Mathematical epidemiology has been playing an important role in better understanding how an infectious disease expands in a population from a theoretical viewpoint and it can serve to offer practical disease controls. In this paper, we extend the classical SEIS model as a stochastic point pattern dynamics in which a certain number of points are distributed over continuous space and each point status changes stochastically from susceptible S to exposed E to infectious I and back to S. Assuming an infection kernel as a function of distance from an I to a S, we implement and simulate the stochastic point pattern dynamics. This stochastic process can be mathematically described as a hierarchical dynamics of singlet probabilities, pair probabilities, and triplet probabilities, etc. We put our interest on its spatial distribution of Ss, E s, I s at equilibrium. Using a simple closure to approximate triplet probabilities using singlet and pair probabilities, we analytically derive equilibrium singlet and pair probabilities. We finally compare simulation results with analytically derived equilibrium for a range of parameters. It turns out that analytically derived equilibrium can well predict simulation results under a certain condition.