Abstract

OLARTE, Julián Alejandro  and  MUNOZ, Anibal. Modeling the dengue fever transmission in a periodic environment. Rev.colomb.mat. [online]. 2021, vol.55, n.1, pp.71-107.  Epub Nov 17, 2021. ISSN 0034-7426.  https://doi.org/10.15446/recolma.v55n1.99099.

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.

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