[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-86553-en":3,"doc-seo-86553-105":30,"detail-sidebar-cat-0-en-105":84},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},86553,1374391974564,"Clementine","https://ap-avatar.wpscdn.com/avatar/14000253aa45c000a9e?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779874745381141002",8,"Research & Report","Optimal Control of Pandemic Dynamics via Model Predictive Control: A Health–Economic Trade-off Analysis","This paper addresses optimal epidemic control under conflicting socioeconomic objectives. It proposes an economic Model Predictive Control (MPC) framework applied to an extended SEIR–V compartmental model to govern disease spread while minimizing economic disruption. The controller updates social interaction (transmission rate β) and vaccination to minimize a constrained nonlinear objective that penalizes fatalities, healthcare-capacity violations, and economic losses. Sensitivity analysis over prediction horizon N shows N = 35 days minimizes realized cost, and turnpike analysis yields the Hammer-and-Dance strategy and practical asymptotic stability of the optimal operating point.","Optimal Control of Pandemic Dynamics via Model Predictive  \nControl:  \nA Health–Economic Trade-off Analysis  \nLokman Rachid Melhani∗1, Lars Grüne2 , Antonino Sferlazza 1 , Dominique Persano Adorno 1 , Filippo D’Ippolito 1 , and Alberto Firenze3  \n1 Department of Engineering, University of Palermo, Palermo, Italy  \n2 Department of Mathematics, University of Bayreuth, Bayreuth, Germany  \n3 Department of Internal Medicine “Promise”, University of Palermo, 90127 Palermo, Italy  \narXiv :2607 . 11306v1 [math .OC] 13 Jul 2026  \nAbstract  \nThis paper addresses the optimal control of epidemic dynamics under conflicting socioeconomic objectives. We propose an economic Model Predictive Control (MPC) framework, applied to an extended SEIR–V (Susceptible–Exposed–Infected–Recovered–Vaccinated) compartmental model to govern the spread of an infectious disease while minimizing economic disruption. The control problem is formulated as a constrained nonlinear optimization problem, in which the controller dynamically adjusts social interaction levels (transmission rate β) and vaccination efforts to minimize a composite cost function that penalizes fatalities, healthcare capacity violations, and economic losses. We conduct a rigorous sensitivity analysis of the prediction horizon N , demonstrating that the closed loop is robust to the horizon choice and that N = 35 days minimizes the realized cost. Furthermore, both the closed-loop solution and an open-loop turnpike analysis across diverse initial conditions reveal that the celebrated “Hammer and Dance” mitigation strategy emerges naturally as the mathematical optimum: the optimal trajectories anchor to a unique suppression turnpike (maximum lockdown) to drive hospitalizations toward the disease-free equilibrium before progressively reopening the economy. Through a turnpike-based argument we establish practical asymptotic stability of the optimal operating point, providing a mathematically grounded decision-support tool for pandemic policy.  \nKeywords: Model Predictive Control; Epidemic Modeling; SEIR Model; Optimization; Public Health Policy  \n1 Introduction  \nThe outbreak of the COVID-19 pandemic exposed a fundamental vulnerability in global crisis management: the lack of quantitative, feedback-driven tools to balance competing societal objectives. Governments worldwide were forced to navigate a “lives versus livelihoods” dilemma, choosing between strict Non-Pharmaceutical Interventions (NPIs) such as lockdowns, which suppress viral transmission but cripple economic activity, and relaxed measures that preserve economic flow atthe cost of public health surges.  \n∗ Corresponding author: [lokmanrachid.melhani@unipa.it](lokmanrachid.melhani@unipa.it)  \nFrom a systems engineering perspective, an epidemic is a dynamic, nonlinear process governed by biological parameters such as incubation periods and transmission rates. Traditional epidemiological approaches [1] have largely focused on prediction, forecasting infection curves under static assumptions. However, effective pandemic management is inherently a control problem. The objective is not merely to observe the system but to regulate it: steering the state trajectory (infection levels) toward a safe equilibrium while minimizing the control effort (economic cost) .  \nThis paper addresses the optimal control of pandemic dynamics using Model Predictive Control (MPC) . Unlike open-loop strategies, which fix policies months in advance and fail to adapt to stochastic disturbances, MPC solves a finite-horizon optimization problem at every time step. [2] This approach allows for real-time adaptation to changing infection rates and ensures that distinct system constraints are rigorously respected, as demonstrated in recent applications of control theory to COVID-19 . [3, 4]  \n1.1 Contributions  \nThe contributions of this work are threefold:  \n1. Integrated and calibrated Modeling. We extend the classical SEIR framework to an SEIR–V model, incorporating vac","cbCaiu4BWqCfBekl","https://ap.wps.com/l/cbCaiu4BWqCfBekl","pdf",560057,5,1,17,"English","en",105,"# Introduction\n## Contributions\n# Problem Formulation and Pandemic Modeling\n## State Space Representation","[{\"question\":\"What do the sensitivity and turnpike analyses conclude about the optimal mitigation strategy?\",\"answer\":\"Sensitivity analysis identifies a prediction horizon N = 35 days that minimizes realized cost. Turnpike analysis shows that the optimal policy naturally reproduces the “Hammer and Dance” strategy, anchoring trajectories to a unique suppression turnpike before reopening progressively.\"}]",1784212589,43,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":79,"head_meta":81,"extra_data":83,"updated_unix":28},"optimal-control-of-pandemic-dynamics-via-model-predictive-control-a-healtheconomic-trade-off-analysis","",{"@graph":36,"@context":78},[37,54,69],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/optimal-control-of-pandemic-dynamics-via-model-predictive-control-a-healtheconomic-trade-off-analysis/86553/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":24,"description":14,"dateModified":62,"datePublished":63,"encodingFormat":61,"isAccessibleForFree":64,"interactionStatistic":65},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-07-24","2026-07-16",true,{"@type":66,"interactionType":67,"userInteractionCount":20},"InteractionCounter",{"@type":68},"ViewAction",{"@type":70,"mainEntity":71},"FAQPage",[72],{"name":73,"@type":74,"acceptedAnswer":75},"What do the sensitivity and turnpike analyses conclude about the optimal mitigation strategy?","Question",{"text":76,"@type":77},"Sensitivity analysis identifies a prediction horizon N = 35 days that minimizes realized cost. Turnpike analysis shows that the optimal policy naturally reproduces the “Hammer and Dance” strategy, anchoring trajectories to a unique suppression turnpike before reopening progressively.","Answer","https://schema.org",{"og:url":52,"og:type":80,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":82,"canonical":52},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":85},[86,90,94,98,102,107,112,115,120,123,127],{"id":21,"doc_module":4,"doc_module_name":46,"category_name":87,"show_sort_weight":88,"slug":89},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":91,"show_sort_weight":92,"slug":93},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":95,"show_sort_weight":96,"slug":97},"Exam",70,"exam",{"id":20,"doc_module":4,"doc_module_name":46,"category_name":99,"show_sort_weight":100,"slug":101},"Comic",60,"comic",{"id":103,"doc_module":4,"doc_module_name":46,"category_name":104,"show_sort_weight":105,"slug":106},6,"Technology",50,"technology",{"id":108,"doc_module":4,"doc_module_name":46,"category_name":109,"show_sort_weight":110,"slug":111},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":113,"slug":114},30,"research-report",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},9,"Religion & Spirituality",20,"religion-spirituality",{"id":118,"doc_module":4,"doc_module_name":46,"category_name":121,"show_sort_weight":118,"slug":122},"World Cup","world-cup",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":124,"slug":126},10,"Lifestyle","lifestyle",{"id":128,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":20,"slug":130},19,"General","general"]