Infectious diseases in animal farms can cause severe livestock mortality and substantial economic losses. We consider the farms and their mutual spreading relationships as a latent graph. The spreading relationships between farms are typically unobserved and may vary over time. Moreover, the occurrence of infection is driven by intra-farm recurrence and inter-farm spreading. Thus, we regard the infection outbreaks across all farms as a high-dimensional multivariate point process. Meanwhile, the node-specific intensity also shows spatial correlation across nearby farms. Therefore, we propose a high-dimensional multivariate Hawkes process allowing dynamic interactions across farms. We further incorporate a spatial Gaussian process to account for the spatial heterogeneity of node-specific intensities. Then, we develop a Markov chain Monte Carlo algorithm to conduct posterior inference. Extensive simulation studies evaluate the MCMC algorithm. Finally, we analyze livestock epidemic data in China to infer the latent disease-spreading trajectory.