Modelling the stochastic importation dynamics and establishment of novel pathogenic strains using a general branching processes framework

• Published in: Mathematical biosciences Vol. 380; p. 109352
• Main Authors: Curran-Sebastian, Jacob, Andersen, Frederik Mølkjær, Bhatt, Samir
• Format: Journal Article
• Language: English
• Published: United States Elsevier Inc 01.02.2025
• Subjects: Branching process; COVID-19 - epidemiology; COVID-19 - transmission; Disease Outbreaks - statistics & numerical data; Early disease dynamics; Humans; Importation of cases; Mathematical Concepts; Models, Biological; Population Dynamics; SARS-CoV-2 - pathogenicity; Stochastic Processes; Time-varying infectivity; Importation of cases; Time-varying infectivity; Branching process; Early disease dynamics
• ISSN: 0025-5564; 1879-3134; 1879-3134
• DOI: 10.1016/j.mbs.2024.109352

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 into account 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. •Early disease dynamics including importation are highly stochastic.•Our general model combines random importation with internal disease dynamics.•We calculate cases and extinction probabilities using generating functions.•We show trade-offs in reducing importation versus controlling transmission.