Figure 1.
Tourism and temperature data for the island of Madeira.
(A) Mean of minimum (green), average (blue) and maximum (red) temperatures per day between 2002 and 2012. Coloured areas are the standard deviation. (B) Number of airline passengers entering Madeira per year (dashed, black) and local investment in tourism per year (solid, grey). (C) Relative weight (bubbles) of each country in the total number of passengers arriving at Madeira per year (columns). Data compiled from the 30 most frequent cities of origin for airline passengers per year. Portuguese cities were excluded - Oporto, Lisbon, Porto Santo (Madeira) and Ponta Delgada (Azores). (D) Map representation of (C), including Portugal. Colours match the weight of each country with the 4 highest highlighted in green.
Figure 2.
Climate and dengue outbreak data for the island of Madeira.
Mean of minimum temperatures per week (solid, green), precipitation (solid, cyan) and dengue reported cases per week (dotted, black) for August-2012 to March-2013.
Table 1.
Temperature-dependent parameters.
Figure 3.
Model fitting to Madeira's dengue outbreak data.
(A,B) Reported cases (incidence and cumulative) per week (dotted, black) and example of model fitting (solid, purple). Coloured area (purple) is the standard deviation of all accepted steps in the MCMC chain. The dashed vertical line represents the date of the first reported clinical cases. The red dashed line represents the epidemic progression ignoring the first week in November, when a new surveillance method was introduced. (C) Stationary distributions of the estimated timepoint of first case for 30 independent MCMC runs with random initial conditions and 1 million steps.
Figure 4.
Model-derived epidemiological and entomological parameter estimates for 2012.
(A) Example of estimated values for 2012 (solid, red) together with the weekly minimum temperatures for 2012 (solid, blue) and long-term average of minimum temperatures (2001–2011, dashed green). The dashed red line marks the epidemic threshold
. (B) Example of estimated number of mosquitoes per human (solid, black), incubation period (solid, cyan) and adult life-span (solid, orange) for 2012.
Figure 5.
Model-derived epidemic potential for the island of Madeira.
(A) Temperatures for the year of 2012 (red, solid line) and average temperatures for the past 10 years (2001–2011; blue, solid line). The points mark the mean outbreak size (number of cases) for 100 stochastic introductions at different timepoints using temperature data from 2012 (red) and the average over the past 10 years (blue). (B) Derived real-time (red, solid line) for 2012, with an annual mean of
(dashed line). (C) Derived real-time
(blue, solid line) for the past 10 year, with an annual mean of
(dashed line). (B,C) Grey shaded areas are the frequency of simulations (in 100) achieving either more than 3 (light grey) or 1000 (dark grey) cases.
Table 2.
Constant parameters.
Table 3.
Estimated parameters.