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Estimation of the reproduction number of dengue fever from spatial epidemic data. (English) Zbl 1119.92055
Summary: Dengue, a vector-borne disease, thrives in tropical and subtropical regions worldwide. A retrospective analysis of the 2002 dengue epidemic in Colima located on the Mexican central Pacific coast is carried out. We estimate the reproduction number from spatial epidemic data at the level of municipalities using two different methods: (1) Using a standard dengue epidemic model and assuming pure exponential initial epidemic growth, and (2) Fitting a more realistic epidemic model to the initial phase of the dengue epidemic curve.
Using Method I, we estimate an overall mean reproduction number of 3.09 (95% CI: 2.34, 3.84) as well as local reproduction numbers whose values range from 1.24 (1.15, 1.33) to 4.22 (2.90, 5.54). Using Method II, the overall mean reproduction number is estimated to be 2.0 (1.75, 2.23) and local reproduction numbers ranging from 0.49 (0.0, 1.0) to 3.30 (1.63, 4.97). Method I systematically overestimates the reproduction number relative to the refined Method II, and hence it would overestimate the intensity of interventions required for containment. Moreover, optimal intervention with defined resources demands different levels of locally tailored mitigation. Local epidemic peaks occur between the 24 th and 35 th week of the year, and correlate positively with the final local epidemic sizes $$(\rho = 0.92, P$$-value $$< 0.001$$). Moreover, final local epidemic sizes are found to be linearly related to the local population size ($$P$$-value $$< 0.001$$). This observation supports a roughly constant number of female mosquitoes per person across urban and rural regions.

##### MSC:
 92D30 Epidemiology 34C60 Qualitative investigation and simulation of ordinary differential equation models 62P10 Applications of statistics to biology and medical sciences; meta analysis
##### Keywords:
Dengue hemorrhagic fever; Stage progression; Colima; Mexico
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##### References:
 [1] Anderson, R.M.; May, R.M., Infectious diseases of humans, (1991), Oxford University Press Oxford, UK [2] Blower, S.M.; Dowlatabadi, H., Sensitivity and uncertainty analysis of complex models of disease transmission: an HIV model, as an example, International statistical review, 62, 2, 229-243, (1994) · Zbl 0825.62860 [3] Brauer, F.; Castillo-Chavez, C., Mathematical models in population biology and epidemiology, (2000), Springer Verlag New York · Zbl 1302.92001 [4] Bowman, C.; Gumel, A.B.; van den Driessche, P.; Wu, J.; Zhu, H., A mathematical model for assessing control strategies against west nile virus, Bulletin of mathematical biology, 67, 1107-1133, (2005) · Zbl 1334.92392 [5] Burr, T.L.; Chowell, G., Observation and model error effects on parameter estimates in susceptible-infected-recovered epidemic model, Far east journal of theoretical statistics, 19, 163-183, (2006) · Zbl 1116.62118 [6] Chitnis, N.; Cushing, J.M.; Hyman, J.M., Bifurcation analysis of a mathematical model for malaria transmission, SIAM journal of applied mathematics, 67, 24-45, (2006) · Zbl 1107.92047 [7] Chowell, G.; Castillo-Chavez, C.; Fenimore, P.W.; Kribs-Zaleta, C.; Arriola, L.; Hyman, J.M., Model parameters and outbreak control for SARS, Emerging infectious diseases, 10, 1258-1263, (2004) [8] Chowell, G.; Hyman, J.M.; Diaz-Dueñas, P.; Hengartner, N.W., Predicting scorpion sting incidence in an endemic region using climatological variables, International journal of environmental health research, 15, 425-435, (2005) [9] Chowell, G.; Rivas, A.L.; Smith, S.D.; Hyman, J.M., Identification of case clusters and counties of greater infective connectivity in the 2001 uruguayan foot-and-mouth disease epidemic, American journal of veterinary research, 67, 1-12, (2006) [10] Chowell, G.; Sanchez, F., Climate-based descriptive models of dengue fever, Journal of environmental health, 68, 60-63, (2006) [11] Christophers, R., aedes aegypti (L.), the yellow fever mosquito, (1960), Cambridge University Press Cambridge [12] Cummings, D.A.; Schwartz, I.B.; Billings, L.; Shaw, L.B.; Burke, D.S., Dynamic effects of antibody-dependent enhancement on the fitness of viruses, Pnas, 102, 15259-15264, (2005) [13] Instituto Nacional de Estadística Geografia e Informática. XII census of population and household, 2000, accessed March 10, 2005. Available from: http://www.inegi.gob.mx/inegi/default.asp. [14] Diekmann, O.; Heesterbeek, J., Mathematical epidemiology of infectious diseases: model building, analysis and interpretation, (2000), Wiley New York · Zbl 0997.92505 [15] van den Driessche, P.; Watmough, J., Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Mathematical biosciences, 180, 29-48, (2002) · Zbl 1015.92036 [16] Efron, B.; Tibshirani, R., Bootstrap methods for standard errors, confidence intervals, and other measures of statistical accuracy, Statistical science, 1, 54-75, (1986) · Zbl 0587.62082 [17] Espinoza-Gómez, F.; Hernández-Suarez, C.M.; Coll-Cardenas, R., Factores que modifican los indices larvarios de aedes aegypti en colima, Mexico [factors that modify the larval indices of aedes aegypti in colima, mexico], Pan American journal of public health, 10, 6-12, (2001) [18] Espinoza-Gómez, F.; Hernández-Suarez, C.M.; Rendón-Ramrez, R.; Carrillo-Alvarez, M.L.; Flores-González, J.C., Transmisión interepidémica del dengue en la ciudad de colima, Mexico [interepidemic transmission of dengue in the city of colima, mexico], Salud publica Mexico, 45, 365-370, (2003) [19] Esteva, L.; Vargas, C., Coexistence of different serotypes of dengue virus, Journal of mathematical biology, 46, 31-47, (2003) · Zbl 1015.92023 [20] Favier, C.; Degallier, N.; Rosa-Freitas, M.G.; Boulanger, J.P.; Costa Lima, J.R.; Luitgards-Moura, J.F.; Menkes, C.E.; Mondet, B.; Oliveira, C.; Weimann, E.T.; Tsouris, P., Early determination of the reproduction number for vector-borne diseases: the case of dengue in Brazil, Tropical medicine and international health, 11, 332-340, (2006) [21] Favier, C.; Schmit, D.; Muller-Graf, C.D.; Cazelles, B.; Degallier, N.; Mondet, B.; Dubois, M.A., Influence of spatial heterogeneity on an emerging infectious disease: the case of dengue epidemics, Proceedings biological sciences, 272, 1171-1177, (2005) [22] Feng, Z.; Velasco-Hernandez, X., Competitive exclusion in a vector-host model for the dengue fever, Journal of mathematical biology, 35, 523-544, (1997) · Zbl 0878.92025 [23] Ferguson, N.M.; Donnelly, C.A.; Anderson, R.M., Transmission dynamics and epidemiology of dengue: insights from age-stratified sero-prevalence surveys, Philosophical transactions of the royal society of London B, 354, 757-768, (1999) [24] Focks, D.A.; Daniels, E.; Haile, D.G.; Keesling, J.E., A simulation model of the epidemiology of urban dengue fever: literature analysis, model development, preliminary validation, and samples of simulation results, American journal of tropical medicine and hygiene, 53, 489-506, (1995) [25] Mexican National Center for Epidemiological Surveillance and Disease Control (CENAVE). Dengue Serotypes Circulating in Mexico, accessed March 04, 2006. Available from: http://www.cenave.gob.mx/dengue/default.asp?id=14. [26] Gubler, D.J., Dengue and dengue hemorrhagic fever, Clinical microbiology reviews, 11, 480-496, (1998) [27] Gúzman, M.G.; Kouri, G., Dengue and dengue hemorrhagic fever in the americas: lessons and challenges, Journal of clinical virology, 27, 1-13, (2003) [28] Hyman, J.M.; Li, J.; Stanley, E.A., The differential infectivity and staged progression models for the transmission of HIV, Mathematical biosciences, 155, 77-109, (1999) · Zbl 0942.92030 [29] Jacquez, J.A., Compartmental analysis in biology and medicine, (1996), Michigan Thompson-Shore Inc. Michigan · Zbl 0703.92001 [30] Jetten, T.H.; Focks, D.A., Potential changes in the distribution of dengue transmission under climate warming, American journal tropical medicine and hygiene, 57, 285-297, (1997) [31] Koopman, J.S.; Prevots, D.R.; Vaca Marin, M.A.; Gomez