zbMATH — the first resource for mathematics

Influence of vertical and mechanical transmission on the dynamics of dengue disease. (English) Zbl 0970.92011
Summary: We formulate a nonlinear system of differential equations that models the dynamics of transmission of dengue fever. We consider vertical and mechanical transmission in the vector population, and study the effects that they have on the dynamics of the disease. A qualitative analysis as well as some numerical examples are given for the model.

92C50 Medical applications (general)
92C60 Medical epidemiology
34D05 Asymptotic properties of solutions to ordinary differential equations
Full Text: DOI
[1] Barreau, C.; Jousset, F.X.; Bergoin, M., Venereal and vertical transmission of the aedes albopictus parvovirus in aedes aegypti mosquitoes, Am. J. trop. med. hyg., 57, 2, 126, (1997)
[2] Berman, A.; Plemmons, R.J., Nonnegative matrices in the mathematical sciences, (1979), Academic New York · Zbl 0484.15016
[3] Bosio, C.F.; Thomas, R.E.; Grimstad, P.R.; Rai, K.S., Variation in the efficiency of vertical transmission of dengue-1 virus by strains of aedes albopictus (diptera: culicidae), J. med. entomol., 29, 6, 985, (1992)
[4] de Souza, M.; Freier, J.E., Vertical transmission of dengue 1 virus by haemagogus equinus mosquitoes, J. am. mosq. control assoc., 7, 1, 118, (1991)
[5] Esteva, L.; Vargas, C., Analysis of a dengue disease transmission model, Math. biosci., 150, 131, (1998) · Zbl 0930.92020
[6] Esteva, L.; Vargas, C., A model for dengue disease with variable human population, J. math. biol., 38, 220, (1999) · Zbl 0981.92016
[7] Freier, J.E.; Rosen, L., Vertical transmission of dengue viruses by mosquitoes of the aedes scutellaris group, Am. J. trop. med. hyg., 37, 3, 640, (1987)
[8] Freier, J.E.; Rosen, L., Vertical transmission of dengue viruses by aedes mediovittatus, Am. J. trop. med. hyg., 39, 2, 218, (1988)
[9] D.J. Gubler, Dengue, in: T.P. Monath (Ed.), The Arbovirus: Epidemiology and Ecology, vol. 2, CRC, Boca Raton, FL, 1986, p. 213
[10] Hale, J.K., Ordinary differential equations, (1969), Wiley New york · Zbl 0186.40901
[11] Halstead, S.B., The xxth century dengue pandemic: need for surveillance and research, World health stat. quart., 45, 292, (1992)
[12] Hethcote, H.W.; Thieme, H.R., Stability of the endemic equilibrium in epidemic models with subpopulations, Math. biosci., 75, 205, (1985) · Zbl 0582.92024
[13] Hull, B.; Tikasingh, E.; de Souza, M.; Martı́nez, R., Natural Transovarian transmission of dengue 4 virus in aedes aegypti in trinidad, Am. J. trop. med. hyg., 33, 1248, (1984)
[14] Joshi, V.; Singhi, M.; Chaudhary, R.C., Transovarial transmission of dengue 3 virus by aedes aegypti, Trans. R. soc. trop. med. hyg., 90, 643, (1996)
[15] Klowden, M.J.; Lea, A.O., Blood meal size as a factor affecting hostseeking by aedes aegypti (L.), Am. J. trop. med. hyg., 27, 827, (1978)
[16] Krasnoselskii, M.A., Positive solutions of operator equations, (1964), Noordhoff Groningen
[17] Landsdowne, C.; Hacker, C.S., The effect of fluctuating temperature and humidity on the adult life table characteristics of five strains of aedes aegypti, J. med. entomol., 11, 6, 723, (1975)
[18] Méndez Galván, J.F.; Castellanos, R.M., Manual para la vigilancia epidemiológica del dengue, (1994), Secretarı́a de salud DF, México
[19] C.J. Mitchel, B.R. Miller, Vertical transmission of dengue viruses by strains of Aedes albopictus recently introduced into Brazil, J. Am. Mosq. Control Assoc. 6 (2) (1990) 251
[20] T.P. Monath, Dengue: the risk to developed and developing countries, in: Proceedings of the National Academy of Science, USA 91, 1994, p. 2395
[21] Newton, E.A.C.; Reiter, P., A model for 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., 47, 709, (1992)
[22] Platt, K.B.; Linthicum, K.B.; Myint, K.S.; Innis, B.L.; Lerdthusnee, K.; Vaughn, D.W., Impact of dengue virus infection on feeding behavior of aedes aegypti, Am. J. trop. med. hyg., 57, 2, 119, (1997)
[23] Roche, J.C.; Cordellier, R.; Hervy, J.P.; Digoutte, J.P.; Monteny, N., Isolement de souches 96 de virus dengue 2 à partir de mosquitoes capturés en coté d’ivoire et haute-volta, Ann. virol. E, 134, 233, (1983)
[24] Rosen, L.; Tesh, R.B.; Lien, J.C.; Cross, J.H., Transovarial transmission of Japanese encephalitis virus by mosquitoes, Science, 199, 909, (1978)
[25] Rosen, L.; Shroyer, D.A.; Tesh, R.B.; Freiery, J.E.; Lien, J.Ch., Transovarial transmission of dengue viruses by mosquitoes: aedes albopictus and aedes aegypti, Am. J. trop. med. hyg., 32, 5, 1108, (1983)
[26] Shroyer, D.A., Vertical maintenance of dengue-1 virus in sequential generation of aedes albopictus, J. am. mosq. control assoc., 6, 2, 312, (1990)
[27] Watts, D.M.; Burke, D.S.; Harrison, B.A.; Whitmire, R.E.; Nisalak, A., Effect of temperature on the vector efficiency of aedes aegypti for dengue 2 virus, Am. J. trop. med. hyg., 36, 143, (1987)
[28] World Health Organization, Dengue haemorrhagic fever: diagnosis treatment and control, Geneva, 1986
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.