# A multi-scale area-interaction model for spatio-temporal point patterns

## TL;DR

This paper introduces a novel multi-scale area-interaction model for spatio-temporal point processes that captures interactions at multiple scales and incorporates covariates, demonstrated on varicella case data.

## Contribution

It extends spatial multi-scale area-interaction models to a spatio-temporal setting, allowing for complex interactions and covariate inclusion.

## Key findings

- Small scale clustering observed in data
- Higher scale regularity identified
- Model effectively fits varicella case distribution

## Abstract

Models for fitting spatio-temporal point processes should incorporate spatio-temporal inhomogeneity and allow for different types of interaction between points (clustering or regularity). This paper proposes an extension of the spatial multi-scale area-interaction model to a spatio-temporal framework. This model allows for interaction between points at different spatio-temporal scales and the inclusion of covariates. We fit the proposed model to varicella cases registered during 2013 in Valencia, Spain. The fitted model indicates small scale clustering and regularity for higher spatio-temporal scales.