Mathematical and statistical analyses of the spread of dengue

Dengue Bulletin

Volumn 30, Issue , 2006, Pages 51-67

  Nishiura, Hiroshi ^a,b  

^a UNIVERSITY OF TÜBINGEN   (Germany)

^b NAGASAKI UNIVERSITY   (Japan)

Author keywords

Basic reproduction number; Dengue; Epidemiology; Mathematical model; Periodicity; Population theory; Statistical model

Indexed keywords

ANTIBODY; INTRINSIC FACTOR;

AGE DISTRIBUTION; ARTICLE; BASIC REPRODUCTION NUMBER; DENGUE; EPIDEMIC; GROWTH RATE; HEALTH STATISTICS; INFECTION CONTROL; MATHEMATICAL ANALYSIS; MATHEMATICAL MODEL; PERIODICITY; SEASONAL VARIATION; SEROTYPE; STATISTICAL ANALYSIS; STRATEGIC PLANNING; VACCINATION; VIRUS PATHOGENESIS; VIRUS TRANSMISSION;

EID: 34848898990     PISSN: 1020895X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (72)

1. Bartlett MS. The relevance of stochastic models for large-scale epiderniological phenomena. Applied Statistics 1964;13(1):2-8.
2. Fischer DB, Halstead SB. Observations related to pathogenesis of dengue hemorrhagic fever. V. Examination of age-specific sequential infection rates using a mathematical model. Yale J Biol Med 1970 Apr;42(5):329-49.
3. de Moor PP, Steffens FE. A computer-simulated model of an arthropod-borne virus transmission cycle, with special reference to Chikungunya virus. Trans R Soc Trop Med Hyg 1970;64(6):927-34.
4. Griffiths DA. A bivariate birth-death process which approximates to the spread of a disease involving a vector. Journal of Applied Probability 1972;9(1):65-75.
5. Radcliffe J. A note on the recurrence of yellow fever epidemics in urban populations. Journal of Applied Probability 1974;11(1):170-173.
6. Dietz K. Transmission and control of arbovirus diseases. In: Ludwig D, Cooke KL editors. Epidemiology. SIAM, Philadelphia, 1975. p. 104-121.
7. Koopman JS, Prevots DR, Vaca Marin MA, Gomez Dantes H, Zarate Aquino ML, Longini IM Jr, Sepulveda Amor J. Determinants and predictors of dengue infection in Mexico. Am J Epidemiol 1991 Jun 1;133(11):1168-78.
8. Newton EA, Reiter P. A model of the transmission of dengue fever with an evaluation of the impact of ultra-low volume (ULV) insecticide applications on dengue epidemics. Am J Trop Med Hyg 1992 Dec;47(6):709-20.
9. Focks DA, Haile DG, Daniels E, Mount GA. Dynamic life table model for Aeries aegypti (Diptera: Culicidae): analysis of the literature and model development. J Med Entomol 1993 Nov;30(6):1003-17.
10. Focks DA, Haile DG, Daniels E, Mount GA. Dynamic life table model for Aedes aegypti (Diptera: Culicidae): simulation results and validation. J Med Entomol 1993 Nov;30(6):1018-28.
11. Marques CA, Forattini OP, Massad E. The basic reproduction number for dengue fever in Sao Paulo state, Brazil: 1990-1991 epidemic. Trans R Soc Trop Med Hyg 1994 Jan-Feb;88(1):58-9.
12. Focks DA, Daniels E, Haile DG, Keesling JE. 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 1995 Nov;53(5):489-506.
13. Feng Z, Velasco-Hernandez JX. Competitive exclusion in a vector-host model for the dengue fever. J Math Biol 1997 May;35(5):523-44.
14. Esteva L, Vargas C. Analysis of a dengue disease transmission model. Math Biosci 1998 Jun 15;150(2):131-51.
15. Esteva L, Vargas C. A model for dengue disease with variable human population. J Math Biol 1999 Mar;38(3):220-40.
16. Esteva L, Vargas C. Influence of vertical and mechanical transmission on the dynamics of dengue disease. Math Biosci 2000 Sep;167(1):51-64.
17. Ferguson NM, Donnelly CA, Anderson RM. Transmission dynamics and epidemiology of dengue: insights from age-stratified seroprevalence surveys. Philos Trans R Soc Lond B Biol Sci 1999 Apr 29;354(1384):757-68.
18. Ferguson N, Anderson R, Gupta S. The effect of antibody-dependent enhancement on the transmission dynamics and persistence of multiple-strain pathogens. Proc Natl Acad Sci U S A 1999 Jan 19;96(2):790-4.
19. Focks DA, Brenner RJ, Hayes J, Daniels E. Transmission thresholds for dengue in terms of Aedes aegypti pupae per person with discussion of their utility in source reduction efforts. Am J Trop Med Hyg 2000 Jan;62(1):11-8.
