Dengue model with early-life stage of vectors and age-structure within host

Sanchez, Fabio; Calvo, Juan G.; Sanchez, Fabio; Calvo, Juan G.

doi:10.15517/rmta.v27i1.39966

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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.v27i1.39966

Artículo

Dengue model with early-life stage of vectors and age-structure within host

Modelo de dengue con etapa temprana en vectores y estructura de edad en el huésped

Fabio Sanchez¹

Juan G. Calvo²

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

^²University of Costa Rica, CIMPA, School of Mathematics, San José, Costa Rica; juan.calvo@ucr.ac.cr

Abstract

We construct an epidemic model for the transmission of dengue fever with an early-life stage in the vector dynamics and age-structure within hosts. The early-life stage of the vector is modeled via a general function that supports multiple vector densities. The basic reproductive number and vector demographic threshold are computed to study the local and global stability of the infection-free state. A numerical framework is implemented and simulations are performed.

Keywords: dengue fever; epidemic models; mathematical modeling; vectorborne diseases; age-structured model.

Resumen

Se construye un modelo epidémico para la dinámica de transmisión de la fiebre del dengue con etapa temprana de vida en los vectores y estructura de edad en las clases de los huéspedes. La etapa de vida temprana del vector, se modela a través de una función general que admite múltiples densidades de vectores. El número reproductivo básico y vector de umbral demográfico, se calculan para estudiar la estabilidad local y global del estado libre de infección. Se implementa además un marco numérico y se realizan simulaciones.

Palabras clave: dengue; modelos epidémicos; modelizaje matemático; enfermedades vectoriales; modelos con estructura de edad.

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: August 26, 2019; Accepted: September 18, 2019

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