To investigate the temporal and regional variability of the 2001–2002 dengue outbreak in Havana City where 12 889 cases, mostly of DENV-3 type, were reported over a period of 7 months.
To investigate the temporal and regional variability of the 2001–2002 dengue outbreak in Havana City where 12 889 cases, mostly of DENV-3 type, were reported over a period of 7 months.
A simple mathematical model, the Richards model, was used to fit the weekly reported dengue case data by municipality, in order to quantify the transmissibility and temporal changes in the epidemic in each municipality via the basic reproduction number R0.
Model fits indicate either a 2-wave or 3-wave outbreak in all municipalities. Estimates for R0 varied greatly, from 1.97 (95% CI: 1.94, 2.01), for Arroyo Naranjo, to 61.06 (60.44, 61.68), for Boyeros, most likely due to heterogeneity in community structure, geographical locations and social networking.
Our results illustrate the potential impact of climatological events on disease spread, further highlighting the need to be well prepared for potentially worsening disease spread in the aftermath of natural disasters such as hurricanes/typhoons.
Etudier la variabilité temporelle et régionale de l’épidémie de dengue de 2001–2002 à La Havane où 12.889 cas, pour la plupart de type DENV-3, ont été signalés sur une période de 7 mois.
Un modèle mathématique simple, le modèle de Richards, a été utilisé pour ajuster les données hebdomadaires de cas de dengue déclarés par municipalité, afin de quantifier la transmissibilité et les changements temporels de l’épidémie dans chaque commune, par le nombre de reproduction de base R0.
Les ajustements du modèle indiquent une épidémie à 2 ou 3 vagues dans toutes les municipalités. Les estimations de R0 variaient considérablement, allant de 1,97 (IC95%: 1,94–2,01) pour Arroyo Naranjo à 61,06 (60,44–61,68) pour Boyeros, probablement en raison de l'hétérogénéité de la structure des communautés, des situations géographiques et des réseaux sociaux.
Nos résultats illustrent l'impact potentiel des événements climatiques sur la propagation de la maladie, soulignant la nécessité de bien se préparer contre la propagation potentiellement aggravée de la maladie à la suite de catastrophes naturelles telles que les ouragans/typhons.
Investigar la variabilidad temporal y regional del brote de dengue del 2001–2002 en la ciudad de La Habana donde se reportaron 12,889 casos, la mayoría del tipo DENV-3, y a lo largo de un período de 7 meses.
Se utilizó un modelo matemático simple, el modelo de Richards, para ajustar los datos semanales de casos por municipalidad con el fin de cuantificar la transmisibilidad y los cambios temporales de la epidemia en cada municipalidad mediante el número básico de reproducción R0.
Los ajustes del modelo indican un brote en 2 o en 3 olas en todas las municipalidades. Los cálculos de R0 variaban muchísimo, desde 1.97 (IC 95%: 1.94, 2.01) para Arroyo Naranjo a 61.06 (60.44, 61.68) para Boyeros, probablemente debido a la heterogeneidad de la estructura comunitaria, a la localización geográfica y a las redes sociales.
Nuestros resultados ilustran el potencial impacto que los eventos climatológicos tienen sobre la propagación de las enfermedades, enfatizando la necesidad de estar bien preparados para un posible empeoramiento de la propagación después de un desastre natural, como un huracán o un tifón.
Dengue virus infection in humans causes a spectrum of illness ranging from asymptomatic or mild febrile illness to severe and fatal haemorrhagic disease, namely dengue fever (DF) and dengue haemorrhagic fever/dengue shock syndrome (DHF/DSS), for which secondary infection is considered the main individual risk factor (Nimmannitya et al. 1987; Halstead 1988; Guzman & Kouri 2002). Infection with any of the four known serotypes of dengue (DENV-1, DENV-2, DENV-3 and DENV-4) causes a similar clinical presentation that may vary in severity, depending on the strain and serotype of the infecting virus and the immune status, age and genetic background of the human host, and induces life-long protective immunity to the infecting serotype, accompanied by short-term cross-protective immunity against the other viruses (Sabin 1952). Due to its widespread and multiple serotypes, the disease, even in the absence of fatal forms, produces significant economic and social costs in terms of absenteeism, immobilisation, debilitation, medication and death.
