Bulletin of Mathematical Biology

, Volume 80, Issue 10, pp 2633–2651 | Cite as

Analysis of a Dengue Model with Vertical Transmission and Application to the 2014 Dengue Outbreak in Guangdong Province, China

  • Lan Zou
  • Jing Chen
  • Xiaomei Feng
  • Shigui RuanEmail author
Original Article


There is evidence showing that vertical transmission of dengue virus exists in Aedes mosquitoes. In this paper, we propose a deterministic dengue model with vertical transmission in mosquitoes by including aquatic mosquitoes (eggs, larvae and pupae), adult mosquitoes (susceptible, exposed and infectious) and human hosts (susceptible, exposed, infectious and recovered). We first analyze the existence and stability of disease-free equilibria, calculate the basic reproduction number and discuss the existence of the disease-endemic equilibrium. Then, we study the impact of vertical transmission of the virus in mosquitoes on the spread dynamics of dengue. We also use the model to simulate the reported infected human data from the 2014 dengue outbreak in Guangdong Province, China, carry out sensitivity analysis of the basic reproduction number in terms of the model parameters, and seek for effective control measures for the transmission of dengue virus.


Dengue Vertical transmission Mathematical model Basic reproduction number Disease-free and disease-endemic equilibra 



The authors would like to thank the two anonymous reviewers for their helpful comments and suggestions.


