Dengue Fever and the Zika Virus

  • Fred Brauer
  • Carlos Castillo-Chavez
  • Zhilan Feng
Part of the Texts in Applied Mathematics book series (TAM, volume 69)


While there have been cases of probable dengue fever more than 1000 years ago, the first recognized dengue epidemics occurred in Asia, Africa, and North America in the 1780s. There have been frequent outbreaks since then, and the number of reported cases has been increasing rapidly recently. According to the World Health Organization, approximately 50,000,000 people worldwide are infected with dengue. Symptoms may include fever, headaches, joint and muscle pain, and nausea, but many cases are very mild. There is no cure for dengue fever, but most patients recover with rest and fluids. There are at least four different strains of dengue fever, and there is some cross-immunity between strains. Dengue fever is transmitted by the mosquito aedes aegypti, and most control strategies are aimed at mosquito control.


  1. 1.
    Adams, B. and M. Boots (2010) How important is vertical transmission in mosquitoes for the persistence of dengue? Insights from a mathematical model, Epidemics 2: 1–10Google Scholar
  2. 2.
    Adams, B. and D.D. Kapan (2009) Man bites mosquito: understanding the contribution of human movement to vector-borne disease dynamics, PLos One 4(8); e6373. Scholar
  3. 3.
    Arunachalam, N., S.C. Tewari, V. Thenmozhi,R. Rajendran, R. Paramasivan, R. Manavalan, K. Ayanar and B.K. Tyagi (2008) Natural vertical transmissionof dengue viruses by Aedes aegyptiin Chennai, Tamil Nadu, India, Indian J Med Res 127: 395–397.Google Scholar
  4. 4.
    Balmaseda, A., S.N. Hammond, L. Perez, Y. Tellez, S.I. Saborio, J.C. Mercado, J.C., R. Cuadra, J. Rocha, M.A. Perez, S. Silva et al (2006) Serotype-specific differences in clinical manifestations of dengue, Am. J. of tropical medicine and hygiene 74: 449.CrossRefGoogle Scholar
  5. 5.
    Bichara, D., S.A. Holechek, J. Velasco-Castro,, A.L. Murillo and C. Castillo-Chavez (2016) On the dynamics of dengue virus type 2 with residence times and vertical transmission, to appearGoogle Scholar
  6. 6.
    Bichara, D., Y. Kang, C. Castillo-Chavez, R. Horan and C. Perringa (2015) SIS and SIR epidemic models under virtual dispersal, Bull. Math. Biol. 77 (2015):2004–2034.MathSciNetCrossRefGoogle Scholar
  7. 7.
    Bonnet, D.D. and D.J. Worcester (1946) The dispersal of Aedes albopictus in the territory of Hawaii, Am J.of tropical medicine and hygiene, 4: 465–476.CrossRefGoogle Scholar
  8. 8.
    Bosio, C.F., R.E.X.E. Thomas, P.R. Grimstad and K.S. Rai (1992) Variation in the efficiency of vertical transmission of dengue-1 virus by strains of Aedes albopictus (Diptera: Culicidae, J. Medical Entomology 29: 985–989.CrossRefGoogle Scholar
  9. 9.
    Brauer, F., S.M. Towers, A. Mubayi, & C, Castillo-Chavez (2016) Some models for epidemics of vector - transmitted diseases, Infectious Disease Modelling 1: 79–87.CrossRefGoogle Scholar
  10. 10.
    Burke, D.S., A. Nisalak, D.E. Johnson and R.M.N. Scott (1988) A prospective study of dengue infections in Bangkok, Am. J. of Tropical Medicine and Hygiene 38: 172.,CrossRefGoogle Scholar
  11. 11.
    CDC (2010) CDC, Report Suggests Nearly 5 Percent Exposed to Dengue Virus in Key West, Url =,
  12. 12.
    Cecílio, A.B. E.S. Campanelli, K.P.R. Souza, L.B. Figueiredo and M.C. Resende (2009) Natural vertical transmission by Stegomyia albopicta as dengue vector in Brazil, Brazilian Journal of Biology 69: 123–127.CrossRefGoogle Scholar
  13. 13.
    Chowell, G., P. Diaz-Duenas, J.C. Miller, A. Alcazar-Velasco, J.M. Hyman, P.W. Fenimore, and C. Castillo-Chavez (2007) Estimation of the reproduction number of dengue fever from spatial epidemic data, Math. Biosc. 208: 571–589.MathSciNetCrossRefGoogle Scholar
  14. 14.
    Cushing, J.M. and O. Diekmann (2016) The many guises of \(\mathcal {R}_0\) (a didactic note), J. Theor. Biol. 404: 295–302.CrossRefGoogle Scholar
  15. 15.
