Duan Wei
College of Systems Engineering, National University of Defense Technology, Changsha 410073, China.
Int J Environ Res Public Health. 2021 May 26;18(11):5716. doi: 10.3390/ijerph18115716.
Heterogeneities of individual attributes and behaviors play an important role in the complex process of epidemic spreading. Compared to differential equation-based system dynamical models of infectious disease transmission, individual-based epidemic models exhibit the advantage of providing a more detailed description of realities to capture heterogeneities across a population. However, the higher granularity and resolution of individual-based epidemic models comes with the cost of increased computational complexities, which result in difficulty in formulating individual-based epidemic models with mathematics. Furthermore, it requires great effort to understand and reproduce existing individual-based epidemic models presented by previous researchers. We proposed a mathematical formulation of heterogeneous individual-based epidemic models using matrices. Matrices and vectors were applied to represent individual attributes and behaviors. We derived analytical results from the matrix-based formulations of individual epidemic models, and then designed algorithms to force the computation of matrix-based individual epidemic models. Finally, we used a SARS epidemic control as a case study to verify the matrix-based formulation of heterogeneous individual-based epidemic models.
个体属性和行为的异质性在疫情传播的复杂过程中起着重要作用。与基于微分方程的传染病传播系统动力学模型相比，基于个体的疫情模型具有优势，能够更详细地描述现实情况，以捕捉人群中的异质性。然而，基于个体的疫情模型更高的粒度和分辨率伴随着计算复杂性增加的代价，这导致难以用数学方法构建基于个体的疫情模型。此外，理解和重现先前研究人员提出的现有基于个体的疫情模型需要付出巨大努力。我们提出了一种使用矩阵的基于个体异质性的疫情模型的数学公式。矩阵和向量被用于表示个体属性和行为。我们从基于矩阵的个体疫情模型公式中得出分析结果，然后设计算法来推动基于矩阵的个体疫情模型的计算。最后，我们以非典疫情控制为例进行研究，以验证基于矩阵的个体异质性疫情模型公式。