  1. Adams B, Boots M (2010) How important is vertical transmission in mosquitoes for the persistence of dengue? Insights from a mathematical model. Epidemics 2:1–10CrossRefGoogle Scholar
  2. Andraud M, Hens N, Beutels P (2013) A simple periodic-forced model for dengue fitted to incidence data in Singapore. Math Biosci 244:22–28MathSciNetCrossRefGoogle Scholar
  3. Atkinson MP, Zheng S, Alphey N, Alphey LS, Coleman PG, Wein LM (2007) Analyzing the control of mosquito-borne diseases by a dominant lethal genetic system. Proc Natl Acad Sci USA 104(22):9540–9545CrossRefGoogle Scholar
  4. Bai L, Morton LC, Liu Q (2013) Climate change and mosquito-borne diseases in China: a review. Global Health 9:10CrossRefGoogle Scholar
  5. Bartley LM, Donnelly CA, Garnett GP (2002) The seasonal pattern of dengue in endemic areas: mathematical models of mechanisms. Trans R Soc Trop Med Hyg 96:387–397CrossRefGoogle Scholar
  6. Buckner EA, Alto BW, Lounibos LP (2013) Vertical transmission of Key West Dengue-1 virus by Aedes aegypti and Aedes albopictus (Diptera: culicidae) mosquitoes from Florida. J Med Entomol 50(6):1291–1297CrossRefGoogle Scholar
  7. Centers for Disease Control and Prevention (CDC) (2016) Dengue, Page last updated: January 19, 2016
  8. Chao DL, Longini IM Jr, Halloran ME (2013) The effects of vector movement and distribution in a mathematical model of dengue transmission. PLoS ONE 8(10):e76044CrossRefGoogle Scholar
  9. Chen B, Liu Q (2015) Dengue fever in China. Lancet 385:1621–1622CrossRefGoogle Scholar
  10. Cheng Q, Jing Q, Spear RC, Marshall JM, Yang Z, Gong P (2017) The interplay of climate, intervention and imported cases as determinants of the 2014 dengue outbreak in Guangzhou. PLoS Negl Trop Dis 11(6):e0005701CrossRefGoogle Scholar
  11. Chowell G, Fuentes R, Olea A, Aguilera X, Nesse H, Hyman JM (2013) The basic reproduction number \(R_0\) and effectiveness of reactive interventions during dengue epidemics: the 2002 dengue outbreak in Easter Island, Chile. Math Biosci Eng 10:1455–1474MathSciNetCrossRefGoogle Scholar
  12. Coutinho FAB, Burattini M, Lopez L, Massad E (2006) Threshold conditions for a non-autonomous epidemic system describing the population dynamics of dengue. Bull Math Biol 68:2263–2282MathSciNetCrossRefGoogle Scholar
  13. Diekmann O, Heesterbeek JAP, Roberts MG (1990) On the definition and the computation of the basic reproduction ratio \(R_{0}\) in models for infectious diseases in heterogeneous populations. J Math Biol 28:365–382MathSciNetCrossRefGoogle Scholar
  14. Diekmann O, Heesterbeek JAP, Roberts MG (2010) The construction of next-generation matrices for compartmental epidemic models. J R Soc Interface 7:873–885CrossRefGoogle Scholar
  15. Esteva L, Vargas C (2000) Influence of vertical and mechanical transmission on the dynamics of dengue disease. Math Biosci 167:51–64CrossRefGoogle Scholar
  16. Favier C, Schmit D, Graf CDMM, Cazelles B, Degallier N, Mondet B, Dubois MA (2005) Influence of spatial heterogeneity on an emerging infectious disease: the case of dengue epidemics. Proc R Soc B 272(1568):1171–1177CrossRefGoogle Scholar
  17. Feng Z, Velasco-Hernandez JX (1997) Competitive exclusion in a vector-host model for the dengue fever. J Math Biol 35:523–544MathSciNetCrossRefGoogle Scholar
  18. Focks DA, Daniels E, Haile DG, Keesling JE (1995) A simulation model of the epidemiology of urban dengue fever: literature analysis, model development, preliminary validation, and samples of simulation results. Am J Trop Med Hyg 53:489–506CrossRefGoogle Scholar
  19. Guangdong Meteorological Service (GMS) (2013) The climatic characteristics of Guangdong Province, Accessed October (2013)
  20. Guangdong Meteorological Service (GMS) (2016) The climatic characteristics of Guangdong Province in September 2014, Accessed October (2016)
  21. Guangdong Meteorological Service (GMS) (2016) The climatic characteristics of Guangdong Province in November 2014, Accessed October 2016
  22. Guzman MG, Harris E (2015) Dengue. Lancet 385:453–465CrossRefGoogle Scholar
  23. Halstead SB (2007) Dengue. Lancet 370:1644–1652CrossRefGoogle Scholar
  24. Health Department of Guangdong Province (HDGP) (2014) The report on dengue of Guangdong Province (Dec. 8, 2014),
  25. Health Department of Guangdong Province (HDGP) (2017) Reported infectious diseases of Guangdong Province, Accessed November 2017
  26. Hull B, Tikasingh E, De Souza M, Martinez R (1984) Natural transovarial transmission of dengue 4 virus in Aedes aegypti in Trinidad. Am J Trop Med Hyg 33:1248–1250CrossRefGoogle Scholar
  27. Katri P (2010) Modeling the transmission dynamics of the dengue virus, Ph.D. Thesis, University of Miami. Open Access Dissertations.
  28. Kow CY, Koon LL, Yin PF (2001) Detection of dengue viruses in field caught male Aedes aegypti and Aedes albopictus (Diptera: Culicidae) in Singapore by typespecific PCR. J Med Entomol 38:475–479CrossRefGoogle Scholar
  29. Li M, Sun G, Yakob L, Zhu H, Jin Z, Zhang W (2016) The driving force for 2014 dengue outbreak in Guangdong, China. PLoS ONE 11(11):e0166211CrossRefGoogle Scholar
  30. Monath T, Heinz FX (1996) Flaviviruses. In: Fields BN et al (eds) Virology. Lippincott-Raven, Philadelphia, pp 961–1034Google Scholar
  31. Pherez FM (2007) Factors affecting the emergence and prevalence of vector borne infections (VBI) and the role of vertical transmission (VT). J Vector Borne Dis 44:157–163Google Scholar
  32. Pinho STR, Ferreira CP, Esteva L (2010) Modelling the dynamics of dengue real epidemics. Phil Trans R Soc A 368:5679–5693MathSciNetCrossRefGoogle Scholar
  33. Rigau-Pérez JG, Clark GG, Gubler DJ, Reiter P, Sanders EJ, Vance Vorndam A (1998) Dengue and dengue haemorrhagic fever. Lancet 352:971–977CrossRefGoogle Scholar
  34. Robert MA, Christofferson RC, Silva NJB, Vasquez C, Mores CN, Wearing HJ (2016) Modeling mosquito-borne disease spread in U.S. urbanized areas: the case of dengue in Miami. PLoS ONE 11(8):e0161365CrossRefGoogle Scholar
  35. Scott TW, Amerasinghe PH, Morrison AC (2000) Longitudinal studies of Aedes aegypti (Diptera: Culicidae) in Thailand and Puerto Rico: blood feeding frequency. J Med Entnmol 37:89–101CrossRefGoogle Scholar
  36. Shen S-Q, Wei H-X, Fu Y-H (2015) Multiple source of infection and potential endemic characteristics of the large outbreak of dengue in Guangdong in 2014. Sci Rep 5:16913CrossRefGoogle Scholar
  37. Statistics Bureau of Guangdong Province (SBGP) (2013) The annual report of economy and social development in Guangdong Province in 2013. Accessed October 2013
  38. Statistics Bureau of Guangdong Province (SBGP) (2014) Guangdong statistical yearbook. China Statistics Press, BeijingGoogle Scholar
  39. Stoddard ST, Wearing HJ, Reiner RC (2014) Long-term and seasonal dynamics of Dengue in Iquitos, Peru. PLoS Negl Trop Dis 8(7):e3003CrossRefGoogle Scholar
  40. Tang B, Xiao Y, Tang S, Wu J (2016) Modelling weekly vector control against dengue in the Guangdong Province of China. J Theoret Biol 410:65–76CrossRefGoogle Scholar
  41. van den Driessche P, Watmough J (2002) Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math Biosci 180:29–48MathSciNetCrossRefGoogle Scholar
  42. Wearing HJ, Rohani P (2006) Ecological and immunological determinants of dengue epidemics. Proc Natl Acad Sci USA 103:11802–11807CrossRefGoogle Scholar
  43. World Health Organization (WHO) (2018) Dengue and severe dengue, Accessed 2 Feb 2018
  44. Wu J, Lun Z, James AA, Chen X (2010) Review: dengue fever in mainland China. Am J Trop Med Hyg 83(3):664–671CrossRefGoogle Scholar

Copyright information

© Society for Mathematical Biology 2018

Authors and Affiliations

  1. 1.Department of MathematicsSichuan UniversityChengduChina
  2. 2.Halmos College of Natural Sciences and OceanographyNova Southeastern UniversityFort LauderdaleUSA
  3. 3.Department of MathematicsYuncheng UniversityYunchengChina
  4. 4.Department of MathematicsUniversity of MiamiCoral GablesUSA

Personalised recommendations