Mathematics Subject Classification: 92D25, 92D30, 92B99.
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Artículo
A delay differential equations model for disease transmission dynamics
Un modelo de ecuaciones diferenciales con retraso para la dinámica de transmisión de enfermedades
1Arizona State University, Simon A. Levin Mathematical, Computational and Modeling Sciences Center, Tempe AZ, United States. mustafa.erdem@asu.edu
2Arizona State University, Simon A. Levin Mathematical, Computational and Modeling Sciences Center, Tempe, United States. Mansoura University, Mathematics Department, Faculty of Science, Mansoura, Egypt. Umm Al-Qura University, Department of Mathematical Sciences, Faculty of Applied Sciences, Makkah, Saudi Arabia. muntaser_safan@yahoo.com
3Arizona State University, Simon A. Levin Mathematical, Computational and Modeling Sciences Center, Tempe AZ, United States; Brown University, Visiting Provost Professor of Applied Mathematics. carlos_castillo-chavez@brown.edu
A delay differential equations epidemic model of SIQR (Susceptible-Infective-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.
Keywords: delay differential equation; integro-differential equation; epidemic model; quarantine; stability switch; oscillations; stage structure.
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.
Palabras clave: ecuación diferencial con retraso; ecuación integro-diferencial; modelo epidémico; cuarentena; cambio de estabilidad; oscilaciones; estructura por etapas.
Mathematics Subject Classification: 92D25, 92D30, 92B99.
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Acknowledgements
Authors thank the reviewers as well as the editors for their effort.
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Recibido: 18 de Mayo de 2019; Revisado: 20 de Junio de 2019; Aprobado: 17 de Septiembre de 2019