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Modelling weekly vector control against Dengue in the Guangdong Province of China. (English) Zbl 1348.92162
Summary: We develop a mathematical model to closely mimic the integrated program of impulsive vector control (every Friday afternoon since the initiation of the program) and continuous patient treatment and isolation implemented in the Guangdong Province of China during its 2014 dengue outbreak. We fitted the data of accumulated infections and used the parameterized model to carry out a retrospective analysis to estimate the basic reproduction number 1.7425 (95% CI 1.4443–2.0408), the control reproduction number 0.1709, and the mosquito-killing ratios 0.1978, 0.2987, 0.6158 and 0.5571 on October 3, 10, 17 and 24, respectively. This suggests that integrated intervention is highly effective in controlling the dengue outbreak. We also simulated outbreak outcomes under different variations of the implemented interventions. We showed that skipping one Friday for vector control would not result in raising the control reproduction number to the threshold value 1 but would lead to significant increase in the accumulated infections at the end of the outbreak. The findings indicate that quick and persistent impulsive implementation of vector control result in an effective reduction in the control reproduction number and hence lead to significant decline of new infections.

92D30 Epidemiology
92C50 Medical applications (general)
Full Text: DOI
[1] Adams, B.; Boots, M., How important is vertical transmission in mosquitoes for the persistence of dengue? insights from a mathematical model, Epidemics, 2, 1-10, (2010)
[2] Andraud, M.; Hens, N.; Marais, C.; Beutels, P., Dynamic epidemiological models for dengue transmissiona systematic review of structural approaches, PLoS One, 7, 11, e49085, (2012)
[3] Atkinson, M. P.; Su, Z.; Alphey, N., Analyzing the control of mosquito-borne diseases by a dominant lethal genetic system, Proc. Natl. Acad. Sci. U.S.A., 104, 9540-9545, (2007)
[4] Bainov, D.D., Simeonov, P.S., 1989. Systems with Impulse Effect, Theory and Applications. Mathematics and Applications. Ellis-Horwood, Chichester, UK. · Zbl 0671.34052
[5] Bainov, D.D., Simeonov, P.S., 1993. Impulsive Differential Equations: Periodic Solutions and Applications. Pitman Monographs and Surveys in Pure and Applied Mathematics, vol. 66. Longman, Harlow. · Zbl 0815.34001
[6] Burattini, M. N.; Chen, M.; Chow, A., Modelling the control strategies against dengue in Singapore, Epidemiol. Infect., 136, 309-319, (2008)
[7] Bailey, N. T.J., The mathematical theory of infectious diseases and its applications, (1975), Griffin London · Zbl 0334.92024
[8] Blower, S. M.; Dowlatabadi, H., Sensitivity and uncertainty analysis of complex models of disease transmissionan HIV model, as an example, Int. Stat. Rev., 62, 229-243, (1994) · Zbl 0825.62860
[9] Cummings, D. A.T.; Iamsirithaworn, S.; Lessler, J. T., The impact of the demographic transition on dengue in thailandinsights from a statistical analysis and mathematical modeling, PLoS Med., 6, 9, e1000139, (2009)
[10] Coutinho, F. A.B.; Burattini, M.; Lopez, L.; Massad, E., Threshold conditions for a non-autonomous epidemic system describing the population dynamics of dengue, Bull. Math. Biol., 68, 2263-2282, (2006) · Zbl 1296.92226
[11] Chowell, G.; Diaz-Dueñas, P.; Miller, J. C., Estimation of the reproduction number of dengue fever from spatial epidemic data, Math. Biosci., 208, 571-589, (2007) · Zbl 1119.92055
