With the unfolding of the COVID-19 pandemic, mathematical modelling of epidemics has been perceived and used as a central element in understanding, predicting, and governing the pandemic event. However, soon it became clear that long-term predictions were extremely challenging to address. In addition, it is still unclear which metric shall be used for a global description of the evolution of the outbreaks. Yet a robust modelling of pandemic dynamics and a consistent choice of the transmission metric is crucial for an in-depth understanding of the macroscopic phenomenology and better-informed mitigation strategies. In this study, we propose a Markovian stochastic framework designed for describing the evolution of entropy during the COVID-19 pandemic together with the instantaneous reproductive ratio. Then, we introduce and use entropy-based metrics of global transmission to measure the impact and the temporal evolution of a pandemic event. In the formulation of the model, the temporal evolution of the outbreak is modelled by an equation governing the probability distribution that describes a nonlinear Markov process of a statistically averaged individual, leading to a clear physical interpretation. The time-dependent parameters are formulated by adaptive basis functions, leading to a parsimonious representation. In addition, we provide a full Bayesian inversion scheme for calibration together with a coherent strategy to address data unreliability. The time evolution of the entropy rate, the absolute change in the system entropy, and the instantaneous reproductive ratio are natural and transparent outputs of this framework. The framework has the appealing property of being applicable to any compartmental epidemic model. As an illustration, we apply the proposed approach to a simple modification of the susceptible–exposed–infected–removed model. Applying the model to the Hubei region, South Korean, Italian, Spanish, German, and French COVID-19 datasets, we discover significant difference in the absolute change of entropy but highly regular trends for both the entropy evolution and the instantaneous reproductive ratio.

随着 COVID-19 大流行的蔓延，流行病的数学建模已被视为理解、预测和管理大流行病事件的核心要素，并被用作核心要素。然而，很快人们就发现，长期预测极难解决。此外，目前尚不清楚应使用哪种指标来全面描述疫情的演变。然而，对流行病动态进行稳健的建模和对传输指标的一致选择对于深入了解宏观现象学和更明智的缓解策略至关重要。在这项研究中，我们提出了一个马尔可夫随机框架，旨在描述 COVID-19 大流行期间熵的演变以及瞬时繁殖率。然后，我们引入并使用基于熵的全球传播指标来衡量大流行事件的影响和时间演变。在模型的制定中，爆发的时间演变由一个控制概率分布的方程建模，该方程描述了统计平均个体的非线性马尔可夫过程，从而产生清晰的物理解释。时间相关参数由自适应基函数制定，导致简约表示。此外，我们还提供了用于校准的完整贝叶斯反演方案以及解决数据不可靠性的连贯策略。熵率的时间演化、系统熵的绝对变化和瞬时再生比是该框架自然而透明的输出。该框架具有适用于任何隔间流行病模型的吸引人的特性。作为说明，我们将所提出的方法应用于易感-暴露-感染-移除模型的简单修改。将该模型应用于湖北地区、韩国、意大利、西班牙、德国和法国的 COVID-19 数据集，我们发现熵的绝对变化存在显着差异，但熵演化和瞬时繁殖率的趋势非常规律。