In the past decades, it has been widely recognized that spatial structure can fundamentally alter consequences of simple population dynamics where all individuals are assumed to be “well-mixed” (no spatial structure).

Extended Nicholson-Bailey models of host-parasite dynamics on lattice space have already shown that various spatial patterns can emerge and persist.

Enabling coexistence of host and parasite populations which is otherwise impossible in well-mixed system. But these previous models focus only on phenomena at population level, ignoring birth and death process at individual level.

In this talk, fully mechanistic birth and death processes of host and parasite individuals in continuous space are implemented as an individual-based model which we name “Spatial and special IBM(SPIBM)”. Using SPIBM, we aim to enrich our previous knowledge on the effect of space viewed at individual level.

We found that the SPIBM can also generate spiral patterns and that these spatio-temporal patterns can persist for a long time despite the considerable stochasticity inherent in individual’s birth, death, and movement. A method to detect spiral patterns was developed and conditions for stable spirals to persist was investigated.

We discuss about how our SPIBM is useful to generally theoretical study of spatial ecology.