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Recent analysis indicates that the numbers of dengue cases may be as high as 400 million/year in the world. According to the Ministry of Brazilian Health, in 2015, there were 1,621,797 probable cases of dengue in the country including all classifications except discarded, the highest number recorded in the historical series since 1990. Many studies have found associations between climatic conditions and dengue transmission, especially using generalized models. In this study, Generalized Additive Models (GAM) was used associated to visreg package to understand the effect of climatic variables on capitals of Northeast Brazilian, from 2001 to 2012. From 12 climatic variables, it was verified that the relative humidity was the one that obtained the highest correlation to dengue. Afterwards, GAM associated with visreg was applied to understand the effects between them. Relative humidity explains the dengue incidence at an adjusted rate of 78.0% (in S ão Luis-MA) and 82.3% (in Teresina-PI) delayed in, respectively, -1 and -2 months.

Dengue Fever is fast emerging pandemic-prone viral disease in many parts of the world. Dengue flourishes in urban poor areas, suburbs and the countryside but also affects more affluent neighbor hoods in tropical and subtropical countries. Dengue is a mosquito-borne viral infection causing a severe flu-like illness and, sometimes causing a potentially lethal complication called severe dengue. The incidence of dengue has increased 30-fold over the last 50 years. Up to 50 - 100 million infections are now estimated to occur annually in over 100 endemic countries, putting almost half of the world’s population at risk [

Tropical countries are the most heavily affected due to environmental, climatic, and social conditions. Studies of climatic variables can improve knowledge and prediction of epidemic seasonality. The climate is an important factor in the temporal and spatial distribution of vector-transmitted diseases as dengue fever [

Many works sought to identify climatic influences on dengue, and to evaluate the ability of the climate-based dengue models to describe associations between climate and dengue, simulate outbreaks by generalized additive models―GAMs [

We assessed the potential contribution of climatic variables on Dengue Fever (DF) incidences based in GAM, according Hastie and Tibshirani (1990) [

Mordecai et al. (2017) [

Ferreira et al. (2017) [

This work aims to identify the risk of DF incidence by the occurrence limits parametrization of climatic variables as a function of the time (months and years), in capitals of the NEB, from January 2001 to December 2012, as from visualizing the fit of regression models arising from of GAM, assuming Poisson Distribution, by cross-sectional plots using two-dimensional contour, by “visreg” package function.

To understand the risk of DF incidence by the occurrence limits parametrization of climatic variables on capitals of the NEB, we conducted the GAM analysis by average monthly data observed from 9 capitals of Brazilian Northeast (NEB), in the period of January 2001 to December 2012. These capitals and their respective codes of the Federative Unit (referring to their States): Aracaju-SE, Fortaleza-CE, João Pessoa-PB, Maceió-AL, Natal-RN, Recife-PE, Salvador-BA, São Luís-MA and Teresina-PI, according

1) Climatological variables: rainfall, in mm, (PRP); minimum, average and maximum temperature, in ˚C, (respectively, T-min, T-mean and T-max); relative humidity, in % (RH); all collected by Meteorological Databank for Education and Research―BDMEP^{1}, from the National Institute of Meteorology―INMET. From these variables collected, we calculated:

a) Vapour pressure deficit (VPD) and saturated vapour pressure deficit (SVPD), all according Allen et al. (1998) [

b) Evapotranspiration of Reference (ETO), according Thornthwaite (1948) [

c) Annual and monthly heat index, respectively, HI-a and HI-m; as well as, its Function (HI-f), both according to Steadman (1979) [

d) Human comfort index (HCI), according to Rosenberg (1983) [

2) DF cases collected by the site SINAN-Net^{2}, from the Departamento de Informática do Sistema Único de Saúde―DATASUS; and transformed into DF Incidence Rate; and

3) Annual population size for each of the nine capitals studied, collected by the Sistema de Recuperação Automática―SIDRA^{3}, from the Brazilian Institute of Geography and Statistics―IBGE.

The monthly reporting DF cases were converted to DF incidence rates, which, according to the Ministry of Health [

DF incidence= number of confirmed dengue cases in residents Total resident population in the given period × 100 , 000 (1)

DF incidence are classified by occurrence bands, as criteria of the National Program for Dengue Control―PNCD/MS [

All analyses were conducted using the R-Project Software, Version 3.0.3^{4}.

