Control of rare events in reaction and population systems by deterministic processes and the speedup of disease extinction

TL;DR

This paper explores how deterministic interventions can exponentially influence rare events in reaction and population systems, including disease extinction, and compares their efficiency to rate modulation methods.

Contribution

It introduces a novel approach of controlling rare events through deterministic state transitions and compares its effectiveness with traditional rate modulation techniques.

Findings

Deterministic control can exponentially alter rare event rates.

Controlling transitions directly can be more efficient than modulating rates.

Optimal control strategies for disease extinction are analyzed.

Abstract

We consider control of reaction and population systems by deterministically imposed transitions between the states with different numbers of particles or individuals. Even where the imposed transitions are significantly less frequent than spontaneous transitions, they can exponentially strongly modify the rates of rare events, including switching between metastable states or population extinction. We also study optimal control of rare events, and specifically, optimal control of disease extinction for a limited vaccine supply. A comparison is made with control of rare events by modulating the rates of elementary transitions rather than imposing transitions. It is found that, unexpectedly, for the same mean control parameters, controlling the transitions rates can be more efficient.