Introducing the Outbreak Threshold in Epidemiology

Matthew Hartfield,Samuel Alizon,Glenn F Rall

doi:10.1371/journal.ppat.1003277

Abstract

When a pathogen is rare in a host population, there is a chance that it will die out because of stochastic effects instead of causing a major epidemic. Yet no criteria exist to determine when the pathogen increases to a risky level, from which it has a large chance of dying out, to when a major outbreak is almost certain. We introduce such an outbreak threshold (T0), and find that for large and homogeneous host populations, in which the pathogen has a reproductive ratio R0, on the order of 1/Log(R0) infected individuals are needed to prevent stochastic fade-out during the early stages of an epidemic. We also show how this threshold scales with higher heterogeneity and R0 in the host population. These results have implications for controlling emerging and re-emerging pathogens.

Highlights

When a pathogen is rare in a host population, there is a chance that it will die out because of stochastic effects instead of causing a major epidemic
It has seldom been addressed how many infected individuals are needed to declare that an outbreak is occurring: that is, when the pathogen can go extinct due to stochastic effects, to when it infects a high enough number of hosts such that the outbreak size increases in a deterministic manner (Figure 1A)
If the host population is homogeneous and large enough so that depletion of the pool of susceptible hosts is negligible, the probability of pathogen extinction if I infected hosts are present is (1/R0)I ([6], details in Material S.1 in Text S1)

Summary

Introduction

When a pathogen is rare in a host population, there is a chance that it will die out because of stochastic effects instead of causing a major epidemic. The classic prediction for pathogen outbreak is that the pathogen’s reproductive ratio (R0), the number of secondary infections caused by an infected host in a susceptible population, has to exceed one [4,5].

Results

Conclusion