Reducing the peak time of an epidemic disease in order for slowing down the eventual dynamics and getting prepared for the unavoidable epidemic wave is utmost significant to fight against the risks of a contagious epidemic disease. To serve to this purpose, the well-documented infection model of SIR is examined in the current research to propose an analytical approach for providing an explicit formula associated with a straightforward computation of peak time of outbreak. Initially, the time scale from the relevant autonomous SIR epidemic model is formulated analytically via an integral based on the fractions of susceptible and infected compartments. Afterwards, through a series expansion of the logarithmic term of the resultant integrand, the peak time is shown to rely upon the fraction of susceptible, the infectious ratio as well as the initial fractions of ill and susceptible individuals. The approximate expression is shown to rigorously capable of capturing the time threshold of illness for an epidemic from the semi-time SIR epidemiology. Otherwise, it is also successful to predict the peak time from a past history of a disease when all-time epidemic model is adopted. Accuracy of the derived expressions are initially confirmed by direct comparisons with recently reported approximate formulas in the literature. Several other epidemic disease samples including the COVID-19 often studied in the recent literature are eventually attacked with favourable performance of the presented formulae for assessing the peak time occurrence of an epidemic. A quick evaluation of the peak time of a disease certainly enables the governments to take early effective epidemic precautions.

缩短疫情高峰时间，减缓最终的流行趋势，为不可避免的疫情浪潮做好准备，对于应对传染病风险至关重要。为了实现这一目的，当前的研究对有据可查的 SIR 感染模型进行了检查，提出了一种分析方法，用于提供与直接计算爆发高峰时间相关的明确公式。最初，相关自主 SIR 流行病模型的时间尺度是通过基于易感区和感染区的分数的积分来分析制定的。然后，通过对所得到的被积函数的对数项进行级数展开，发现峰值时间取决于易感者比例、感染率以及患病个体和易感个体的初始比例。该近似表达式被证明能够严格地从半时间 SIR 流行病学中捕获流行病的患病时间阈值。另外，当采用历史流行模型时，从过去的疾病史预测高峰时间也是成功的。通过与文献中最近报道的近似公式的直接比较，初步证实了推导表达式的准确性。最近文献中经常研究的包括 COVID-19 在内的其他几种流行病样本最终都受到了所提出的用于评估流行病发生高峰时间的公式的良好性能的影响。快速评估疾病的高峰时间无疑有助于政府及早采取有效的疫情预防措施。