Environmental factors such as climate and geography affect the spatio-temporal patterns of dengue transmission (Johansson et al. 2009). For example, climatological factors often affect the development, maturation and survival of the vector Aedes aegypti (Jetten & Focks 1997; Mourya et al. 2004), as well as its role in the human-vector dengue transmission cycle. In particular, the extrinsic incubation period (or the time for infected female mosquitoes to become infectious after biting an infectious individual) is influenced by ambient temperature (Keating 2001; Chowell & Sanchez 2006; Chowell et al. 2011). Moreover, factors such as high spatial heterogeneity levels in vector or host density play an important role in determining the risk of dengue outbreaks and the reproduction number. Interestingly, a recent study (Chowell et al. 2011) shows significant heterogeneity in seasonality and timing of dengue epidemics at the province level across Peru, suggesting that dengue is frequently imported into coastal regions through infective sparks from endemic regions of neighbouring endemic countries, where propitious environmental conditions promote year-round mosquito breeding sites. This pattern is associated with climatologic conditions as well as connectivity among geographical regions.
In Cuba, dengue viruses are transmitted by the Aedes aegypti mosquito. The mosquito is characterised by its biting pattern, which consists of multiple blood meals during each egg-laying cycle, and its ability to grow in water reservoirs during its immature stages (i.e. egg, larva and pupa). These features make it an ideal vector for dengue virus transmission, especially in large urban areas where the human population density is high and provides abundant artificial containers in where the aquatic stages of Aedes aegypti flourish (Hammond et al. 2007). Aedes aegypti is infected by sucking infected human blood, while humans are infected with dengue viruses when bitten by an infective mosquito. The global spread of dengue can be directly attributable to the proliferation and adaptation of mosquitoes.
Currently, the only way to control and reduce dengue transmission is to implement alternative strategies such as (i) reduction in vector populations in both the adult (by fumigation and/or by other chemical/biological treatments, e.g. Thomé et al. 2010) and the immature stages (by eliminating breeding sites); (ii) early detection of infected humans to prevent the virus transmission to susceptible mosquitoes. In Cuba, the rainy season (lasting 6 months from May to October) produces a proliferation of mosquito populations, including Aedes aegypti. Its persistent presence, together with the increased international arrivals from dengue-endemic countries in recent years, has led to several outbreaks including a major 2001 outbreak in Havana City (Pelaez et al. 2004).
In the Caribbean region, the first major outbreaks of DF (with a significant number of severe cases) occurred in Cuba in 1977 (with DENV-1) and in 1981 (with DENV-2). Both epidemics affected the entire country, producing more than 500 000 and 300 000 dengue cases, respectively. In 2000, a minor outbreak of dengue was detected in Havana City with 138 cases of DF, when DENV-3 and DENV-4 viruses were isolated. In 2001, dengue transmission was detected in Havana City where 12 889 cases, mostly of DENV-3 type, were reported with 78 DHF cases and three deaths due to dengue (Pelaez et al. 2004).
To ascertain how this epidemic came to pass, we employed a simple mathematical model to investigate the temporal progression of the epidemic in various municipalities in Havana City and to quantify the transmissibility of the epidemic via the basic reproduction number R0.
The 2001–2002 dengue outbreak case data by reporting week (epidemiological week or e-week) for each of the 15 municipalities in Havana City were obtained from the Pedro Koury Tropical Medicine Institute (IPK) in Havana, Cuba, which spans from 30 May 2001 when the first case was reported in Playa (Figure 1), to the last reported case on 27 February 2002. Subsequently, the data spanned 40 weeks, from e-week 22 of 2001 (27 May to 2 June 2001) to e-week 9 of 2002 (24 February to 2 March 2002).
