A Model of Dengue Transmission

Marcos A. Capistrán (), Ignacio Barradas Bribiesca () and Gladys E. Salcedo ()
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Marcos A. Capistrán: Centro de Investigación en Matemáticas A.C. Unidad Mérida
Ignacio Barradas Bribiesca: Centro de Investigación en Matemáticas A.C.
Gladys E. Salcedo: University of Quindío, Department of Mathematics

A chapter in Handbook of Visual, Experimental and Computational Mathematics, 2026, pp 1499-1515 from Springer

Abstract: Abstract This chapter combines a dengue transmission model and dengue notification records from three cities in Brazil, Colombia, and México to analyze the role of mosquito oviposition rate and density-dependent juvenile mosquito mortality rate on the timing and size of dengue outbreaks. Data-driven model analysis of dengue outbreaks remains a challenging problem. Indeed, the morbidity and mortality caused by dengue virus are a major societal burden. Dengue virus is a mosquito-borne, single positive-stranded RNA virus of the family Flaviviridae, genus Flavivirus. Dengue fever is a viral infection that is transmitted to humans by mosquitoes that are vectors for the virus. Dengue fever is a common disease in the tropical and subtropical regions. It is especially common in Southeast Asia, the Caribbean, and South America. This chapter presents a simple first-principles dengue outbreak model with a seasonal oviposition rate and density-dependent juvenile mosquito mortality rate, based in part on the results of several previous models. Vertical transmission within the mosquito is ignored in the new model. The net reproduction rate and the basic reproduction number are used as quantities of interest to show the role of mosquito larval development and survival in shaping dengue outbreaks. This chapter provides an argument for the size and timing of dengue outbreaks in terms of mosquito population dynamics. The analysis presented in this chapter may be used in a generalized model that includes weather covariates.

Keywords: Dengue fever; Vector-borne diseases; Data-driven modeling; Bayesian inference; Nonlinear dynamics (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1007/978-3-032-16368-4_35

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