We built a model capturing most of the features likely to influence the dynamics of dengue transmission and, after validating it against epidemiological data from Southern Vietnam, tested different hypotheses for their ability to reproduce the observed epidemiology of dengue in this highly endemic area. Our results highlight the critical role of short-term cross-protection that desynchronizes the epidemic cycles of the four dengue serotypes, resulting in 5–6 year-cycles consistent with those observed in Southern Vietnam. Wearing and Rohani reached the same conclusion after comparing a model with Thai data 
. In a recent analysis, Endy et al. 
also pointed out the importance of cross-protection to explain the results observed in a cohort of Thai children.
Our model suggests that the duration of cross-protection is in the range 6–17 months but did not point to a specific duration. However, our model assumption that this duration follows an exponential distribution may be inaccurate since this implies large variation on the duration of cross-protection from one individual to another. As dengue is a seasonal disease in southern Vietnam, it is plausible that cross-protection of shorter duration, associated with a narrower temporal distribution would suffice to desynchronize epidemics. Cross-protection against disease symptoms alone was insufficient to reproduce the observed multiannual cycles but this result was obtained for a scenario in which asymptomatic infections significantly contribute to disease transmission.
In our model, cross-enhancement without cross-protection did not reproduce the observed epidemiology of dengue in Southern Vietnam. This, however, does not invalidate the existence of immunological cross-enhancement that has been considered in many dengue transmission models 
. Indeed, several models combining cross-protection and cross-enhancement were able to reproduce dengue dynamics. More importantly, adding cross-enhancement increased the proportion of symptomatic cases caused by secondary infections to a value (59–74% overall, 85–91% for 15+ years cases), comparable with that reported by Phuong et al for Southern Vietnam (84%) 
. The model used to assess the impact of vaccination in the presence of cross-enhancement was also characterized by a higher proportion of severe cases among secondary infections than among primary infections (70% versus 60%). This higher proportion has been argued to indicate the existence of antibody-dependent enhancement 
These analyses also provide insights into other aspects of the transmission dynamics of dengue. Consistent with findings reported by Wikramaratna et al. 
our model provided a better fit to observations under the assumption that individuals can become sequentially infected by all four serotypes, rather than when two infections were assumed to provided complete protection. Among demographic factors, we notably observed that a decrease in birth rate increased the average age of dengue cases and increased the interval between major outbreaks. The same pattern was identified by Cummings et al. 
as the main explanation of the recent evolution of dengue epidemiology in Thailand.
By exploring the effect of the relative size of the human and vector populations, we saw that temporarily reducing the size of the vector population had only a short term effect of the transmission dynamics. We equate this with the impact of temporary vector control activities, some of which have had short term success but have not succeeded in maintaining disease reductions in the long run 
. The results obtained indicate that any interruption (or reduction) in vector control may counteract previous health benefits. The situation in Latin America where dengue reemerged in the seventies after being certified free of dengue between 1952 and 1965 provides a good illustration of this phenomenon 
. Dengue resurgence in Singapore after 2 decades of successful control is another example of the difficulties of controlling dengue through vector control 
Our model was sensitive to the disassociation of the growth rate of the human and vector populations. This can be equated with lifestyle or environmental changes, such as urbanization or global warming, which have consequences on the ecology of the vector population and thereby on dengue transmission 
. Although our model reproduces some general trends regarding the impact of vector control activities and environmental change, it is however important to stress that it is clearly not adapted to a detailed analysis of these phenomena.
Our analysis was based on two complementary sources of information: routine surveillance in Southern Vietnam and a prospective cohort study with active surveillance conducted in the area 
. Routine surveillance systems can provide a critical general overview of epidemiology and its evolution over extended periods. In contrast, prospective studies can provide a more accurate estimation of epidemiology over a short period, including estimations for serotype-specific rate of infection, such as those used in our model. Furthermore, when feasible, surveillance data and data collected prospectively, such as that reported by Tien et al. 
, can be compared to estimate the level of under-reporting to the surveillance system. Using this approach, Tien et al. estimated that the actual number of dengue cases was 6 times higher than that reported to the surveillance system and that severe cases are also more likely to be reported. Similar findings were reported from Thailand 
There are, however, some limitations to the combined use of these data sources. The data collection period differed between the two sources (1972–2007 for the routine surveillance data 2004–2007 for the prospective cohort study, see Text S1
), as did the data catchment area (the surveillance system covered the entire south of Vietnam, whereas the study covered the Long Xuyen area only), and the age range (restricted to 3–15 years in the prospective study). Other possible limitations include the accuracy of dengue serological tests 
and the quality of surveillance, which evolves with time 
. This notably led us, in the absence of direct information for adults, to use the same expansion factor across all ages and it is plausible that the level of under-reporting varies according to age.
We did not identify one single scenario of cross-interactions. This can be seen as a limitation of our analysis. Considering the heterogeneous nature of data available to us and the complex nature of dengue dynamics, we in fact deliberately chose to assess the impact of vaccination for a range of plausible scenarios of interactions between serotypes. A more direct estimation of the duration of cross-protection or of the characteristics of cross-enhancement using recent advances in statistical methods for transmission models 
is however an important direction for future research. Although the tests we performed indicated that this assumption is reasonable, another possible limitation of the analysis performed is our consideration in the calibration procedure that dengue epidemiology is globally stable in Southern Vietnam despite large interannual variations. A direct consideration of epidemiological or demographic changes in the calibration procedure could also be explored in future research.
Assessing the potential impact of vaccination was an important motivation behind the development of this model. Results suggest that vaccination will not only reduce disease incidence but will also modify the transmission dynamics. Indeed, vaccination was seen to decrease the frequency and magnitude of outbreaks, and to alter the age distribution of cases. The overall impact of vaccination as indicated by our model depends not only on vaccine efficacy, but also on the duration of protection conferred and on the level of vaccination coverage.
In contrast to the findings discussed above, that may be applicable to a range of vaccine-preventable disease, cross-enhancement is more specific to the immunopathology of dengue. Vaccination was shown to have a greater impact in scenarios that only considered short term cross-protection, but the difference between these scenarios and those combining cross-protection and cross-enhancement is limited in most cases. It should be noted that this finding was based on the assumption that cross-enhancement would apply equally after vaccination and natural infection. This is a conservative assumption as none of the preclinical or clinical data accumulated to date support the hypothesis that vaccination can lead to enhanced disease 
In conclusion, we developed a model capable of reproducing the epidemiology of dengue in Southern Vietnam to provide a theoretical framework for future studies on dengue prevention and vaccination. Our results highlight the importance of short-term cross-protection in the transmission dynamics of these viruses. In addition to vaccination results presented here, this model could readily be expanded to consider for example: the optimum age for vaccination; the value of combining vaccination with other prevention measures; the way epidemiological or demographic changes affect the impact of vaccination, or the relative short and long-term benefits of various strategies based on routine and/or mass vaccination campaigns.