Dantes, H.; Zarate Aquino, M.L.; Longini, I.M.; Sepulveda Amor, J., Determinants and predictors of dengue infection in Mexico, American journal of epidemiology, 133, 1168-1178, (1991) [32] Li, C.F.; Lim, T.W.; Han, L.L.; Fang, R., Rainfall, abundance of aedes aegypti and dengue infection in selangor, Malaysia, Southeast Asian journal of tropical medicine and public health, 16, 560-568, (1985) [33] Lorono-Pino, M.A.; Cropp, C.B.; Farfan, J.A.; Vorndam, A.V.; Rodriguez-Angulo, E.M.; Rosado-Paredes, E.P.; Flores-Flores, L.F.; Beaty, B.J.; Gubler, D.J., Common occurrence of concurrent infections by multiple dengue virus serotypes, American journal of tropical medicine and hygiene, 61, 725-730, (1999) [34] Luz, P.M.; Codeco, C.T.; Massad, E.; Struchiner, C.J., Uncertainties regarding dengue modeling in Rio de Janeiro, Brazil, Memórias do instituto oswaldo cruz, 98, 871-878, (2003) [35] MacDonald, G., The epidemiology and control of malaria, chapter epidemics, (1957), Oxford University Press London, pp. 45-62 [36] Marques, C.A.; Forattini, O.P.; Massad, E., The basic reproduction number for dengue fever in São paulo state, Brazil: 1990-1991 epidemic, Transactions of the royal society of tropical medicine and hygiene, 88, 58-59, (1994) [37] Massad, E.; Coutinho, F.A.; Burattini, M.N.; Lopez, L.F., The risk of yellow fever in a dengue-infested area, Transactions of the royal society of tropical medicine and hygiene, 95, 370-374, (2001) [38] Singapore Ministry of Health. The communicable disease surveillance in Singapore 2004, accessed May 04, 2006. Available from: http://www.moh.gov.sg/cmaweb/attachments/publication/36c375c79a8t/Vector-Borne_Diseases.pdf. [39] Mourya, D.T.; Yadav, P.; Mishra, A.C., Effect of temperature stress on immature stages and susceptibility of aedes aegypti mosquitoes to chikungunya virus, American journal tropical medicine and hygiene, 70, 346-350, (2004) [40] Muir, L.E.; Kay, B.H., aedes aegypti survival and dispersal estimated by mark – release – recapture in northern Australia, American journal of tropical medicine and hygiene, 58, 277-282, (1998) [41] Navarrete-Espinosa, J.; Gomez-Dantes, H.; Celis-Quintal, J.G.; Vazquez-Martinez, J.L., Clinical profile of dengue hemorrhagic fever cases in Mexico, Salud publica Mexico, 47, 193-200, (2005) [42] Ooi, E.-E.; Goh, K.-T.; Gubler, D.J., Dengue prevention and 35 years of vector control in Singapore, Emerging infectious diseases, 12, 6, 887-893, (2006) [43] World Health Organization. Clinical diagnosis of dengue, accessed April 04, 2006. Available from: http://www.who.int/csr/resources/publications/dengue/012-23.pdf. [44] World Health Organization. Dengue and dengue hemorrhagic fever, accessed March 04, 2006. Available from: http://www.who.int/mediacentre/factsheets/fs117/en/. [45] Otero, M.; Solari, H.G.; Schweigmann, N., A stochastic population dynamics model for aedes aegypti: formulation and application to a city with temperate climate, Bulletin of mathematical biology, 68, 1945-1974, (2006) · Zbl 1296.92215 [46] Ross, R., The prevention of malaria, (1910), John Murray London [47] Schultz, G.W., Seasonal abundance of dengue vectors in manila, republic of the philippines, Southeast Asian journal of tropical medicine and public health, 24, 369-375, (1993) [48] Smith, D.L.; Dushoff, J.; Mckenzie, F.E., The risk of a mosquito-borne infection in a heterogeneous environment, Plos biology, 2, 1957-1964, (2004) [49] Vaughn, D.W.; Green, S.; Kalayanarooj, S.; Innis, B.L.; Nimmannitya, S.; Suntayakorn, S.; Endy, T.P.; Raengsakulrach, B.; Rothman, A.L.; Ennis, F.A.; Nisalak, A., Dengue viremia titer, antibody response pattern, and virus serotype correlate with disease severity, Journal of infectious diseases, 181, 2-9, (2000) [50] Wearing, H.J.; Rohani, P.; Keeling, M.J., Appropriate models for the management of infectious diseases, Plos medicine, 2, e174, (2005) [51] Wearing, H.J.; Rohani, P., Ecological and immunological determinants of dengue epidemics, Pnas, 103, 11802-11807, (2006)
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