We proposed a new generalized model based on the classical Hawkes process with environmental multipliers, which is called an environmentally-adaptive Hawkes (EAH) model. Compared to the classical self-exciting Hawkes process, the EAH model exhibits more flexibility in a macro environmentally temporal sense, and can model more complex processes by using dynamic branching matrix. We demonstrate the well-definedness of this EAH model. A more specified version of this new model is applied to model COVID-19 pandemic data through an efficient EM-like algorithm. Consequently, the proposed model consistently outperforms the classical Hawkes process.

翻译：我们提出了一个基于传统霍克斯进程和环境乘数的新型通用模型,称为适应环境的霍克斯(EAH)模型。与传统的自我激发霍克斯(Hawks)模型相比,EAH模型在宏观环境时间意义上表现出更大的灵活性,并且可以通过动态分支矩阵来模拟更复杂的过程。我们展示了这种EAH模型的清晰定义。这一新模型的更具体版本通过有效的EM类算法适用于模型COVID-19流行病数据。因此,拟议的模型始终优于传统的霍克斯进程。