During the 2001–2002 dengue III epidemic in Havana, all suspected DF cases were tested. Dengue infection was confirmed in 17.86% through serological studies. The initial test was carried out at the Provincial Epidemiological Center of Havana using the ultramicro-enzyme-linked immunosorbent assay for dengue IgM detection. A second seroconversion test was carried out 2–3 weeks after illness onset to confirm seroconversion, at the National Reference Center for dengue in Cuba at the Tropical Medicine Institute ‘Pedro Kouri’. For more information, see Pelaez et al. (2004).
We fit the data to the Richards model (Richards 1959): , where C(t) is the cumulative number of cases reported at time t (in weeks). Here, the prime ‘′’denotes the rate of change with respect to time. The model parameter K is the maximum case number (or final outbreak size) over a single phase of outbreak, r is the per capita growth rate of the infected population, and a is the exponent of deviation. The solution of the Richards model is , where ti is the turning point of the epidemic (or the inflection point of the cumulative case curve), , and ln denotes the natural logarithm. Using the Richards model, we can directly fit empirical data from a cumulative epidemic curve to obtain estimates of epidemiological meaningful parameters, including the growth rate r.
In such a model formulation, the basic reproduction number R0 is given by the formula R0 = exp(rT), where T is the disease generation time defined as the average time interval from infection of an individual to infection of his or her contacts. To take into account the extrinsic and intrinsic incubation periods as well as the duration of viraemia, we use an estimated generation time of T = 24 days with a range of 16–34 days (see Hsieh & Chen 2009; for detailed explanation). An expression of the dengue reproduction number that more explicitly connects the intrinsic growth rate and the epidemiology of host/vector can also be found in, for example, Favier et al. (2006). It has been shown mathematically that, given the growth rate r, the equation R0 = exp (rT) provides the upper bound of the basic reproduction number regardless of the distribution of the generation interval used (Wallinga & Lipsitch 2007). Additional technical details regarding the Richards model are described in Hsieh et al. (2004), Hsieh and Cheng (2006), or Hsieh (2008).
The turning point or inflection point ti of the cumulative case data, defined as the time when the rate of case accumulation changes from increasing to decreasing (or vice versa), can be easily pinpointed as the point where the rate of change transitions from positive to negative, that is, the moment at which the trajectory begins to decline. For epidemics with two or more phases, a variation in the S-shaped Richards model has been proposed (Hsieh & Cheng 2006). This multistaged Richards model distinguishes between two types of turning points: the initial S-shaped cumulative case curve, which signifies the first turning point that ends initial exponential growth, or simply the time where peak incidence of a wave of cases occurs; and a second type of turning point in the cumulative epidemic curve, where the growth rate of the number of cumulative cases begins to increase again, signifying the beginning of the next wave. This variant of Richards model provides a systematic method of determining whether an outbreak is single- or multiphase in nature, and can be used to distinguish true turning points from peaks and valleys resulting from random variability in case counts (see Hsieh and Ma (2009) and Hsieh and Chen (2009) for its applications to dengue; Hsieh (2010) and Hsieh et al. (2010, 2011a,b) for applications to 2009 H1N1 and Wang et al. (2012) for the connection between the Richards model and the traditional SIR compartmental model). Model parameter estimates based on the explicit solution of the Richards model can be obtained easily and efficiently using any standard software with a least-squares approximation tool, such as sas or matlab.
The results of the best Richards model fit for 14 of 15 municipalities in Havana City, with estimates for ti, r, K, R0 and their respective 95% confidence intervals (CI), are listed in Tables 1 and 2. The Akaike Information Criterion (AIC, Akaike 1974; values are also given as a measure of the respective goodness of fit for each wave of the local outbreak. The municipality of Cotorro had only 34 cases reported very late after e-week 40 (in September) and scattered over the next 20 weeks and hence cannot be fitted to the Richards model. We also fitted the combined total case data of all 15 municipalities in Havana City including Cotorro (see Table 2), for the purpose of comparison. Note that the week in which the true turning point for each wave occurred is ti weeks (third column in the tables) after the first week of the wave, rounding off to the next integer week. For example, the turning points for the three waves in Playa occurred in e-week 39 (24 + 14.3 in the first row of Table 1), e-week 46 (43 + 2.46) and e-week 4 of 2002 (51 + 4.38), respectively.
