Extinction and Persistence in a Stochastic Mpox Model with Hawkes-type Self-Excitation

TL;DR

This paper introduces a stochastic Mpox transmission model incorporating Hawkes processes to capture transmission spikes, providing new insights into outbreak thresholds, extinction, and persistence conditions influenced by environmental factors and control measures.

Contribution

It develops a novel stochastic model combining diffusion noise with Hawkes self-excitation for Mpox, and derives explicit thresholds for extinction and persistence in the coupled human-rodent system.

Findings

Hawkes processes effectively model transmission spikes.

Thresholds for extinction and persistence are explicitly derived.

Environmental variability influences outbreak dynamics.

Abstract

We develop a stochastic human-rodent compartment model for Mpox transmission that combines diffusion noise with Hawkes self-exciting jumps in the human infection dynamics. Including Hawkes processes allows, for instance, to model the short but significant spikes in transmission happening after crowded events. For the coupled human-rodent system, we prove global existence, uniqueness and positivity of solutions, derive a basic reproduction number R_0 that guarantees almost sure extinction when R_0 < 1, and obtain explicit persistence-in-the-mean conditions for both infected rodents and humans, which define persistence thresholds for the joint dynamics. Numerical experiments show how clustered human transmission events, environmental variability and control measures shift these thresholds and shape the frequency and size of Mpox outbreaks.