A delay differential equations model for disease transmission dynamics

• ERDEM, MUSTAFA ^[1] ; SAFAN, MUNTASER ^[1] ; CASTILLO-CHAVEZ, CARLOS ^[1]
  1. [1] Arizona State University

     Arizona State University

     Estados Unidos

     
• Localización: Revista de Matemática: Teoría y Aplicaciones, ISSN 2215-3373, ISSN-e 2215-3373, Vol. 27, Nº. 1, 2020 (Ejemplar dedicado a: Revista de Matemática: Teoría y Aplicaciones), págs. 49-71
• Idioma: inglés
• DOI: 10.15517/rmta.v27i1.39948
• Títulos paralelos:
  • Un modelo de ecuaciones diferenciales con retraso para la dinámica de transmisión de enfermedades
• Enlaces
  • Texto completo (pdf)
• Resumen
  • español

    Se propone un modelo epidémico de ecuaciones diferenciales con retraso del tipo SIQR (por sus siglas en inglés) (Susceptible-Infeccioso-En cuarentena-Recuperado), con períodos arbitrariamente distribuidos en la clase de aislamiento o cuarentena. Se analizan sus características matemáticas esenciales. Además, se identifican las condiciones que respaldan la existencia de soluciones periódicas a través de la bifurcación de Hopf. Los tiempos de espera no exponenciales en la clase de cuarentena/aislamiento conducen no solo a oscilaciones sino que también pueden soportar cambios de estabilidad.

  • English

    A delay differential equations epidemic model of SIQR (SusceptibleInfective-Quarantined-Recovered) type, with arbitrarily distributed periods in the isolation or quarantine class, is proposed. Its essential mathematical features are analyzed. In addition, conditions that support the existence of periodic solutions via Hopf bifurcation are identified. Nonexponential waiting times in the quarantine/isolation class lead not only to oscillations but can also support stability switches.

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