Intervention-Based Stochastic Disease Eradication

TL;DR

This paper investigates how random, intervention-based disease control strategies, modeled as Poisson processes, can significantly accelerate disease extinction times in large populations, outperforming traditional periodic approaches.

Contribution

It introduces a stochastic model of intervention control based on mean period and treatment fraction, demonstrating exponential improvements in disease extinction times.

Findings

Random intervention controls exponentially reduce extinction times.

Poisson-distributed interventions outperform periodic schedules under certain conditions.

Parameter regimes identified where randomness yields optimal results.

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. Thus intervention controls, such as vaccination of susceptible individuals and/or treatment of infectives, are typically based on a deterministic schedule, such as periodically vaccinating susceptible children based on school calendars. 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.