    Deubel, V., R.M. Kinney and D.W. Trent (1988) Nucleotide sequence and deduced amino acid sequence of the nonstructural proteins of dengue type 2 virus, Jamaica genotype: comparative analysis of the full-length genome. Virology 65: 234–244.CrossRefGoogle Scholar
  16. 16.
    Duffy, M.R., T.H. Chen, W.T. Hancock, A.M. Powers, J.L. Kool, R.S. Lanciotti, et al. (2009) Zika virus outbreak on Yap Island, federated states of Micronesia, NEJM 360:2536–2543.CrossRefGoogle Scholar
  17. 17.
    Espinoza, B., Moreno, V., Bichara, D., Castillo-Chavez, C. (2016) Assessing the Efficiency of Movement Restriction as a Control Strategy of Ebola. In Mathematical and Statistical Modeling for Emerging and Re-emerging Infectious Diseases, 2016, 123–145, Springer International Publishing.Google Scholar
  18. 18.
    Esteva, L. and C. Vargas (2000) Influence of vertical and mechanical transmission on the dynamics of dengue disease, Math. Biosc. 167: 51–64.CrossRefGoogle Scholar
  19. 19.
    Gao, D., Y. Lou, D. He, T.C. Porco, Y. Kuang, G. Chowell, S. Ruan (2016) Prevention and control of Zika as a mosquito - borne and sexually transmitted disease: A mathematical modeling analysis, Sci. Rep. 6, 28070, Scholar
  20. 20.
    Gunther, J., J.P. Martínez-Muñoz, D.G. Pérez-Ishiwara and J. Salas-Benito (2007) Evidence of vertical transmission of dengue virus in two endemic localities in the state of Oaxaca, Mexico, Intervirology 50: 347–352.CrossRefGoogle Scholar
  21. 21.
    Guzman, G, G. Kouri, Gustavo (2003) Dengue and dengue hemorrhagic fever in the Americas: lessons and challenges. J. Clinical Virology 27: 1–13.CrossRefGoogle Scholar
  22. 22.
    Halstead, S.B, S. Nimmannitya and S.N. Cohen (1970) Observations related to pathogenesis of dengue hemorrhagic fever. IV. Relation of Yale Journal of Biology and Medicine 42: 311.Google Scholar
  23. 23.
    Halstead, S. B, N.T.Lan, T.T. Myint, T.N. Shwe, A. Nisalak S. Kalyanarooj, S. Nimmannitya, S. Soegijanto, D.W. Vaughn and T.P. Endy (2002) Dengue hemorrhagic fever in infants: research opportunities ignored, Emerging infectious diseases 8: 1474–1479.CrossRefGoogle Scholar
  24. 24.
    Harris, E., E. Videa, L. Perez, E. Sandoval, Y. Tellez, M. Perez, R. Cuadra, J. Rocha, W. Idiaquez, and R.E. Alonso et al (2000) Clinical, epidemiologic, and virologic features of dengue in the 1998 epidemic in Nicaragua, Am. J. of tropical medicine and hygiene 63: 5.CrossRefGoogle Scholar
  25. 25.
    State of Hawaii (2015) Dengue outbreak 2015, Department of Health
  26. 26.
    Hawley, W.A, P. Reiter, R.S. Copeland, C.B. Pumpuni and G.B. Craig Jr (1987) Aedes albopictus in North America: probable introduction in used tires from northern Asia, Science 236: 1114.CrossRefGoogle Scholar
  27. 27.
    Knox, T.B, B.H. Kay, R.A. Hall and P.A. Ryan (2003) Enhanced vector competence of Aedes aegypti (Diptera: Culicidae) from the Torres Strait compared with mainland Australia for dengue 2 and 4 viruses, J. Medical Entomology 40: 950–956.CrossRefGoogle Scholar
  28. 28.
    Kucharski, A.J., S. Funk, R.M. Egge, H-P. Mallet, W.J. Edmunds and E.J. Nilles (2016) Transmission dynamics of Zika virus in island populations: a modelling analysisof the 2013–14 French Polynesia outbreak, PLOS Neglected tropical Diseases DOI 101371Google Scholar
  29. 29.
    Kwok, Y. (2010) Dengue Fever Cases Reach Record Highs, in Time, Sept. 24, 2010.Google Scholar
  30. 30.
    Kyle, J.L. and E. Harris (2008) Global spread and persistence of dengue, Ann. Rev. of Microbiology.Google Scholar
  31. 31.
    Lewis, J.A., G.J. Chang, R.S. Lanciotti, R.M. Kinney, L.W. Mayer and D.W. Trent (1993) Phylogenetic relationships of dengue-2 viruses, Virology 197: 216–224.CrossRefGoogle Scholar
  32. 32.
    Montoya, Y.,S. Holechek, O. Cáceres, A. Palacios, J. Burans, C. Guevara, F. Quintana, V. Herrera, E. Pozo, E. Anaya, et al (2003) Circulation of dengue viruses in North-Western Peru, 2000–2001, Dengue Bulletin 27 Google Scholar
  33. 33.