|Region||E-week||AIC||Turning point ti||Growth rate r||Case number K||R 0|
|Playa||24–43||155.7||14.3 (14.0, 14.6)||0.393 (0.364, 0.422)||1601 (1564, 1638)||3.85 (3.82, 3.87)|
|43–51||52.7||2.5 (1.3, 3.7)||0.019 (0.014, 0.023)||1764 (1706, 1822)||1.07 (1.06, 1.07)|
|51–6a||71.8||4.4 (4.1, 4.6)||0.274 (0.247, 0.301)||79 (76, 81)||2.56 (2.54, 2.56)|
|Plaza||33–44||97.9||7.7 (7.2, 8.3)||0.660 (0.145, 1.175)||845 (627, 1064)||9.61 (9.17, 10.05)|
|44–1a||61.7||3.8 (3.2, 4.3)||0.106 (0.092, 0.119)||1389 (1336, 1442)||1.44 (1.43, 1.45)|
|1a–8a||44.6||1.8 (1.1, 2.5)||0.025 (0.018, 0.031)||1468 (1459, 1476)||1.09 (1.08, 1.09)|
|Central Havana||32–44||99.2||9.8 (8.9, 10.7)||0.747 (0.475, 1.018)||613 (534, 693)||12.94 (12.70, 13.17)|
|44–52||65.7||3.6 (2.3, 5.0||0.137 (0.093, 0.182)||1366 (1184, 1549)||1.60 (1.31, 1.90)|
|52–7a||50.1||2.6 (2.0, 3.2)||0.044 (0.037, 0.052)||1564 (1543, 1585)||1.16 (0.87, 1.46)|
|Old Havana||33–44||64.6||8.4 (7.5, 9.2)||0.655 (0.434, 0.876)||167 (151, 184)||9.44 (9.25, 9.63)|
|44–9a||87.5||11.7 (11.3, 12.0)||0.122 (0.114, 0.129)||817 (800, 834)||1.52 (1.51, 1.53)|
|Diez de Octubre||32–45||103.2||9.90 (9.5, 10.3)||0.327 (0.285, 0.370)||362 (345, 379)||3.07 (3.03, 3.11)|
|45–52||61.5||4.6 (4.1, 5.1)||0.157 (0.133, 0.180)||848 (806, 891)||1.71 (1.69, 1.73)|
|52–7a||29.9||2.8 (0.9, 4.7)||0.636 (0.228, 1.043)||119 (109, 129)||8.84 (8.56, 9.13)|
|Cerro||38–43||5.4||4.1 (4.0, 4.1)||0.483 (0.470, 0.496)||375 (369, 381)||5.23 (5.22, 5.24)|
|43–51||75.1||2.6 (0.3, 4.9)||0.195 (0.056, 0.335)||850 (763, 937)||1.95 (1.85, 2.06)|
|51–8a||78.1||5.9 (4.7, 7.1)||0.030 (0.023, 0.037)||1009 (985, 1033)||1.11 (1.10, 1.11)|
|Marianao||29–44||86.1||12.7 (12.6, 12.8)||0.581 (0.556, 0.605||627 (618, 636)||7.32 (7.30, 7.34)|
|44–1a||61.3||1.7 (0.5, 2.9)||0.122 (0.088, 0.156)||1062 (1037, 1088)||1.52 (1.49, 1.55)|
|1a–6a||33.0||3.4 (2.4, 4.4)||0.028 (0.018, 0.038)||1147 (1130, 1165)||1.10 (1.10, 1.11)|
|Lisa||34–44||39.8||7.7 (7.5, 7.9)||0.760 (0.674, 0.847)||249 (241, 257)||13.56 (13.48, 13.63)|
|44–1a||58.1||4.4 (3.6, 5.2)||0.081 (0.066, 0.097)||426 (406, 445)||1.32 (1.31, 1.33)|
|1a–7a||26.6||1.9 (1.1, 2.8)||0.034 (0.023, 0.044)||478 (472, 483)||1.12 (1.12, 1.13)|
|Region||E-week||AIC||Turning point ti||Growth rate r||Case number K||R 0|
|Boyeros||35–44||53.2||6.7 (5.1, 8.4)||1.199 (0.428, 1.971)||339 (290, 387)||61.06 (60.44, 61.68)|