The class of models known as generalized linear models, or GLMs, was formally introduced by Nelder and Wedderburn (1972) [

temporal (months and years of the time series data) and climatic variables ( X 1 , X 2 , … , X p ) a set of predictors or independent/explanatory variables, a regression procedure can be viewed as a method for estimating the expected value of Y given the values of X i . The standard linear regression model assumes a linear form for the dependency, according Hair Jr. et al. (2005) [

E ( Y ) = β 0 + β 1 X 1 + β 2 X 2 + … + β p X p + ε (2)

where E ( ε ) = 0 and V a r ( ε ) = σ 2 . Given a sample, estimates of β 0 , β 1 , … . β p are usually obtained by the least squares method.

According Hastie and Tibshirani (1990) [

∫ Y ( y ; θ , ∅ ) = exp { y ( θ ) − b ( θ ) a ( ∅ ) + c ( y , ∅ ) } (3)

where θ is called the natural parameter and ∅ is the scale parameter. The conditional mean μ of the response variable x to the linear predictor η is related to the set of covariates X i by a link function g. The quantity:

η ( x ) = s 0 + ∑ i = 1 p f i ( X i ) (4)

defines the additive component, where f i are smooth functions, and the relationship between the conditional mean μ ( x ) and the linear predict η ( x ) is defined by g ( μ ) = η . The most commonly used link function is the canonical link, for which η = θ . Assuming that μ(x), is the mean of the Poisson distribution, the dependence of μ(x) and independent variables X i , the link function for the Poisson model is the log function g ( μ ) = log ( μ ) = η . According Hastie and Tibshirani (1986, 1990) [

E ( Y ) = β 0 + f 1 ( X 1 ) + f 2 ( X 2 ) + … + f p ( X p ) + ε (5)

where f i are smooth functions, E ( ε ) = 0 and V a r ( ε ) = σ 2 .

In order to be estimable, the smooth functions f i have to satisfy standardized conditions such as E ( f i ( X i ) ) = 0 . GAM extends the parametric form of predictors in the linear model to nonparametric forms. Assuming that Y is normally distributed, an additive model is defined as

E ( Y ) = s 0 + ∑ i = 1 p f i ( X i ) (6)

GAM and GLM can be applied in similar situations, but they serve different analytic purposes. GLM emphasizes estimation and inference for the parameters of the model, while GAM focus on non-parametric data, and this is more suitable for exploring the data and visualizing the relationship between dependent and independent variables, considering the estimation of the smoothing terms f i in GAM, described in Equation (6) [

The spatial distribution was modeled using a bi-dimensional smooth function. A smoother is a tool for summarizing the trend of a response measurement Y as a function of one or more predictor measurements X i , … , X p . An important property of a smoother is its nonparametric nature. It does not assume a rigid form for the dependence of Y on X i , … , X p , producing an estimate of the trend that is less variable than Y itself, since of penalized least squares method. Each smoother s i is controlled by a single smoothing parameter, specificity in the model or choose it automatically by the generalized cross validation method [

logit ( Y i ) = β 0 + f ( ∑ i = 0 : 12 t − L β k x k ) + s ( month ) + s ( year ) + e i (7)

where Y i is the response variable, in this work the Dengue incidence simulated index, β ’s are the slope coefficients of the model, so exp ( β 0 ) is the adjusted odds ratio, x k are the climatic variables at the individual and household levels as factor of the monthly lags in 0 - 12 times; s ( month ) and s ( year ) are s spline smooth function, and e i are the residuals. All covariates with a p-value ≤ 0.001 in the climatic variable univariate analysis were considered with high significance in the model.