20. Hay SI, Myers MF, Burke DS, Vaughn DW, Endy T, Ananda N, Shanks GD, Snow RW, Rogers DJ. Etiology of interepidemic periods of mosquito-borne disease. Proc Natl Acad Sci U S A 2000 Aug 1;97(16):9335-9.
21. Massad E, Coutinho FA, Burattini MN, Lopez LF. The risk of yellow fever in a dengue-infested area. Trans R Soc Trop Med Hyg 2001 Jul-Aug;95(4):370-4.
22. Massad E, Burattini MN, Coutinho FA, Lopez LF. Dengue and the risk of urban yellow fever reintroduction in Sao Paulo State, Brazil. Rev Saude Publica 2003 Aug;37(4):477-84.
23. Pongsumpun P, Tang IM. A realistic age structured transmission model for dengue hemorrhagic fever in Thailand. Southeast Asian J Trop Med Public Health 2001 Jun;32(2):336-40.
24. Pongsumpun P, Yoksan S, Tan IM. A comparison of the age distributions in the dengue hemorrhagic fever epidemics in Santiago de Cuba (1997) and Thailand (1998). Southeast Asian J Trop Med Public Health 2002 Jun;33(2):255-8.
25. Bartley LM, Donnelly CA, Garnett GR The seasonal pattern of dengue in endemic areas: mathematical models of mechanisms. Trans R Soc Trop Med Hyg 2002 Jul-Aug;96(4):387-97.
26. Esteva L, Vargas C. Coexistence of different serotypes of dengue virus. J Math Biol 2003 Jan;46(1):31-47.
27. Esteva L, Mo Yang H. Mathematical model to assess the control of Aedes aegypti mosquitoes by the sterile insect technique. Math Biosci 2005 Dec;198(2):132-47.
28. Derouich M, Boutayeb A, Twizell EH. A model of dengue fever. Biomed Eng Online 2003 Feb 19;2:4.
29. Luz PM, Codeco CT, Massad E, Struchiner CJ. Uncertainties regarding dengue modeling in Rio de Janeiro, Brazil. Mem I nst Oswaldo Cruz 2003 Oct;98(7):871-8.
30. Kawaguchi I, Sasaki A, Boots M. Why are dengue virus serotypes so distantly related? Enhancement and limiting serotype similarity between dengue virus strains. Proc Biol Sci 2003 Nov 7;270(1530):2241-7.
31. Pongsumpun P, Patanarapelert K, Sriprom M, Varamit S, Tang IM. Infection risk to travelers going to dengue fever endemic regions. Southeast Asian J Trop Med Public Health 2004 Mar;35(1):155-9.
32. Cummings DA, Irizarry RA, Huang NE, Endy TP, Nisalak A, Ungchusak K, Burke DS. Travelling waves in the occurrence of dengue haemorrhagic fever in Thailand. Nature 2004 Jan 22;427(6972):344-7.
33. Favier C, Schmit D, Muller-Graf CD, Cazelles B, Degallier N, Mondet B, Dubois MA. Influence of spatial heterogeneity on an emerging infectious disease: the case of dengue epidemics. Proc Biol Sci 2005 Jun 7;272(1568):1171-7.
34. Takahashi LT, Maidana NA, Ferreira WC Jr, Pulino P, Yang HM. Mathematical models for the Aedes aegypti dispersal dynamics: travelling waves by wing and wind. Bull Math Biol 2005 May;67(3):509-28.
35. Cummings DA, Schwartz IB, Billings L, Shaw LB, Burke DS. Dynamic effects of antibody-dependent enhancement on the fitness of viruses. Proc Natl Acad Sci U S A 2005 Oct 18;102(42):15259-64.
36. Favier C, Degallier N, Rosa-Freitas MG, Boulanger JP, Costa Lima JR, Luitgards-Moura JF, Menkes CE, Mondet B, Oliveira C, Weimann ET, Tsouris R Early determination of the reproductive number for vector-borne diseases: the case of dengue in Brazil. Trop Med Int Health 2006 Mar;11(3):332-40.
37. Wearing HJ, Rohani R Ecological and immunological determinants of dengue epidemics. Proc Nail Acad Sci U S A 2006 Aug 1;103(31):11802-7.
38. Anderson RM, May RM. Infectious diseases of humans. Oxford: Oxford University Press; 1991.
39. Anderson RM. Population dynamics of infectious diseases: theory and applications. London: Chapman & Hall; 1982.
40. Ross R. The prevention of malaria. 2nd ed. London: Murray; 1911.
41. Macdonald G. The epidemiology and control of malaria. Oxford: Oxford University Press; 1957.
42. Koella JC. On the use of mathematical models of malaria transmission. Acta Trop 1991 Apt;49(1):1-25.
43. Dobson A, Foufopoulos J. Emerging infectious pathogens of wildlife. Philos Trans R Soc Lond B Biol Sci 2001 Jul 29;356(1411):1001-12.
44. Bailey NTJ. The mathematical theory of infectious diseases. 2nd ed. London: Griffin; 1975.
45. Dietz K. The estimation of the basic reproduction number for infectious diseases. Stat Methods Med Res 1993;2(1):23-41.