[12] Coelho, G. E.; Burattini, M. N.; Teixeira, M. D.G.; Coutinho, F. A.; Massad, E., Dynamics of the 2006/2007 dengue outbreak in Brazil, Mem. Inst. Oswaldo Cruz, 103, 6, 535-539, (2008)
[13] Degallier, N.; Favier, C.; Boulanger, J. P.; Menkes, C., Imported and autochthonous cases in the dynamics of dengue epidemics in Brazil, Rev. Saude Publica, 43, 1, 1-7, (2009)
[14] Diekmann, O.; Heesterbeek, J. A.P., Mathematical epidemiology of infectious diseases: model building, analysis and interpretation, (2000), John Wiley Chichester · Zbl 0997.92505
[15] Esteva, L.; Vargas, C., Analysis of a dengue disease transmission model, Math. Biosci., 150, 131-151, (1998) · Zbl 0930.92020
[16] Esteva, L.; Vargas, C., Influence of vertical and mechanical transmission on the dynamics of dengue disease, Math. Biosci., 167, 51-64, (2000) · Zbl 0970.92011
[17] Erickson, R. A.; Presley, S. M.; Allen, L. J.S.; Long, K. R.; Cox, S. B., A stagestructured, aedes albopictus population model, Ecol. Model., 221, 1273-1282, (2010)
[18] Favier, C.; Degallier, N.; Rosa-Freitas, M. G., Early determination of the reproductive number for vector-borne diseasesthe case of dengue in Brazil, Trop. Med. Int. Health, 11, 3, 332-340, (2006)
[19] Ferguson, N. M.; Donnelly, C. A.; Anderson, R. M., Transmission dynamics and epidemiology of dengueinsights from age-stratified seroprevalence surveys, Philos. Trans. R. Soc. Lond. B, 354, 757-768, (1999)
[20] Guangdong Bureau of Health, 2014. http://www.gdwst.gov.cn/a/yiqingxx/index-7.html (accessed 11/08/2016).
[21] Geweke, J., Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments, (Bernardo, J. M.; Berger, J.; Dawid, A. P.; Smith, A. F.M., Bayesian Statistics, vol. 4, (1992), Oxford University Press Oxford), 169-193
[22] Garba, S. M.; Gumel, A. B.; Abu Bakar, M. R., Backward bifurcations in dengue transmission dynamics, Math. Biosci., 215, 11-25, (2008) · Zbl 1156.92036
[23] Haario, H.; Laine, M.; Mira, A.; Saksman, E., Dramefficient adaptive MCMC, Stat. Comput., 16, 339-354, (2006)
[24] Halstead, S. B., Dengue, The Lancet, 370, 1644-1652, (2007)
[25] Heesterbeek, J.; Roberts, M. G., The type-reproduction number T in models for infectious disease control, Math. Biosci., 206, 3-10, (2007) · Zbl 1124.92043
[26] Johansson, M. A.; Hombach, J.; Cummings, D. A.T., Models of the impact of dengue vaccinesa review of current research and potential approaches, Vaccine, 29, 5860-5868, (2011)
[27] Kautner, I.; Robinson, M. J.; Kuhnle, U., Dengue virus infectionepidemiology, pathogenesis, clinical presentation, diagnosis, and prevention, J. Pediatr., 131, 516-524, (1997)
[28] Kurane, I.; Takasaki, T.; Yamada, K., Trends in flavivirus infections in Japan, Emerg. Infect. Dis., 6, 569-571, (2000)
[29] Koopman, J. S.; Prevots, D. R.; Vaca Marin, M. A., Determinants and predictors of dengue infection in Mexico, Am. J. Epidemiol., 133, 11, 1168-1178, (1991)
[30] Li, J.; Blakeley, D.; Smith, R. J., The failure of R_0, Comput. Math. Methods Med., 13, 224-234, (2011) · Zbl 1227.92045
[31] Luz, P. M.; Lima-Camara, T. N.; Bruno, R. V., Potential impact of a presumed increase in the biting activity of dengue-virus-infected aedes aegypti (diptera: culicidae) females on virus transmission dynamics, Mem. Inst. Oswaldo Cruz., 106, 755-758, (2011)
[32] Luz, P. M.; Vanni, T.; Medlock, J.; Paltiel, A. D.; Galvani, A. P., Dengue vector control strategies in an urban settingan economic modelling assessment, The Lancet, 377, 1673-1680, (2011)
[33] Marques, C. A.; Forattini, O. P.; Massad, E., The basic reproduction number for dengue fever in sao paulo state, brazil1990-1991 epidemic, Trans. R. Soc. Trop. Med. Hyg., 88, 58-59, (1994)
