Skip to content
DraconiticResearch
Search Sources API
188,932 studies31 sourcesUpdated 37 min ago
Peer-reviewedCC BY 4.0Mathematics

Multi-Objective Identification and Optimal Control for Generalized SIR Epidemic Models with Time-Dependent Parameters

  • Aníbal Coronel1
  • Ana Paula Chorobura2
  • Camila Isoton3
  • Fernando Huancas4
4 affiliations
  1. 1Departamento de Ciencias Básicas–Centro de Ciencias Exactas, Facultad de Ciencias, Universidad del Bío-Bío, Campus Fernando May, Chillán 3780000, Chile
  2. 2Instituto de Matemática, Universidade Federal de Mato Grosso do Sul, Campo Grande 79074-460, Brazil
  3. 3Faculdade de Ciências Exatas e Tecnologia, Universidade Federal da Grande Dourados, Dourados 79804-970, Brazil
  4. 4Departamento de Matemática, Facultad de Ciencias Naturales, Matemáticas y del Medio Ambiente, Universidad Tecnológica Metropolitana, Las Palmeras No. 3360, Ñuñoa, Santiago 7800003, Chile
Open at sourceDOICite

Abstract

This paper investigates a multi-objective optimization framework for the simultaneous parameter identification and optimal vaccination control of a generalized non-linear SIR epidemic model. In contrast to traditional single-objective approaches, we formulate a vector optimization problem to concurrently minimize deviations from observed trajectories, disease prevalence, and public health operational costs, unlocking the identification of Pareto-optimal strategies. We establish the global existence, uniqueness, and physical invariance of the state solutions within a classical Sobolev space framework by employing a contraction mapping argument under the Bielecki weighted norm. Via the direct method of the calculus of variations and compact Sobolev embeddings, the existence of weak Pareto-optimal solutions is rigorously proved. First-order necessary optimality conditions are subsequently derived using the geometric Dubovitskii–Milyutin functional formalism, which yields a well-posed backward linear adjoint system and a precise characterization of the coupled variational inequalities. Finally, we implement a robust numerical architecture driven by an adjoint-based Augmented Lagrangian Method coupled with a quasi-Newton solver over a piecewise linear continuous subspace for the approximation and simulation of the Pareto-optimal frontier, which is successfully validated through three distinct numerical examples.

Related

  1. A model for mosquito-borne epidemic outbreaks with information-dependent protective behaviour.
    Simone De Reggi, Andrea Pugliese, Mattia Sensi +1
    Journal of mathematical biologyPeer-reviewedCC BYFull textEpidemiology & public healthEurope PMC
  2. Academic-year differences and psychophysiological associations with objective spinal parameters in physiotherapy students: a cross-sectional DIERS formetric 4D study.
    Esra Ateş Numanoğlu, Asude Arık, Esra Pamukçu +2
    BMC medical educationPeer-reviewedCC BY-NC-NDFull textSurgery & anaesthesiaEurope PMCDOAJ
  3. Early detection of immunoglobulin A against a vaccine backbone protein enables fast, durable, and objective identification of individuals vaccinated against Ebola virus
    Olivia Posadas, Irina Maljkovic Berry, Viviane Callier +12
    eBioMedicinePeer-reviewedCC BY 4.0Full textInfectious diseasePMCEurope PMCCrossref
  4. Development of a predictive model and nomogram using CTPA parameters for the identification of group 1 pulmonary arterial hypertension
    Huaxin Yuan, Iokfai Cheang, Gengmin Liang +9
    iSciencePeer-reviewedCC BY 4.0Full textGeneral medicineCell PressCrossrefEurope PMC
  5. Dose‐Dependent Efficacy of Radioiodine Therapy in Pediatric Graves’ Disease: A Retrospective Study of Hypothyroidism Risk and the Predictive Role of Thyroid Hormone Parameters
    Xiaoxue Tian, Dan Zhang, Yihui Wang +6
    iRADIOLOGYPeer-reviewedCC BYFull textEndocrinology & metabolismDOAJ

Cite

BibTeXRIS
BibTeX
@article{coronel2026multiobjective,
  title = {{Multi-Objective Identification and Optimal Control for Generalized SIR Epidemic Models with Time-Dependent Parameters}},
  author = {Aníbal Coronel and Ana Paula Chorobura and Camila Isoton and Fernando Huancas},
  journal = {Mathematics},
  year = {2026},
  month = oct,
  doi = {10.3390/math14213939},
  url = {https://www.mdpi.com/2227-7390/14/21/3939},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Multi-Objective Identification and Optimal Control for Generalized SIR Epidemic Models with Time-Dependent Parameters
AU  - Aníbal Coronel
AU  - Ana Paula Chorobura
AU  - Camila Isoton
AU  - Fernando Huancas
PY  - 2026
DA  - 2026/10/28
JO  - Mathematics
DO  - 10.3390/math14213939
UR  - https://www.mdpi.com/2227-7390/14/21/3939
AB  - This paper investigates a multi-objective optimization framework for the simultaneous parameter identification and optimal vaccination control of a generalized non-linear SIR epidemic model. In contrast to traditional single-objective approaches, we formulate a vector optimization problem to concurrently minimize deviations from observed trajectories, disease prevalence, and public health operational costs, unlocking the identification of Pareto-optimal strategies. We establish the global existence, uniqueness, and physical invariance of the state solutions within a classical Sobolev space framework by employing a contraction mapping argument under the Bielecki weighted norm. Via the direct method of the calculus of variations and compact Sobolev embeddings, the existence of weak Pareto-optimal solutions is rigorously proved. First-order necessary optimality conditions are subsequently derived using the geometric Dubovitskii–Milyutin functional formalism, which yields a well-posed backward linear adjoint system and a precise characterization of the coupled variational inequalities. Finally, we implement a robust numerical architecture driven by an adjoint-based Augmented Lagrangian Method coupled with a quasi-Newton solver over a piecewise linear continuous subspace for the approximation and simulation of the Pareto-optimal frontier, which is successfully validated through three distinct numerical examples.
SN  - 2227-7390
ER  -