Intervention-Based Stochastic Disease Eradication

Grant Lythe,Lora Billings,Luis Mier-Y-Teran-Romero,Brandon Lindley,Ira B Schwartz

doi:10.1371/journal.pone.0070211

Grant Lythe, Lora Billings + Show 3 more

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https://doi.org/10.1371/journal.pone.0070211

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Abstract

Disease control is of paramount importance in public health, with infectious disease extinction as the ultimate goal. Although diseases may go extinct due to random loss of effective contacts where the infection is transmitted to new susceptible individuals, the time to extinction in the absence of control may be prohibitively long. Intervention controls are typically defined on a deterministic schedule. In reality, however, such policies are administered as a random process, while still possessing a mean period. Here, we consider the effect of randomly distributed intervention as disease control on large finite populations. We show explicitly how intervention control, based on mean period and treatment fraction, modulates the average extinction times as a function of population size and rate of infection spread. In particular, our results show an exponential improvement in extinction times even though the controls are implemented using a random Poisson distribution. Finally, we discover those parameter regimes where random treatment yields an exponential improvement in extinction times over the application of strictly periodic intervention. The implication of our results is discussed in light of the availability of limited resources for control.

Highlights

Understanding the processes underlying disease extinction is an important problem in epidemic prediction and control
We quantified how treatment enhances the extinction of epidemics using a stochastic, discrete-population framework
We used a WKB approximation to the master equation of the stochastic process to calculate the average time to extinction starting from the endemic state, as a function of the transmissibility of the disease and the strength and frequency of the treatment

Summary

Introduction

Understanding the processes underlying disease extinction is an important problem in epidemic prediction and control. Total eradication of infectious disease is quite rare, but continues to be a major theme in public health. Sometimes called fade out, tends to happen in local spatial regions, and may be followed by the reintroduction of the disease from other regions [1,2,3]. Infectious disease transmission is conjectured to be responsible for certain species extinction [6,7]. Large scale amphibian species have had major declines in population, which have been linked with the spread of disease [8]

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