Estimating Velocities of Infectious Disease Spread Through Spatio‐Temporal Log‐Gaussian Cox Point Processes

Summary Understanding the spread of infectious diseases such as COVID‐19 is crucial for informed decision‐making and resource allocation. A critical component of disease behaviour is the velocity with which disease spreads, defined as the rate of change between time and space. This paper proposes 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 a spatio‐temporal point pattern that arises as a realisation of a spatio‐temporal log‐Gaussian Cox point process. The intensity function of this process is estimated using a fully nonseparable spatio‐temporal model derived from diffusion stochastic partial differential equations (SPDE), and fast Bayesian inference is performed using integrated nested Laplace approximation (INLA). 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 better examine the spread of the disease throughout the region. This method is demonstrated by analysing COVID‐19 spread in Cali, Colombia, during the 2020–2021 pandemic.