The Separatrix Algorithm for synthesis and analysis of stochastic simulations with applications in disease modeling.

Daniel J Klein,Michael Baym,Philip Eckhoff

doi:10.1371/journal.pone.0103467

Abstract

Decision makers in epidemiology and other disciplines are faced with the daunting challenge of designing interventions that will be successful with high probability and robust against a multitude of uncertainties. To facilitate the decision making process in the context of a goal-oriented objective (e.g., eradicate polio by ), stochastic models can be used to map the probability of achieving the goal as a function of parameters. Each run of a stochastic model can be viewed as a Bernoulli trial in which “success” is returned if and only if the goal is achieved in simulation. However, each run can take a significant amount of time to complete, and many replicates are required to characterize each point in parameter space, so specialized algorithms are required to locate desirable interventions. To address this need, we present the Separatrix Algorithm, which strategically locates parameter combinations that are expected to achieve the goal with a user-specified probability of success (e.g. 95%). Technically, the algorithm iteratively combines density-corrected binary kernel regression with a novel information-gathering experiment design to produce results that are asymptotically correct and work well in practice. The Separatrix Algorithm is demonstrated on several test problems, and on a detailed individual-based simulation of malaria.

Highlights

Decision makers are tasked with the challenging job of determining how best to achieve specific program goals despite large amounts of uncertainty
To illustrate the main contributions of this work, we have prepared a variety of results that demonstrate the Separatrix Algorithm, which has been implemented in Matlab [55]
We begin with a simple one-dimensional problem to show the full distribution of the estimated success probability function, and to clearly illustrate the experiment design process for generating subsequent sample points

Summary

Introduction

Decision makers are tasked with the challenging job of determining how best to achieve specific program goals despite large amounts of uncertainty. Poliomyelitis has been the target of a global eradication initiative since 1988 [2], wherein oral [3] and inactivated [4] polio vaccines are distributed through various routine and supplementary immunization activities [5] To achieve these goals with high probability, complex interactions between decisions (e.g. deploy bednets to 80% of the population) and mechanistic uncertainties (e.g. the extent to which mosquitoes feed indoors) must be considered systematically. Computer models enable these interactions to be simulated thousands of times in silico before trying in the real world. Efficient algorithms are required to best use limited computational resources, that increasinglydetailed computational models are being used directly in guiding policy decisions in HIV [6, 7], and in campaign design for influenza [8,9,10,11], polio [12], and malaria [13,14,15,16,17]

Methods

Results

Discussion

Conclusion