|44–52||56.2||3.0 (1.8, 4.2)||0.230 (0.092, 0.367)||896 (766, 1025)||2.20 (2.09, 2.30)|
|52–8a||42.4||1.1 (0.1, 2.1)||0.038 (0.029, 0.048)||960 (946, 973)||1.14 (1.13, 1.15)|
|Regla||42–52||56.6||5.1 (4.4, 5.8)||0.420 (0.181, 0.659)||188 (162, 214)||4.22 (4.02, 4.41)|
|52–7a||25.4||2.0 (1.2, 2.7)||0.058 (0.042, 0.075)||208 (206, 211)||1.22 (1.21, 1.23)|
|Havana del. Este||35–45||43.2||7.7 (4.9, 10.6)||0.841 (0.203, 1.479)||158 (113, 204)||17.88 (17.35, 18.41)|
|45–52||37.3||4.8 (4.6, 5.0)||0.210 (0.196, 0.223)||437 (423,451)||2.05 (2.04, 2.06)|
|52–8a||54.9||2.3 (1.4, 3.2)||0.085 (0.062, 0.108)||633 (620, 646)||1.34 (1.32, 1.36)|
|Guanabacoa||37–52||100.6||8.8 (8.1, 9.5)||0.490 (0.201, 0.780)||199 (177, 220)||5.37 (5.11, 5.63)|
|52–6a||24.3||2.5 (1.2, 3.8)||0.048 (0.029, 0.067)||234 (217, 252)||1.18 (1.17, 1.19)|
|Arroyo Naranjo||29–47||178.8||13.1 (12.2, 13.9)||0.198 (0.163, 0.233)||625 (576, 675)||1.97 (1.94, 2.01)|
|47–52||27.8||3.3 (2.8, 3.8)||0.066 (0.055, 0.076)||833 (816, 850)||1.25 (1.25, 1.26)|
|52–7a||47.9||3.5 (2.6, 4.4)||0.028 (0.021, 0.035)||954 (941, 968)||1.10 (1.10, 1.11)|
|SMP||28–44||55.3||13.3 (13.0, 13.6)||0.460 (0.403, 0.516)||74 (71, 78)||4.84 (4.79, 4.89)|
|44–52||70.3||6.2 (5.6, 6.7)||0.256 (0.209, 0.302)||408 (372, 445)||2.41 (2.37, 2.44)|
|52–8a||59.8||4.1 (3.5, 4.7)||0.082 (0.068, 0.097)||616 (603, 629)||1.33 (1.32, 1.34)|
|Havana City Total||24–44||216.0||17.5 (17.4, 17.7)||0.316 (0.305, 0.327)||5933 (5771, 6095)||2.96 (2.95, 2.97)|
|44–52||94.2||4.5 (4.1, 4.8)||0.095 (0.087, 0.103)||11003 (10578, 11418)||1.39 (1.38, 1.39)|
|52–9a||101.2||3.0 (2.7, 3.4)||0.037 (0.034, 0.041)||12879 (12820, 12938)||1.14 (1.13, 1.14)|
The model fits for the most severely affected municipalities, namely Playa (with the first reported case of this epidemic), Plaza, Central Havana and Old Havana, as well as for all 15 municipalities of Havana City, are given in Figure 2. All model fits indicate a 2-wave or 3-wave outbreak for each of the 14 municipalities as well as for all of Havana City. Outbreaks in Old Havana, Regla and Guanabacoa only are 2-wave, while all other municipalities exhibit 3-wave outbreaks. For the purpose of comparing regional heterogeneity, we also provide timeline graphs of the 14 fitted municipalities in Figure 3.
