Optimal control of a SIR epidemic model with general incidence function and a time delays

• Autores: Moussa Barro, Aboudramane Guiro, Dramane Ouedraogo
• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 20, Nº. 2, 2018, págs. 53-66
• Idioma: inglés
• DOI: 10.4067/S0719-06462018000200053
• Enlaces
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• Resumen
  • español

    RESUMEN En este artículo, introducimos un control óptimo para un modelo SIR gobernado por un sistema de EDOs con retardo temporal. Extendemos los estudios de estabilidad del modelo (2) en la sección 2, incorporando controles apropiados. Consideramos dos estrategias de control en el modelo de control óptimo, llámense: las estrategias de vacunación y tratamiento. El modelo tiene un retardo en el tiempo que representa el período de incubación. Derivamos las condiciones necesarias de primer orden para el control óptimo y realizamos simulaciones numéricas para mostrar la efectividad y también la aplicabilidad del modelo para diferentes valores de los retardos temporales Estas simulaciones numéricas muestran que el modelo es sensible a los retardos que representan el período de incubación.

  • English

    ABSTRACT In this paper, we introduce an optimal control for a SIR model governed by an ODE system with time delay. We extend the stability studies of model (2.2) in section 2, by incorporating suitable controls. We consider two control strategies in the optimal control model, namely: the vaccination and treatment strategies. The model has a time delays that represent the incubation period. We derive the first-order necessary conditions for the optimal control and perform numerical simulations to show the effectiveness as well as the applicability of the model for different values of the time delays. These numerical simulations show that the model is sensitive to the delays representing the incubation period.

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