A spatial SIS point pattern model with movement.

Abstract

Spatial epidemic dynamics are strongly affected by local interactions and by the movement of individuals. This study develops a susceptible-infected-susceptible (SIS) model based on point pattern dynamics with individual movement. The model extends the spatial SIS point pattern framework of Hamada and Takasu by allowing susceptible and infected points to move in continuous space. Disease transmission is represented by a distance-dependent infection kernel, and Gaussian, step-function, and exponential kernels are compared. Heuristic singlet and pair-density equations are derived to describe how infection, recovery, birth, death, and movement affect the spatial distribution of susceptible and infected individuals. Numerical simulations are used to illustrate the effects of kernel shape, infection range, and movement on singlet densities, pair correlations, and the temporal evolution of point patterns. The results show how spatial movement and distance-dependent transmission jointly shape infection spread in a recurrent-infection framework.