According Zuur et al. (2007) [

x 2 ( X , Y ) = ∑ i = 1 k ( X i − Y i ) 2 Y i (8)

This interface was used in this work for visualize the fit of regression models arising from of GAM, as from constructing surface by cross-sectional plots using two-dimensional contour or perspective plots. In addition to estimates of this relationship, the package also provides pointwise confidence bands and partial residuals to allow assessment of variability as well as outliers and other deviations from modeling assumptions [

Pearson correlation coefficient (r) [

r = ∑ ( x i − X ¯ ) ( y i − Y ¯ ) ∑ ( x i − X ¯ ) 2 ∑ ( y i − Y ¯ ) 2 (9)

where Pearson correlation coefficient or product moment correlation coefficient (r) is a measure of shared variance between two variables, x i and y i based in their averages X ¯ and Y ¯ , and their standard deviations S_{x} and S_{y}. The sign indicates a positive or negative direction of the correlation, and the value suggests the power of the relationship between the variables, which value r can vary from −1 to +1, indicating a perfect and very strong positive linear relationship (r = +1), a perfect and very strong negative linear relationship (r = −1), or no linear relationship (r = 0) between the variables [

In

Capital of the NEB | Climatic Variable | Pearson | CI Lower | 95% Upper | p-value |
---|---|---|---|---|---|

São Luis-MA | PRP | 0.0740 | −0.0907 | 0.2347 | 0.3783 |

Teresina-PI | PRP | 0.0844 | −0.0803 | 0.2446 | 0.3147 |

Fortaleza-CE | PRP | 0.2707 | 0.1121 | 0.4158 | 0.001 |

Natal-RN | PRP | 0.2430 | 0.0827 | 0.3911 | 0.0033 |

João Pessoa-PB | PRP | 0.2811 | 0.1232 | 0.4252 | <0.001 |

Recife-PE | PRP | 0.1384 | −0.0257 | 0.2953 | 0.0980 |

Maceió-AL | PRP | 0.2633 | 0.1043 | 0.4093 | 0.0014 |

Aracaju-SE | PRP | 0.2827 | 0.1249 | 0.4266 | <0.001 |

Salvador-BA | PRP | −0.0056 | −0.169 | 0.1582 | 0.9472 |

São Luis-MA | RH | 0.2494 | 0.0895 | 0.3968 | 0.0026 |

Teresina-PI | RH | 0.3196 | 0.1646 | 0.4592 | <0.001 |

Fortaleza-CE | RH | 0.3392 | 0.1859 | 0.4763 | <0.001 |

Natal-RN | RH | 0.3681 | 0.2177 | 0.5015 | <0.001 |

João Pessoa-PB | RH | 0.2683 | 0.1095 | 0.4137 | 0.0011 |

Recife-PE | RH | 0.1009 | −0.6377 | 0.2601 | 0.2290 |

Maceió-AL | RH | 0.3794 | 0.2302 | 0.5112 | <0.001 |

Aracaju-SE | RH | 0.1131 | −0.0514 | 0.2717 | 0.1770 |

Salvador-BA | RH | −0.0386 | −0.2009 | 0.1258 | 0.6462 |

São Luis-MA | T-min | −0.0740 | −0.2347 | 0.0907 | 0.3780 |

Teresina-PI | T-min | −0.1512 | −0.3072 | 0.0127 | 0.0704 |

Fortaleza-CE | T-min | −0.2012 | −0.3531 | −0.0389 | 0.0156 |

Natal-RN | T-min | −0.3023 | −0.4439 | −0.1459 | <0.001 |

João Pessoa-PB | T-min | −0.1533 | −0.3091 | 0.0106 | 0.0667 |

Recife-PE | T-min | 0.1045 | −0.0601 | 0.2636 | 0.2127 |

Maceió-AL | T-min | 0.1833 | 0.0204 | 0.3368 | 0.0279 |

Aracaju-SE | T-min | 0.0264 | −0.1378 | 0.1891 | 0.7539 |

Salvador-BA | T-min | 0.1231 | −0.0413 | 0.281 | 0.1416 |

São Luis-MA | T-mean | −0.1867 | −0.3399 | −0.0239 | 0.025 |

Teresina-PI | T-mean | −0.3747 | −0.5072 | −0.2249 | <0.001 |

Fortaleza-CE | T-mean | −0.2634 | −0.4093 | −0.1043 | 0.0014 |

Natal-RN | T-mean | −0.1622 | −0.3173 | 0.0015 | 0.0522 |

João Pessoa-PB | T-mean | −0.1426 | −0.2992 | 0.0215 | 0.0881 |

Recife-PE | T-mean | 0.0504 | −0.1141 | 0.2122 | 0.5485 |

Maceió-AL | T-mean | −0.0073 | −0.1707 | 0.1564 | 0.9306 |

Aracaju-SE | T-mean | 0.0381 | −0.1263 | 0.2004 | 0.6504 |

Salvador-BA | T-mean | 0.1231 | −0.0413 | 0.2811 | 0.1414 |

São Luis-MA | T-max | 0.1281 | −0.2857 | 0.0362 | 0.1259 |

Teresina-PI | T-max | −0.3757 | −0.508 | −0.2260 | <0.001 |

Fortaleza-CE | T-max | −0.2458 | −0.3936 | −0.0857 | 0.0030 |
---|---|---|---|---|---|