[34] Massad, E.; Burattini, M. N.; Coutinho, F. A.; Lopez, L. F., Dengue and the risk of urban yellow fever reintroduction in sao paulo state, Brazil, Rev. Saude Publica, 37, 4, 477-484, (2003)
[35] Massad, E.; Coutinho, F. A.; Burattini, M. N.; Lopez, L. F., The risk of yellow fever in a dengue-infested area, Trans. R. Soc. Trop. Med. Hyg., 95, 4, 370-374, (2001)
[36] Mckay, M. D.; Beckman, R. J.; Conover, W. J., A comparison of three methods for selecting values of input variables in the analysis of output from a computer code, Technometrics, 21, 239-245, (1979) · Zbl 0415.62011
[37] Marino, S.; Ian, B.; Hogue, I. B.; Ray, C. J.; Kirschner, D. E., A methodology for performing global uncertainty and sensitivity analysis in systems biology, J. Theor. Biol., 254, 178-196, (2008)
[38] Messer, W. B.; Gubler, D. J.; Harris, E.; Sivananthan, K.; de Silva, A. M., Emergence and global spread of a dengue serotype 3, subtype III virus, Emerg. Infect. Dis., 9, 800-809, (2003)
[39] Newton, E. A.C.; 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., 47, 709-720, (1992)
[40] Nagao, Y.; Koelle, K., Decreases in dengue transmission may act to increase the incidence of dengue hemorrhagic fever, Proc. Natl. Acad. Sci. U.S.A., 105, December, 2238-2243, (2008)
[41] Pongsumpun, P.; Patanarapelert, K.; Sriprom, M.; Varamit, S.; Tang, I. M., Infection risk to travelers going to dengue fever endemic regions, Southeast Asian J. Trop. Med. Public Health, 35, 155-159, (2004)
[42] Rocco, I. M.; Kavakama, B. B.; Santos, C. L.S., First isolation of dengue 3 in Brazil from an imported case, Rev. Inst. Med. Trop. Sao Paulo, 43, 55-57, (2001)
[43] Roberts, M. G.; Heesterbeek, J., A new method to estimate the effort required to control an infectious disease, Proc. R. Soc. Lond. B, 270, 1359-1364, (2003)
[44] Supriatna, A. K.; Soewono, E.; van Gils, S. A., A two-age-classes dengue transmission model, Math. Biosci., 216, 114-121, (2008) · Zbl 1151.92019
[45] Sierra, B.; Perez, A. B.; Vogt, K., Secondary heterologous dengue infection riskdisequilibrium between immune regulation and inflammation?, Cell Immunol., 262, 134-140, (2010)
[46] Scott, T. W.; Amerasinghe, P. H.; Morrison, A. C., Longitudinal studies of aedes aegypti (diptera: culicidae) in Thailand and puerto ricoblood feeding frequency, J. Med. Entomol., 30, 94-99, (2000)
[47] Tewa, J. J.; Dimi, J. L.; Bowong, S., Lyapunov functions for a dengue disease transmission model, Chaos Solitons Fractals, 39, 936-941, (2009) · Zbl 1197.34099
[48] Tang, S. Y.; Xiao, Y. N.; Lin, Y.; Check, R. A.; Wu, J. H., Campus quarantine (fengxiao) for curbing emergent infectious diseaseslessons from mitigating A/H1N1 in Xi’an, China, J. Theor. Biol., 295, 47-58, (2012) · Zbl 1336.92088
[49] van den Driessche, P.; Watmough, J., Reproduction numbers and subthreshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180, 29-48, (2002) · Zbl 1015.92036
[50] Wei, H. M.; Li, X. Z.; Martcheva, M., An epidemic model of a vector-borne disease with direct transmission and time delay, J. Math. Anal. Appl., 342, 895-908, (2008) · Zbl 1146.34059
[51] Xiao, J. P.; He, J. F.; Deng, A. P., Characterizing a large outbreak of dengue fever in guangdong province, China. Infect. Dis. Poverty, 5, 44, (2016)
[52] Xinhua News, 2014. 〈http://news.xinhuanet.com/politics/2014-10/09/c_1112752842.htm〉 (accessed 11/08/2016).
[53] Xinlang News, 2014. 〈http://gd.sina.com.cn/news/b/2014-10-16/1058134284.html〉 (accessed 11/08/2016).
[54] Yang, H. M.; Ferreira, C. P., Assessing the effects of vector control on dengue transmission, Appl. Math. Comput., 198, 401-413, (2008) · Zbl 1133.92015
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