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Revista Colombiana de Matemáticas
Print version ISSN 0034-7426
Rev.colomb.mat. vol.55 no.1 Bogotá Jan./June 2021 Epub Nov 17, 2021
https://doi.org/10.15446/recolma.v55n1.99099
ORIGINAL ARTICLES
Modeling the dengue fever transmission in a periodic environment
Modelando la transmisión de la fiebre del dengue en un entorno periódico
1 Universidad del Quindío, Armenia, Colombia
A mathematical model for dengue fever transmission is analyzed, which incorporates relevant biological and ecological factors: vertical transmission and seasonality in the interaction between the vector (Aedes aegypti females) and the host (human). The existence and uniqueness of a positive disease-free periodic solution is proved; the global stability of the disease-free solution and the effect of periodic migrations of mosquitoes carrying the virus on the transmission of dengue are analyzed utilizing the mathematical definition of the Basic Reproductive Number in periodic environments; finally, it is numerically corroborated with the help of the Basic Reproductive Number that dengue cannot invade the disease-free state if it is less than one and can invade if it is greater than one, however, in both threshold conditions when vertical transmission occurs, the number of infected people and carrier vectors rises, representing a mechanism for the persistence of dengue cases in a community throughout a natural year.
Keywords: Dengue; seasonality; Aedes aegypti; vertical transmission; Basic Reproductive Number
Se propone un modelo matemático para la transmisión de la fiebre del dengue que incorpora factores biológicos y ecológicos relevantes: transmisión vertical y estacionalidad en la interacción entre el vector (Aedes aegypti) y el hospedero (humano). Se demuestra la existencia y unicidad de una solución periódica positiva libre de la enfermedad; la estabilidad global de la solución libre de la enfermedad y el efecto de las inmigraciones periódicas de mosquitos portadores del virus en la transmisión del dengue se analizan mediante la definición matemática del Número Reproductivo Básico en ambientes periódicos; finalmente, se corrobora numéricamente con ayuda del Número Reproductivo Básico que el dengue no puede invadir el estado libre de la enfermedad si es menor que uno y puede invadir si es mayor que uno, sin embargo, cuando en ambas condiciones de umbral ocurre transmisión vertical, se eleva el número de personas infectadas y vectores portadores, representando un mecanismo para la persistencia de casos de dengue en una comunidad a lo largo de un año natural.
Palabras clave: Dengue; estacionalidad; Aedes aegypti; transmisión vertical; Número Reproductivo Básico
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Received: December 06, 2020; Accepted: March 01, 2021
This is an open-access article distributed under the terms of the Creative Commons Attribution License
