EPIDEMIOPTIM: A TOOLBOX FOR THE OPTIMIZATION OF CONTROL POLICIES IN EPIDEMIOLOGICAL MODELS

Abstract

Epidemiologists model the dynamics of epidemics in order to propose control strategies based on pharmaceutical and non-pharmaceutical interventions (contact limitation, lock down, vaccination, etc). Hand-designing such strategies is not trivial because of the number of possible interventions and the difficulty to predict long-term effects. This task can be cast as an optimization problem where state-of-the-art machine learning algorithms such as deep reinforcement learning, might bring significant value. However, the specificity of each domainepidemic modelling or solving optimization problem -requires strong collaborations between researchers from different fields of expertise. This is why we introduce EpidemiOptim, a Python toolbox that facilitates collaborations between researchers in epidemiology and optimization. EpidemiOptim turns epidemiological models and cost functions into optimization problems via a standard interface commonly used by optimization practitioners (OpenAI Gym). Reinforcement learning algorithms based on Q-Learning with deep neural networks (DQN) and evolutionary algorithms (NSGA-II) are already implemented. We illustrate the use of EpidemiOptim to find optimal policies for dynamical on-off lock-down control under the optimization of death toll and economic recess using a Susceptible-Exposed-Infectious-Removed (SEIR) model for COVID-19. Using EpidemiOptim and its interactive visualization platform in Jupyter notebooks, epidemiologists, optimization practitioners and others (e.g. economists) can easily compare epidemiological models, costs functions and optimization algorithms to address important choices to be made by health decision-makers.

1. INTRODUCTION

The recent COVID-19 pandemic highlights the destructive potential of infectious diseases in our societies, especially on our health, but also on our economy. To mitigate their impact, scientific understanding of their spreading dynamics coupled with methods quantifying the impact of intervention strategies along with their associated uncertainty, are key to support and optimize informed policy making. For example, in the COVID-19 context, large scale population lock-downs were enforced based on analyses and predictions from mathematical epidemiological models (Ferguson et al., 2005; 2006; Cauchemez et al., 2019; Ferguson et al., 2020) . In practice, researchers often consider a small number of relatively coarse and pre-defined intervention strategies, and run calibrated epidemiological models to predict their impact (Ferguson et al., 2020) . This is a difficult problem for several reasons: 1) the space of potential strategies can be large, heterogeneous and multi-scale (Halloran et al., 2008) ; 2) their impact on the epidemic is often difficult to predict; 3) the problem is multi-objective by essence: it often involves public health objectives like the minimization of the death toll or the saturation of intensive care units, but also societal and economic sustainability. For these reasons, pre-defined strategies are bound to be suboptimal. Thus, a major challenge consists in leveraging more sophisticated and adaptive approaches to identify optimal strategies. Machine learning can be used for the optimization of such control policies, with methods ranging from deep reinforcement learning to multi-objective evolutionary algorithms. In other domains, they have proven efficient at finding robust control policies, especially in high-dimensional nonstationary environments with uncertainty and partial observation of the state of the system (Deb et al., 2007; Mnih et al., 2015; Silver et al., 2017; Haarnoja et al., 2018; Kalashnikov et al., 2018; Hafner et al., 2019 ). Yet, researchers in epidemiology, in public-health, in economics, and in ma-

