[C20] Infectious Diseases

[C20-01] Point pattern approach to study spatial epidemic dynamics

*Fugo Takasu¹ (1. Nara Women's University (Japan))

Keywords:

Spatial population dynamics,Point process,Individual-based model

In this talk, I focus on "point pattern approach" to explore spatial epidemic dynamics. In this approach, individuals are represented as points on continuous space and each point gives birth, dies, moves and changes its status (Susceptible, Infectious, etc.) with a certain rule. This approach allows us to implement mechanistic interactions at individual level as an individual-based model. Individual-based models are inherently stochastic and these are easy to simulate using pseudo-random numbers. However, simulation results are often difficult to interpret because each realization differs and we need to run a large number of realizations to capture ensemble-averaged behaviors. To better understand stochastic simulation results, we need "mathematical analysis" of individual-based rules. A point pattern can be quantified by focusing on the number of points (or singlets) as the 1st order structure, pairs made by two points displaced by a certain vector as the 2nd order structure, and triplets made by three points as the 3rd order structure, etc. To mathematically analyze this system, the method of moments has been proposed that translates a set of individual-based rules (birth, death and movement) to the dynamics of the 1st moment as the density of points N and the 2nd moment as the density of pairs C(ξ) displaced by vector ξ. I show that the method of moments can be extended to handle "status change" of each point, e.g., Susceptible to Infectious to Removed, etc. Analysis of the derived moment dynamics as integro-differential equations is a key issue.