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Revista de Matemática Teoría y Aplicaciones

Print version ISSN 1409-2433

Rev. Mat vol.27 n.1 San José Jan./Jun. 2020

http://dx.doi.org/10.15517/rmta.v27i1.39977 

Artículo

Transmission dynamics of dengue in Costa Rica: the role of hospitalizations

Dinámica de la transmisión de dengue en costa rica: el rol de las hospitalizaciones

Fabio Sanchez1 

Jorge Arroyo-Esquivel2 

Paola Vásquez3 

1University of Costa Rica; CIMPA; School of Mathematics; San José; Costa Rica; fabio.sanchez@ucr.ac.cr

2University of California Davis; Department of Mathematics; Davis; California; USA; jarroyoe@ucdavis.edu

3University of Costa Rica; School of Public Health; San José; Costa Rica; paola.vasquez@ucr.ac.cr

Abstract

For decades, dengue virus has caused major problems for public health officials in tropical and subtropical countries around the world. We construct a compartmental model that includes the role of hospitalized individuals in the transmission dynamics of dengue in Costa Rica. The basic reproductive number, ℛ 0 , is computed, as well as a sensitivity analysis on ℛ 0 parameters. The global stability of the disease-free equilibrium is established. Numerical simulations under specific parameter scenarios are performed to determine optimal prevention/control strategies.

Keywords: dengue fever; mathematical modeling; epidemic model; vector-borne diseases.

Resumen

Durante décadas, el virus del dengue ha causado grandes problemas a los funcionarios de salud pública en países tropicales y subtropicales de todo el mundo. Construimos un modelo compartimental que incluye el papel de las personas hospitalizadas en la dinámica de transmisión del dengue en Costa Rica. Calculamos el número básico reproductivo, ℛ 0 , así como un análisis de sensibilidad en los parámetros de ℛ 0 y discutimos la importancia de las políticas de salud pública. Se establece la estabilidad local y global del estado libre de enfermedad. Se hacen simulaciones numéricas bajo escenarios específicos para determinar estrategias óptimas de prevención y control.

Palabras clave: dengue; modelo matemático; modelo epidémico; enfermedades vectoriales.

Mathematics Subject Classification: 93A30, 92B99, 37N25.

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Acknowledgements

We thank the Research Center in Pure and Applied Mathematics and the Mathematics Department at Universidad de Costa Rica for their support during the preparation of this manuscript. The authors gratefully acknowledge institutional support for project B8747 from an UCREA grant from the Vice-Rectory for Research at Universidad de Costa Rica.

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Received: August 07, 2019; Revised: September 13, 2019; Accepted: September 20, 2019

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