The Markovian approach, which assumes constant transmission rates and thus leads to exponentially distributed inter-infection 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 SIRVS 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 relatively low incidence among the population in case of future epidemics, regardless of the infectiousness profiles.

翻译：马尔可夫方法假定恒定传播速率，从而产生指数分布的感染间隔时间，这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变化。本文提出了一种包含非马尔可夫感染过程的SIRVS流行病模型。该模型可轻松调整，以准确捕捉新兴传染病的代际时间分布，这对精确的流行病预测至关重要。我们观察到，在相同的基波繁殖数R0下，不同传染性特征下的瞬态行为存在显著差异。理论分析表明，仅有R0和疫苗接种个体的平均免疫期会影响实现群体免疫所需的临界疫苗接种率。在临界疫苗接种率下的接种水平能够确保未来疫情中人群维持相对较低的发病率，无论传染性特征如何。