46. Anderson RM. Discussion: the Kermack-McKendrick epidemic threshold theorem. Bull Math Biol 1991;53(1-2):3-32.
47. 0 in models for infectious diseases in heterogeneous populations. J Math Biol 1990; 28(4):365-82.
48. Anderson RM, May RM. Directly transmitted infectious diseases: control by vaccination. Science 1982 Feb 26;215(4536):1053-60.
49. Halstead SB, Deen J. The future of dengue vaccines. Lancet 2002 Oct 19;360(9341):1243-5.
50. Edelman R. Dengue and dengue vaccines. J Infect Dis 2005 Mar 1;191(5):650-3.
51. Sangkawibha N, Rojanasuphot S, Ahandrik S, Viriyapongse S, Jatanasen S, Salitul V, Phanthumachinda B, Halstead SB. Risk factors in dengue shock syndrome: a prospective epidemiologic study in Rayong, Thailand. I. The 1980 outbreak. Am J Epidemiol 1984 Nov;120(5):653-69.
52. Halstead SB. Pathogenesis of dengue: challenges to molecular biology. Science 1988 Jan 29;239(4839):476-81.
53. Guzman MG, Kouri G, Valdes L, Bravo J, Alvarez M, Vazques S, Delgado I, Halstead SB. Epidemiologic studies on dengue in Santiago de Cuba, 1997. Am J Epidemiol 2000 Nov 1;152(9):793-9.
54. Guzman MG, Kouri G. Dengue: an update. Lancet Infect Dis 2002 Jan;2(1):33-42.
55. Lam SK, Chua KB, Hooi PS, Rahimah MA, Kumari S, Tharmaratnam M, Chuah SK, Smith DW, Sampson IA. Chikungunya infection - an emerging disease in Malaysia. Southeast Asian J Trop Med Public Health 2001 Sep;32(3):447-51.
56. Heffernan JM, Smith RJ, Wahl LM. Perspectives on the basic reproductive ratio. J R Soc Interface 2005 Sep 22;2(4):281-93.
57. Muench H. Catalytic models in epidemiology. Cambridge, MA: Harvard University Press; 1959.
58. Griffiths DA. A catalytic model of infection for measles. Applied Statistics 1974;23(3):330-339.
59. Farrington CR Modelling forces of infection for measles, mumps and rubella. Star Med 1990 Aug;9(8):953-67.
60. Yamashiro T, Disla M, Petit A, Taveras D, Castro-Bello M, Lora-Orste M, Vardez S, Cesin AJ, Garcia B, Nishizono A. Seroprevalence of IgG specific for dengue virus among adults and children in Santo Dorningo, Dominican Republic. Am J Trop Med Hyg 2004 Aug;71(2):138-43.
61. Radcliffe J. The periodicity of endemic malaria. Journal of Applied Probability 1974;11 (2): 562-567.
62. Aron JL, May RM. The population dynamics of malaria. In: Anderson RM, editors. The population dynamics of infectious diseases: theory and applications. London: Chapman & Hall; 1982. p. 139-179.
63. Heesterbeek JAP, Roberts MG. Threshold quantities for infectious diseases in periodic environments. Journal of Biological Systems 1995;3(3):779-87.
64. Bacaer N, Guernaoui S. The epidemic threshold of vector-borne diseases with seasonality: The case of cutaneous leishmaniasis in Chichaoua, Morocco. J Math Biol 2006 Sep;53(3):421-36.
65. Anderson RM, Grenfell BT, May RM. Oscillatory fluctuations in the incidence of infectious disease and the impact of vaccination: time series analysis. J Hyg (Lond) 1984 Dec;93(3):587-608.
66. Chatfield C. The analysis of time series: an introduction. 6th ed. London: Chapman & Hall; 2004.
67. Ministry of Public Health, Thailand. Annual epidemiological surveillance report (1983-2005). Division of Epiderniology, Ministry of Public Health, Bangkok, Thailand; 1984-2006.
68. Westaway EG, Blok J. Taxonomy and evolutionary relationships of flaviviruses. In: Gubler DJ, Kuno G, editors. Dengue and dengue hemorrhagic fever. New York, NY: CAB International; 1997. p. 147-173.
69. Halstead SB, Scanlon JE, Umpaivit P, Udomsakdi S. Dengue and chikungunya virus infection in man in Thailand, 1962-1964. IV. Epidemiologic studies in the Bangkok metropolitan area. Am J Trop Med Hyg 1969 Nov;18(6):997-1021.
70. Holmes E, Bartley L, Garnett G. The emergence of dengue: past, present, and future. In: Krause R, editor. Emerging infections. London: Academic Press; 1998. p. 301-325.
71. Zanotto PM, Gould EA, Gao GF, Harvey PH, Holmes EC. Population dynamics of flaviviruses revealed by molecular phylogenies. Proc Natl Acad Sci U S A 1996 Jan 23;93(2):548-53.
72. Nishiura H, Halstead SB. Natural history of dengue virus (DENY)-1 and DENV-4 infections: reanalysis of classic studies. J Infect Dis 2007 Apr 1;195(7):1007-13.