Model Predictive Control for SEIR Epidemic Model without Terminal Ingredients

Core Concepts

MPC without terminal ingredients ensures stability and recursive feasibility in controlling the SEIR epidemic model.

Abstract

The article discusses a model predictive control (MPC) formulation tailored to the SEIR epidemic model without terminal conditions. It rigorously shows recursive feasibility and asymptotic stability of the disease-free equilibrium with a suitable prediction horizon. The paper highlights the importance of stability and recursive feasibility in MPC controllers applied to epidemics. Various numerical simulations demonstrate the impact of different weighting parameters on societal interventions and epidemic duration.

Stats

βnom = 0.44, γnom = 1/6.5, βmin = 0.22, γmax = 0.5, η = 1/4.6, Imax = 0.05. Initial state x0 = (0.5, 0.18, 0.01) Control horizon δ = 1 day, prediction horizon T = 20 days

Quotes

Key Insights Distilled From

MPC without Terminal Ingredients Tailored to the SEIR Compartmental Epidemic Model

by Willem Ester... at arxiv.org 03-15-2024

https://arxiv.org/pdf/2403.09151.pdf

Deeper Inquiries

How does the absence of terminal ingredients affect the stability and feasibility of MPC in controlling epidemics

The absence of terminal ingredients in Model Predictive Control (MPC) for controlling epidemics has significant implications on stability and feasibility. In the context of the SEIR compartmental epidemic model, the absence of terminal ingredients does not hinder the stability and recursive feasibility of the MPC closed-loop system. The study shows that under certain assumptions, it is possible to achieve stability without incorporating terminal conditions in the finite-horizon optimal control problem. This means that with a sufficiently long prediction horizon, recursive feasibility can be maintained, and the closed-loop trajectory can asymptotically reach a desired equilibrium point without needing specific terminal constraints.

What are the implications of different weighting parameters on societal interventions during an epidemic

The weighting parameter λ plays a crucial role in determining societal interventions during an epidemic when using MPC. Different values of λ impact how much importance is given to minimizing deviations from disease-free equilibrium points versus minimizing societal interventions such as social distancing measures or quarantine restrictions. A higher value of λ places more emphasis on reducing infection numbers and exposed individuals by penalizing deviations from equilibrium points more heavily. This results in stricter societal interventions being implemented to control the spread of the disease. Conversely, lower values of λ prioritize maintaining minimal societal intervention levels over achieving rapid eradication of infections. While this may lead to fewer restrictions on daily activities, it could prolong the duration of an epidemic due to reduced efforts towards containment measures.

How can the findings from this study be applied to real-world scenarios like the COVID-19 pandemic

The findings from this study have practical applications for real-world scenarios like managing pandemics such as COVID-19: Optimal Control Strategies: The insights gained from applying MPC without terminal ingredients can help policymakers develop optimal control strategies for managing epidemics efficiently while considering state and input constraints. Adaptive Intervention Policies: By understanding how different weighting parameters affect societal interventions during an epidemic, decision-makers can tailor their policies based on priorities - whether focusing on minimizing infections or limiting social disruptions. Resource Allocation: The ability to adjust parameters like λ allows for flexible resource allocation decisions during a pandemic response, optimizing outcomes based on evolving circumstances and available resources. Scenario Planning: These research findings enable scenario planning by simulating various intervention strategies with different weighting parameters to anticipate potential outcomes and inform proactive decision-making in public health emergencies.