Journal of Mathematical Biology

, Volume 35, Issue 5, pp 523–544

Competitive exclusion in a vector-host model for the dengue fever

  • Zhilan Feng
  • Jorge X. Velasco-Hernández

DOI: 10.1007/s002850050064

Cite this article as:
Feng, Z. & Velasco-Hernández, J. J Math Biol (1997) 35: 523. doi:10.1007/s002850050064


 We study a system of differential equations that models the population dynamics of an SIR vector transmitted disease with two pathogen strains. This model arose from our study of the population dynamics of dengue fever. The dengue virus presents four serotypes each induces host immunity but only certain degree of cross-immunity to heterologous serotypes. Our model has been constructed to study both the epidemiological trends of the disease and conditions that permit coexistence in competing strains. Dengue is in the Americas an epidemic disease and our model reproduces this kind of dynamics. We consider two viral strains and temporary cross-immunity. Our analysis shows the existence of an unstable endemic state (‘saddle’ point) that produces a long transient behavior where both dengue serotypes cocirculate. Conditions for asymptotic stability of equilibria are discussed supported by numerical simulations. We argue that the existence of competitive exclusion in this system is product of the interplay between the host superinfection process and frequency-dependent (vector to host) contact rates.

Key words: Mathematical epidemiologyDengueDifferential equationsVectorborne diseasesPopulation dynamics

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Zhilan Feng
    • 1
  • Jorge X. Velasco-Hernández
    • 2
  1. 1.Biometrics Unit, Cornell University, Ithaca, NY 14853–7801, USAUS
  2. 2.Departamento de Matemáticas, UAM-Iztapalapa, MéxicoXX