In ecology, spatial structure of a population plays a key role and spatial population dynamics has been studied by various mathematical approaches such as reaction-diffusion models, lattice models, and network models. In this study, we adopt "point pattern" approach, an ultimate way to represent spatial distribution of individuals as points, in order to study how infection spreads over space.
　Previous study extended the classical SIS model as point pattern dynamics (Susceptible becomes Infectious becomes Susceptible again) and explored the equilibrium properties (proportion and spatial distribution of S and I). In this study, we focus on SIRS model in which Infectious becomes Removed becomes Susceptible again with immunity loss. We assume distance-dependent infection rate that is common in ecological interactions. We implement stochastic simulation model and derive analytical model that focuses on the dynamics of singlets (probability of a point in S or I or R) and pairs (probability of a pair with two points in S-S, S-I, S-R, I-I, I-R, R-R).
　Simulation and analytical results suggest potential research prospects worth to challenge in future to better understand spatial population dynamics in ecology.