A simple finite delayed multi-type branching process for infectious disease modeling

TL;DR

This paper introduces a delayed multi-type branching process model for infectious disease spread, capturing spatial and temporal effects, with analytical expressions for the process's long-term behavior.

Contribution

It presents a novel, simplified mathematical framework for modeling infectious diseases with spatial and temporal dynamics, including recovery and death outcomes.

Findings

Derived explicit formulas for the process's long-term mean behavior.

Model captures spatial heterogeneity and temporal delays in disease transmission.

Provides a foundation for analyzing complex infectious disease dynamics.

Abstract

We study a model for the spread of an infectious disease which incorporates spatial and temporal effects. The model is a delayed multi-type branching process in which types represent geographic regions while infected individuals reproduce offspring during a finite time interval and have convalescence times and random death/recovery outcomes. We give simple expressions for the limit of the geometrically weighted mean evolution of the process.