Modelling the Stochastic Importation Dynamics and Establishment of Novel Pathogenic Strains using a General Branching Processes Framework

TL;DR

This paper introduces a stochastic branching process model incorporating host heterogeneity and importation dynamics to better predict the early and medium-term spread of novel pathogens, exemplified with COVID-19 data.

Contribution

It presents a flexible, stochastic modeling framework that integrates importation and host variability, enhancing disease outbreak predictions during uncertain early phases.

Findings

Model captures stochasticity in early outbreak stages.

Framework can be tailored to specific diseases.

Combines stochastic and deterministic approaches for long-term projections.

Abstract

The importation and subsequent establishment of novel pathogenic strains in a population is subject to a large degree of uncertainty due to the stochastic nature of the disease dynamics. Mathematical models need to take this stochasticity in the early phase of an outbreak in order to adequately capture the uncertainty in disease forecasts. We propose a general branching process model of disease spread that includes host-level heterogeneity, and that can be straightforwardly tailored to capture the salient aspects of a particular disease outbreak. We combine this with a model of case importation that occurs via an independent marked Poisson process. We use this framework to investigate the impact of different control strategies, particularly on the time to establishment of an invading, exogenous strain, using parameters taken from the literature for COVID-19 as an example. We also demonstrate how to combine our model with a deterministic approximation, such that longer term projections can be generated that still incorporate the uncertainty from the early growth phase of the epidemic. Our approach produces meaningful short- and medium-term projections of the course of a disease outbreak when model parameters are still uncertain and when stochasticity still has a large effect on the population dynamics.