    Morens, D.M. and A.S. Fauci (2008) Dengue and hemorrhagic fever: A potential threat to public health in the United States JAMA 299: 214.Google Scholar
  34. 34.
    Murillo, D., S.A. Holechek, A.L. Murillo, F. Sanchez, and C. Castillo-Chavez (2014) Vertical Transmission in a Two-Strain Model of Dengue Fever, Letters in Biomathematics 1: 249–271.CrossRefGoogle Scholar
  35. 35.
    Niebylski, M.L. and G.B. Craig Jr (1994) Dispersal and survival of Aedes albopictus at a scrap tire yard in Missouri, Journal of the American Mosquito Control Association, 10: 339–343.Google Scholar
  36. 36.
    Nishiura, H. (2006) Mathematical and statistical analyses of the spread of dengue, Dengue Bulletin 30: 51.Google Scholar
  37. 37.
    Reiter, P. and D.J. Gubler (1997) Surveillance and control of urban dengue vectors, Dengue and dengue hemorragic fever : 45–60.Google Scholar
  38. 38.
    Rico-Hesse, R., L.M. Harrison, R.A. Salas, D. Tovar, A. Nisalak, C. Ramos, J. Boshell, M.T.R. de Mesa, H.M.R. Nogueira and A.T. Rosa (1997) Origins of dengue-type viruses associated with increased pathogenicity in the Americas, Virology 230: 344–251.CrossRefGoogle Scholar
  39. 39.
    Rico-Hesse, R., L.M. Harrison, A. Nisalak, D.W. Vaughn, S. Kalayanarooj, S. Green, A.L. Rothman and F.A. Ennis (1998) Molecular evolution of dengue type 2 virus in Thailand, Am.J. of Tropical Medicine and Hygiene 58: 96.CrossRefGoogle Scholar
  40. 40.
    Rosen, L., D.A. Shroyer, R.B. Tesh, J.E. Freier and J.C. Lien (1983) Transovarial transmission of dengue viruses by mosquitoes: Aedes albopictus and Aedes aegypti Am. J. tropical medicine and hygiene 32: 1108–1119.CrossRefGoogle Scholar
  41. 41.
    Sittisombut, N., A. Sistayanarain, M.J. Cardosa, M. Salminen, S. Damrongdachakul, S. Kalayanarooj, S. Rojanasuphot, J. Supawadee and N. Maneekarn (1997) Possible occurence of a genetic bottleneck in dengue serotype 2 viruses between the 1980 and 1987 epidemic seasons in Bangkok, Thailand, Am. J. of Tropical Medicine and Hygiene 57: 100.CrossRefGoogle Scholar
  42. 42.
    Tewari, S.C., V. Thenmozhi, C.R. Katholi, R. Manavalan, A.Munirathinam and A. Gajanana (2004) Dengue vector prevalence and virus infection in a rural area in south India, Tropical Medicine and International Health 9: 499–507.CrossRefGoogle Scholar
  43. 43.
    Towers, S., F. Brauer, C. Castillo-Chavez, A.K.I. Falconer, A. Mubayi, C.M.E. Romero-Vivas (2016) Estimation of the reproduction number of the 2015 Zika virus outbreak in Barranquilla, Columbia, Epidemics 17: 50–55.CrossRefGoogle Scholar
  44. 44.
    Valega-Mackenzie, W. and K. Rios-Soto (2018) Can vaccination save a Zika virus epidemic?, Bull.Math. Biol. 80:598–625.MathSciNetCrossRefGoogle Scholar
  45. 45.
    van den Driessche, P. and J. Watmough (2002) Reproduction numbers and subthreshold endemic equilibria for compartmental models of disease transmission, Math. Biosc. 180:29–48.CrossRefGoogle Scholar
  46. 46.
    WHO (2009) Dengue and dengue hemorrhagic fever. Fact SheetGoogle Scholar
  47. 47.
    World Health Organization (2015) Dengue Control,
  48. 48.
    Zhang, C., M.P. Mammen Jr, P. Chinnawirotpisan, C. Klungthong, P. Rodpradit, A. Nisalak, D.W. Vaughn, S. Nimmannitya, S. Kalayanarooj and E.C. Holmes, E.C. (2006) Structure and age of genetic diversity of dengue virus type 2 in Thailand, Journal of General Virology 87: 873.Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Fred Brauer
    • 1
  • Carlos Castillo-Chavez
    • 2
  • Zhilan Feng
    • 3
  1. 1.Department of MathematicsUniversity of British ColumbiaVancouverCanada
  2. 2.Mathematical and Computational Modeling Center (MCMSC), Department of Mathematics and StatisticsArizona State UniversityTempeUSA
  3. 3.Department of MathematicsPurdue UniversityWest LafayetteUSA

Personalised recommendations