Fig 1.
Dengue epidemiology in Trinidad and Tobago.
Weekly number of confirmed dengue fever cases with circulating serotypes in Trinidad and Tobago over the period 1997–2009.
Table 1.
Characteristics for pattern-oriented modelling.
Fig 2.
System of differential equations and flow diagram of multi-serotype model.
The circles represent the infection related states: susceptible (S), infectious (I), cross-immune (C), partially susceptible (P) and recovered (R), solid arrows depict the transition from one state to another and the dashed arrows indicate transmission. Parameters are described in Table 3. Simulations are based on a four serotype (DENV1-4) model, where i, j and k denote primary (first subscript) or secondary (second subscript) infection with DENV1-4. The full system consists of 26 compartments. For simplicity, the flowchart for one serotype is shown.
Table 2.
Model hypotheses.
Fig 3.
Flow chart of Pattern Oriented Modelling approach.
A set of 6 alternative models are identified and compared with respect to their ability to replicate patterns observed in dengue case data. Each model is run for a set of 5,000 different parameter combinations, sampled from plausible parameter ranges using Latin hypercube sampling. The resulting patterns from each simulation are compared to the observed patterns. The parameter sets that match all 5 patterns of interest are assembled into the passing parameter set, which forms the input for model comparison and the examination of model behaviour.
Table 3.
Model parameters.
Table 4.
Model performance.
Fig 4.
Model parameter distributions.
Parameter distributions for passing parameter sets (G) for different model hypotheses (with ADE = antibody dependent enhancement, CI = cross-immunity) for (A) the transmission rate (β0), (B) seasonality (β1), (C) enhanced susceptibility (αSUS), (D) enhanced infectiousness (αTRANS), and (E) 1/duration of cross-immunity (ρ). The vertical lines depict the median values for each distribution with the colours indicating the corresponding model hypothesis.
Table 5.
Sensitivity analysis of model fit full model.
Fig 5.
Principal component analysis of passing parameter space (G) of the full model (ADEx2+CI). The first component explains 30% of the total variance, the second 25%, the third 18% and fourth 16% and the 5th 11%. The pie charts show the contribution of the parameters to each component. β1 and ρ dominate the first component, indicating reduced identifiability. β0, αSUS and αTRANS dominates the fifth component and thus contribute most to the stiffest (i.e. most sensitive direction in the parameter space).
Fig 6.
Overall vulnerability to control.
Probability of successful control (a maximum of 1 outbreak during 30 years) given the duration (weeks/year) of consecutive control (temporary reduction of transmission: β0(1–90%) for different model hypotheses (with ADE = antibody dependent enhancement, CI = cross-immunity). The probability is defined as the proportion of the passing parameter sets (Gi) that reach successful control. Here i refers to the six models, shown by the individual keys. The dotted line shows the mean probability across all models.
Fig 7.
Vulnerability to control as a function of R0.
Required duration (weeks/year) for achieving successful control is shown with respect to the basic reproduction number R0 (= β0/(γ+μ)) for the different model hypotheses: are base (A), CI (B), ADE (C), ADE+CI (D), ADEx2 (E), and ADEx2+CI (F), with ADE = antibody dependent enhancement, CI = cross-immunity.