Natal-RN | T-max | −0.1407 | −0.2974 | 0.0234 | 0.0926 |

João Pessoa-PB | T-max | −0.0560 | −0.2176 | 0.1086 | 0.5048 |

Recife-PE | T-max | 0.0009 | −0.1627 | 0.1644 | 0.9917 |

Maceió-AL | T-max | −0.1486 | −0.3048 | 0.0153 | 0.0754 |

Aracaju-SE | T-max | 0.0132 | −0.1507 | 0.1764 | 0.8752 |

Salvador-BA | T-max | 0.0807 | −0.0839 | 0.2411 | 0.3360 |

São Luis-MA | SVPD | −0.1824 | −0.3359 | −0.0194 | 0.0287 |

Teresina-PI | SVPD | −0.3765 | −0.5087 | −0.2269 | <0.001 |

Fortaleza-CE | SVPD | −0.2616 | −0.4077 | −0.1024 | 0.0015 |

Natal-RN | SVPD | −0.1607 | −0.3160 | 0.0029 | 0.0543 |

João Pessoa-PB | SVPD | −0.1437 | −0.3002 | 0.0204 | 0.0858 |

Recife-PE | SVPD | 0.0455 | −0.1190 | 0.2075 | 0.5882 |

Maceió-AL | SVPD | −0.0114 | −0.1747 | 0.1524 | 0.8916 |

Aracaju-SE | SVPD | 0.0325 | −0.1318 | 0.1951 | 0.6989 |

Salvador-BA | SVPD | 0.1258 | −0.0386 | 0.2835 | 0.1330 |

São Luis-MA | VPD | 0.2140 | 0.0523 | 0.3648 | 0.0100 |

Teresina-PI | VPD | 0.2153 | 0.0536 | 0.3660 | 0.0095 |

Fortaleza-CE | VPD | 0.2094 | 0.0474 | 0.3606 | 0.0118 |

Natal-RN | VPD | 0.0798 | −0.0849 | 0.2403 | 0.3415 |

João Pessoa-PB | VPD | 0.1018 | −0.0629 | 0.2610 | 0.2249 |

Recife-PE | VPD | 0.1916 | 0.0289 | 0.3444 | 0.0214 |

Maceió-AL | VPD | 0.3869 | 0.2384 | 0.5177 | < 0.001 |

Aracaju-SE | VPD | 0.1110 | −0.0535 | 0.2697 | 0.1853 |

Salvador-BA | VPD | 0.1215 | −0.0429 | 0.2796 | 0.1467 |

São Luis-MA | ETO | 0.2059 | −0.3574 | −0.0438 | 0.0133 |

Teresina-PI | ETO | −0.3558 | −0.4908 | −0.2040 | < 0.001 |

Fortaleza-CE | ETO | −0.3511 | −0.4897 | −0.1989 | < 0.001 |

Natal-RN | ETO | −0.2668 | −0.4124 | −0.1079 | 0.0012 |

João Pessoa-PB | ETO | −0.2293 | −0.3786 | −0.0682 | 0.0057 |

Recife-PE | ETO | −0.0396 | −0.2019 | 0.1248 | 0.6372 |

Maceió-AL | ETO | −0.2027 | −0.3545 | −0.4049 | 0.0148 |

Aracaju-SE | ETO | −0.0264 | −0.1892 | 0.1377 | 0.7532 |

Salvador-BA | ETO | 0.1046 | −0.0600 | 0.2637 | 0.2122 |

São Luis-MA | HCI | −0.0459 | −0.2079 | 0.1185 | 0.5846 |

Teresina-PI | HCI | −0.1681 | −0.3228 | −0.0047 | 0.0440 |

Fortaleza-CE | HCI | −0.0319 | −0.1945 | 0.1324 | 0.7042 |

Natal-RN | HCI | −0.0776 | −0.2382 | 0.0871 | 0.3551 |

João Pessoa-PB | HCI | −0.0613 | −0.2226 | 0.1033 | 0.4657 |

Recife-PE | HCI | 0.1138 | −0.0507 | 0.2723 | 0.1744 |

Maceió-AL | HCI | 0.1305 | −0.0338 | 0.2879 | 0.1191 |
---|---|---|---|---|---|

Aracaju-SE | HCI | 0.0644 | −0.1003 | 0.2256 | 0.4435 |

Salvador-BA | HCI | 0.1259 | −0.0385 | 0.2836 | 0.1328 |

