Understanding the spread of infectious diseases such as COVID-19 is crucial for informed decision-making and resource allocation. A critical component of disease behavior is the velocity with which disease spreads, defined as the rate of change between time and space. In this paper, we propose a spatio-temporal modeling approach to determine the velocities of infectious disease spread. Our approach assumes that the locations and times of people infected can be considered as a spatio-temporal point pattern that arises as a realization of a spatio-temporal log-Gaussian Cox process. The intensity of this process is estimated using fast Bayesian inference by employing the integrated nested Laplace approximation (INLA) and the Stochastic Partial Differential Equations (SPDE) approaches. The velocity is then calculated using finite differences that approximate the derivatives of the intensity function. Finally, the directions and magnitudes of the velocities can be mapped at specific times to examine better the spread of the disease throughout the region. We demonstrate our method by analyzing COVID-19 spread in Cali, Colombia, during the 2020-2021 pandemic.

翻译：理解COVID-19等传染病的传播动态对于科学决策与资源调配至关重要。疾病传播速度作为刻画时空变化率的关键行为指标，是传染病研究的核心要素。本文提出一种时空建模方法用于确定传染病传播速度。该方法将感染者的时空位置信息视为时空点模式数据，并假设其产生于时空对数高斯Cox过程的实现。通过采用集成嵌套拉普拉斯近似（INLA）与随机偏微分方程（SPDE）方法进行快速贝叶斯推断，我们估计了该过程的强度函数。随后利用有限差分法逼近强度函数的偏导数来计算传播速度。最终，可通过绘制特定时刻的速度方向与幅度分布图，更清晰地揭示疾病在区域内的传播态势。我们以2020-2021年大流行期间哥伦比亚卡利市的COVID-19传播为例，验证了所提方法的有效性。