Previous large dengue epidemics in Cuba were associated with DENV-1 (in 1977) and DENV-2 (in 1981). More recently, two smaller dengue outbreaks were reported in 1997 (DENV-2) and September 2000 (DENV-3 and DENV-4) (Pelaez et al. 2004). Subsequently, there was very little pre-existing immunity among the population in Havana for this 2001–2002 DENV-3 epidemic, although some cases of DHF/DSS might have occurred in persons infected with DENV-3 in a background of immunity to DENV-1 and DENV-2 from either the 1981 epidemic or dengue epidemics during or before the 1940s (Alvarez et al. 2006). Tables 1 and 2 indicates that the estimates for R0 in the initial wave vary from 1.97 (95% CI: 1.94, 2.01) for Arroyo Naranjo to 17.88 (17.35, 18.41) for Havana del Este. Only Boyeros had an unusually high disease transmission potential of R0 = 61.06 (60.44, 61.68) in the initial wave starting comparatively late in e-week 35 (Figure 3b), possibly caused by multiple imported cases from neighbouring municipalities with earlier outbreaks, which can affect the estimation of basic reproduction number (Nishiura & Roberts 2010). The wide regional variability exhibited in our estimates is consistent with other reported values of R0 for dengue in the literature in various regions of the world using high-resolution spatial and temporal data (Luz et al. 2003; Favier et al. 2006; Chowell et al. 2007, 2008; Hsieh & Chen 2009), most likely due to heterogeneity in community structure, geographical locations, intervention measures, as well as in social networking. Interestingly, a study (Chowell et al. 2008) using provincial showed a hierarchy of transmission events from large to small population areas during the large 2000–2001 dengue epidemic in Peru. We also note that although variability across municipalities is probably well represented in estimates for R0, the accuracy of the actual R0 levels may be affected by the lack of explicit dependence of climatic conditions on dengue transmission dynamics in our modelling.
Moreover, there is also a clear regional heterogeneity in the temporal trend, where Old Havana, Regla and Guanabacoa were 2-waved while the other municipalities were 3-waved – in particular, Central Havana, which is close to Old Havana, but has a different model fit with one additional (third) wave occurring at the turn of the calendar year (e-week 52).
Except for Playa (which had the earliest outbreak and a turning point as early as e-week 39), Regla and Guanabacoa (regions, along with Cotorro, with outbreaks starting as late as in September), all other municipalities and all of Havana City had a first turning point (peak incidence) during e-weeks 41–43 that indicates a downturn of cases, regardless of whether the data fit exhibits a 2-wave or 3-wave outbreak. Moreover, with the exception of Arroyo Naranjo, Regla and Guanabacoa, all other municipalities as well as all of Havana City had a turning point of second type around e-weeks 43–45 that signals an increase in case number and the beginning of a new wave of cases, regardless of whether it had a 2-wave or 3-wave outbreak. Interestingly, all 14 municipalities had a turning point (peak incidence) during e-weeks 46–51, regardless of the number of waves or the timing of initial outbreak. Finally, for all 11 municipalities with three waves, the third wave started around e-week 51 to e-week 1 of 2002. The last turning point (peak incidence), or a downturn towards the end of the outbreak, came during e-weeks 2–5 of 2002 for all municipalities except Old Havana, which had a 2-wave outbreak.
