccinated-Susceptible epidemic model incorporating non-Markovian infection processes. The model can be easily adapted to accurately capture the generation time distributions of emerging infectious diseases, which is essential for accurate epidemic prediction. We observe noticeable variations in the transient behavior under different infectiousness profiles and the same basic reproduction number R0. The theoretical analyses show that only R0 and the mean immunity period of the vaccinated individuals have an impact on the critical vaccination rate needed to achieve herd immunity. A vaccination level at the critical vaccination rate can ensure a very low incidence among the population in case of future epidemics, regardless of the infectiousness profiles.

翻译：马尔可夫方法假设感染间隔时间服从指数分布，在流行病建模中占据主导地位。然而这一假设并不现实，因为个体的传染性取决于其病毒载量且随时间动态变化。本文提出一个包含非马尔可夫感染过程的易感-感染-康复-接种-易感流行病模型。该模型可便捷调整以精准刻画新兴传染病的代际时间分布，这对准确预测疫情至关重要。研究发现，在相同基本再生数R0条件下，不同传染性曲线会导致显著的暂态行为差异。理论分析表明，仅R0与疫苗接种者的平均免疫期会影响实现群体免疫所需的临界接种率。达到该临界接种率的疫苗接种水平可确保未来疫情中人群发病率维持在极低水平，且该结论不受传染性曲线形态影响。