Fig 1.
Epidemiology of dengue in French Polynesia (directly obtained from data).
(A) Spatial distribution of the number of cases reported between 1979 and 2014, in the different islands of French Polynesia. Each circle represents the size of the population, where the radius is defined as 0.2log10P with the population size P. The colours of the circles represent the number of reported cases. (B) Monthly number of cases reported for DENV-1 to DENV-4. (C) Age distribution of cases, averaged over the period between 1979 and 2014. (D) The results of serological surveys (seroprevalence of antibodies against DENV) conducted in 2014 and 2015. Error bars indicate 95%-Confidence Intervals (CIs).
Fig 2.
Estimated reporting probabilities (obtained from our model).
(A) Reporting probability of primary infections by DENV-1 as a function of time. The grey shaded area shows 95%-CI. (B) Relative strength of the reporting probabilities of secondary infections (DENV-1) compared with primary infections (DENV-1). (C) Comparison of the reporting probabilities for different serotypes, for primary (black circle) and secondary (red circle) infections. The reference group is primary Serotype 1 infection for primary infections and secondary Serotype 1 infection for secondary infections. (D) Variations of the reporting probability with the age group, considering individuals aged 5–9 year old as the reference group. See Section B in S1 Text for the mathematical definitions of the relative risks plotted in these panels.
Fig 3.
Estimated FOI and immunity (obtained from our model).
(A) The observed (dots) and expected (line) number of cases reported annually. Shaded area represents 95%-CI. (B) Fitted FOI for the four serotypes. (C) Average immunity profile of the population. The grey area shows the fraction of the population that were never infected, averaged over age groups. Red, blue, green, and yellow areas represent the fraction of the population who have been infected once by a serotype i (before the time we consider), where i = 1,2,3,4 correspond to red, blue, green, yellow, respectively. Black area represents the fraction of the population who have been infected more than once (before the time we consider).
Fig 4.
Observed and expected age distribution.
(A) Age distributions of the reported case numbers during the epidemic periods (red, blue, green, yellow circles correspond to the serotype 1, 2, 3, 4, respectively). (B) The seroprevalence of antibodies against DENV obtained from the serological survey (red dashed lines with error bars). In both (A) and (B), black solid lines give model predictions, with 95%-CI represented by the grey shaded areas (95%-CI).
Fig 5.
Relation between the proportion of susceptibles and FOI (obtained from our model).
(A) FOI as a function of the fraction of the susceptibles to primary and secondary infections for children (left panel) and general population (right panel). Different colours represent a different circulating serotype. The black solid lines represent the linear regression to the data with 95%-CI as grey shaded areas. Pearson correlation coefficient (PCC) between the FOI and the fraction of the susceptible is also provided in the figure. (B) The probability of occurrence of an epidemic (black solid lines) as a function of the fraction of susceptibles. This probability is estimated using application of the logistic regression to the data (See Materials and methods Section). Grey shaded areas show 95%-CI. Red and green circles show epidemics and non-epidemic time periods, respectively. (C) ROC curve to illustrate the diagnostic ability of predicting an epidemic using the fraction of the population that are susceptible.
Fig 6.
Evaluating the Bayesian inference using synthetic data.
Using the model described in the main text, we generate synthetic data for given model parameters. Using this synthetic data, we then infer the model parameters using the Bayesian inference. The original parameters are plotted as crosses (true), while the inferred results are plotted as lines or circles with 95%-CIs (predictions). In (A), the parameter k for the negative binomial distribution is shown. In (B), the relative strength of the reporting probabilities of secondary infections (DENV-1) compared with primary infections (DENV-1) φ(1,2)/φ(1,1) is shown. In (C), the reporting probabilities relative to serotype 1, φ(i,1)/φ(1,1) for primary infections and φ(i,2)/φ(1,2) for secondary infections, are shown. Here i = 1,2,3,4 corresponds to DENV-i. In (D), the reporting probability of primary infections by DENV-1 T(t) is shown as a function of time. In (E), the age-factor of the reporting probability A(a) is shown. In (F), the FOI is shown as a function of time.