# On the probability of strain invasion in endemic settings: accounting for individual heterogeneity and control in multi-strain dynamics

## TL;DR

This paper models the stochastic process of a new disease strain invading an endemic population, highlighting how control measures and individual heterogeneity influence invasion probabilities and the emergence of drug resistance.

## Contribution

It introduces a branching process framework to quantify invasion probabilities considering heterogeneity and control, revealing scenarios where less-fit strains can invade fitter endemic populations.

## Key findings

- Differential control can enable less-fit strains to invade
- Invasion probability depends on the reproduction number ratio
- Control strategies influence strain invasion dynamics

## Abstract

The rise of antimicrobial drug resistance is an imminent threat to global health that has warranted, and duly received, considerable attention within the medical, microbiological and modelling communities. Outbreaks of drug-resistant pathogens are ignited by the emergence and transmission of mutant variants descended from wild-type strains circulating in the community. In this work we investigate the stochastic dynamics of the emergence of a novel disease strain, introduced into a population in which it must compete with an existing endemic strain. In analogy with past work on single-strain epidemic outbreaks, we apply a branching process approximation to calculate the probability that the new strain becomes established. As expected, a critical determinant of the survival prospects of any invading strain is the magnitude of its reproduction number relative to that of the background endemic strain. Whilst in most circumstances this ratio must exceed unity in order for invasion to be viable, we show that differential control scenarios can lead to less-fit novel strains invading populations hosting a fitter endemic one. This analysis and the accompanying findings will inform our understanding of the mechanisms that have led to past instances of successful strain invasion, and provide valuable lessons for thwarting future drug-resistant strain incursions.