Simulation of an optimal control of epidemiological model reservoir-people
Simulación de un problema de control óptimo del modelo epidemiológico reservorio-personas
Resumen
Este artículo estudia un algoritmo para resolver un problema de control óptimo en un modelo epidemiológico reservorio-personas. El principal objetivo de este trabajo es identificar estrategias óptimas de vacunación y tratamiento que puedan implementarse minimizando los costos materiales y humanos asociados con la epidemia. Para lograr esto, se utiliza el Principio del Máximo de Pontryagin, un resultado matemático que proporciona las condiciones necesarias para encontrar la caracterización del control óptimo asociado con ecuaciones diferenciales ordinarias.Además, se realizan simulaciones numéricas para validar la metodología propuesta. Proporciona una herramienta para la toma de decisiones y la implementación eficiente de la vacunación y el tratamiento en escenarios epidémicos, además de facilitar la planificación de respuestas ante futuras crisis de salud pública.
Citas
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Applied Sciences 45, 6481–6494 (2022)
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Control, Springer, 89–109 (2017)
3. Barro, M., Aboudramane, G. and Ouedraogo, D.: Optimal control of a SIR epidemic model
with general incidence function and time delays, Cubo 20, 53–66 (2018)
4. Chen, T., Yang, J., Zhang, R., Li, X., Ma, J. and Yang, G.: The transmissibility estimation
of influenza with early stage data of small-scale outbreaks in Changsha, China, 2005–2013,
Epidemiology and Infection 145, 1–10 (2016)
5. Chen, T. M., Guo, J., Li, M., Wu, L., Zhang, Z. and Wang, Y.: A mathematical model for
simulating the phase-based transmissibility of a novel coronavirus, Infectious Diseases of
Poverty 9 (2020)
6. Dansana, D., Gupta, V., Singh, A., Sharma, R., Soni, N. and Jain, R.: Using SusceptibleExposed-Infectious-Recovered Model to Forecast Coronavirus Outbreak, Computers, Materials and Continua 67, 1595–1612 (2021)
7. Gerdts, M.: Optimal Control of Ordinary Differential Equations and Differential-Algebraic
Equations, Habilitation, University of Bayreuth (2006)
8. Howerton, E., Rojas, D., Meeker, J. and Wilson, H.: The effect of governance structures on
optimal control of two-patch epidemic models, Journal of Mathematical Biology (2023), in
press
9. Laarabi, H., Karama, A., Benabdallah, H., and Abdelkader, S.: Optimal Control of a Delayed
SIRS Epidemic Model with Vaccination and Treatment, Acta Biotheoretica 63, 87–97 (2015)
10. Lacy, A., Bell, G., Ibarra, G., and Watson, L.: Modeling impact of vaccination on COVID-19
dynamics in St. Louis, Journal of Biological Dynamics 17, 25 (2023)
11. Lenhart, S. and Workman, J.T.: Optimal control applied to biological models, Chapman and
Hall/CRC (2007)
12. Longini, I.M., Halloran, M.E., Nizam, A., Yang, Y. and Gonc¸alo, M.: Containing Pandemic
Influenza at the Source, Science 309, 1083–1087 (2005)
13. Miller Neilan, R. and Lenhart, S.: An Introduction to Optimal Control with an Application in
Disease Modeling, DIMACS Series in Discrete Mathematics 75, (2010)
14. Maurer, H., Altrogge, I. and Goris, N.: Optimization methods for solving bang-bang control
problems with state constraints and the verification of sufficient conditions, Proceedings of the
44th IEEE Conference on Decision and Control, 923–928 (2006)
15. Nababan, S.: A Filippov-type lemma for functions involving delays and its application to
time-delayed optimal control problems, Journal of Optimization Theory and Applications 27,
357–376 (1979)
16. N´unez, C.: ˜ MATLAB code for computing the optimal control of the epidemiological reservoirpeople model (2025)
17. Pormohammad, A., Ghasemi, S. and Mehr, S.: Comparison of influenza type A and B with
COVID-19: A global systematic review and meta-analysis on clinical, laboratory and radiographic findings, Reviews in Medical Virology 31, e2179 (2021)
18. Rahimi, I., Chen, F., Gandomi, A. and Saeed, S.: A review on COVID-19 forecasting models,
Neural Computing and Applications 35, (2021)
19. Shi, Y., Wang, X., Jiang, H. and Luo, J.: An overview of COVID-19, Journal of Zhejiang
University Science B 21, 343–360 (2020)
20. Velasco-Hernandez, J.: Modelos matematicos en epidemiologia: enfoques y alcances, Miscelanea Matematica 44, 11–27 (2007)