Even within Havana City, geographical heterogeneity played a significant role in temporal trends as well as in transmission potential of the infected individuals. Playa, Plaza and Central/Old Havana have more work offices where people commute daily, and hence are important in driving the epidemic (Figure 3a), while the municipalities of Guanabacoa, Regla and Cotorro all contain some less populated areas and therefore have very late and very minor outbreaks. More significant and intriguing is the underlying cause of this multiwave epidemic. For the first wave, we note that Hurricane Michelle, the most destructive hurricane in the history of Cuba based on actual damage (Pielke et al. 2003), struck Cuba on 4 November 2001, the first day of week 24 in our study. Landing on the coast of western and southern Cuba, Michelle was one of the wettest tropical cyclones ever in Cuba, causing four to five foot waves along with a heavy storm surge. Rainfall up to 754 mm was recorded across the island (Instituto Nacional de Recursos Hidráulicos 2003). Previous studies (e.g. Chowell & Sanchez 2006; Wu et al. 2007; Hsieh & Chen 2009) have proposed that extreme weather conditions, such as typhoon or hurricane which brings substantial amount of precipitation, can significantly correlate with the occurrence of a wave of reported dengue cases with a lag of several weeks. Typically, a typhoon/hurricane first brings a sudden drop in temperature causing mosquito inactivity and decreased biting/infection; the ensuing heavy rainfall then leads to more breading reservoirs for the larvae to proliferate. It is hence conceivable that Hurricane Michelle had contributed to, if not actually causing, the new wave of cases in these municipalities after e-week 45. In other words, the dengue epidemic in Havana had started to ease initially around e-weeks 41–43 (first turning point/peak incidence), but spread once again after e-week 45 after Hurricane Michelle, causing a more severe and longer-lasting epidemic. We note that, as the case data are by reporting week, there is a delay of around one week from actual infections to reporting, mainly due to intrinsic dengue incubation period of 4–7 days (Nishiura & Halstead 2007).
Our result illustrates the potential impact of climatological events on disease spread. It further highlights the need for health community to be aware and better prepared, with programmes such as pre-emptive spraying and elimination of reservoirs for larvae, for a potentially worsening disease spread in the aftermath of natural disasters such as hurricanes and typhoons.
After a downturn (peak incidence) around e-weeks 46–51, a new turning point (of second type) for start of a third wave occurred after e-week 51 for all 11 municipalities with 3-wave fit (not including Old Havana, Regla and Guanabacoa). However, we note that Christmas and New Year happened to fall on, respectively, e-week 52 and e-week 1 of 2002. The new wave of reported cases is likely attributable to a decrease in reporting partly due to reluctance on the part of some ill persons to go to hospital during the holidays, and a subsequent surge in cases after the holidays. Hence, the cause for this third wave is human behaviour, rather than anything relating to disease transmission or other environmental or social factors.
During the 1981 dengue epidemic, the Cuban health authorities started a National Program for Eradication of Aedes aegypti, which has continued to the present. The campaign was based on the principles of dengue control established by the Pan American Health Organization (PAHO) Guidelines (Pan American Health Organization 1994) with the involvement of the whole community (governmental and political bodies at all levels, householders, community organisations, etc.), where thousands of workers were mobilised with the task of periodic inspection of housing, detection and elimination of breeding points for the vector, chemical control of mosquitoes and an educational campaign. These activities are carried out regularly and reinforced whenever cases of dengue are detected, where workers clean up empty places looking for larvae and spray all homes within 500-metre radius of the suspected case. The 2001 epidemic was no exception (Pelaez et al. 2004), which may have contributed to the 2001 epidemic being less severe than the previous ones in 1977 and 1981. Community-wide cross pre-immunity from earlier epidemics may also have played a role, which is, however, difficult to gauge without sizable serologic data set.
A further limitation of this work is that the Richards model does not explicitly incorporate vector biology or the effect of temperature on extrinsic incubation period or vector mortality rate, which could affect our results. However, to appropriately consider these biological aspects of the dengue transmission requires a much more complex vector-host model that incorporates environmental factors such as seasonality as well as detailed and high-quality vector and human data, and therefore is beyond the scope of the current work.
YHH is supported by the National Science Council of Taiwan (grants 100-2314-B-039-028-MY3 and 100-2115-M-039-002). This work was carried out during visits to the University of Paris Descartes by YHH and H de A. The authors received support from the French ‘Agence National pour la Recherche’ project ‘Viroscopy’. H de A also received support from the Spanish AECID, from their project PCI D/023835/09. We thank Dr. Gustavo Kouri, who passed away recently, and his colleagues at the Pedro Kouri Tropical Medicine Institute for access to the dengue surveillance data used for this study. The authors also thank the reviewers for constructive comments that greatly improved this manuscript.