São Luis-MA | HI-a | −0.1569 | −0.3124 | 0.0069 | 0.0604 |

Teresina-PI | HI-a | −0.3607 | −0.4950 | −0.2095 | <0.001 |

Fortaleza-CE | HI-a | −0.1980 | −0.3502 | −0.0355 | 0.0174 |

Natal-RN | HI-a | −0.1312 | −0.2886 | 0.0331 | 0.1171 |

João Pessoa-PB | HI-a | −0.1218 | −0.2798 | 0.0427 | 0.1460 |

Recife-PE | HI-a | 0.0717 | −0.0930 | 0.2325 | 0.3931 |

Maceió-AL | HI-a | 0.0398 | −0.1246 | 0.2020 | 0.6360 |

Aracaju-SE | HI-a | 0.0438 | −0.1207 | 0.2059 | 0.6025 |

Salvador-BA | HI-a | 0.1259 | −0.0385 | 0.2836 | 0.1328 |

São Luis-MA | HI-m | −0.1880 | −0.3410 | −0.0252 | 0.0240 |

Teresina-PI | HI-m | −0.3757 | −0.5081 | 0.2260 | <0.001 |

Fortaleza-CE | HI-m | −0.2590 | −0.4054 | −0.0997 | 0.0017 |

Natal-RN | HI-m | −0.1547 | −0.3104 | 0.0091 | 0.0642 |

João Pessoa-PB | HI-m | −0.1466 | −0.3029 | 0.0174 | 0.0796 |

Recife-PE | HI-m | 0.0526 | −0.1119 | 0.2143 | 0.5311 |

Maceió-AL | HI-m | −0.0125 | −0.1757 | 0.1514 | 0.8822 |

Aracaju-SE | HI-m | 0.0333 | −0.1310 | 0.1958 | 0.6918 |

Salvador-BA | HI-m | 0.1228 | −0.0416 | 0.2808 | 0.1425 |

São Luis-MA | HI-f | 0.2959 | 0.1390 | 0.4382 | <0.001 |

Teresina-PI | HI-f | −0.0424 | −0.2046 | 0.1220 | 0.6135 |

Fortaleza-CE | HI-f | 0.0977 | −0.0670 | 0.2571 | 0.2442 |

Natal-RN | HI-f | −0.3653 | −0.4990 | −0.2145 | <0.001 |

João Pessoa-PB | HI-f | 0.3112 | 0.1556 | 0.4518 | <0.001 |

Recife-PE | HI-f | 0.0500 | −0.1146 | 0.2119 | 0.5518 |

Maceió-AL | HI-f | 0.3524 | 0.2004 | 0.4879 | <0.001 |

Aracaju-SE | HI-f | −0.0489 | −0.2108 | 0.1156 | 0.5604 |

Salvador-BA | HI-f | −0.0512 | −0.2130 | 0.1133 | 0.5421 |

95% confidence interval (CI) and p-value, between DF cases and 12 climatic variables, on capital of the NEB. The relative humidity presents the best correlation with DF cases for capitals analyzed, at an absolute average rate of 24.18%, with high significance (p-value < 0.001) observed in four capitals each one. Low correlation is observed with Human Comfort Index and that DF cases, at an absolute rate of 9.1%. In Teresina-PI, there are the best correlations compared to the other capitals tested, at an absolute average rate of 26.67%, and high significance (p-value < 0.001) observed to seven of 12 climatic variables in relationship DF cases. Already, in Aracaju-SE, Recife-PE and Salvador-BA, there are the lower absolute mean correlations and respective no significance p-value observed, suggesting that there are other factors involved in the increase of their DF cases.

Variable | Estimate | SE | z | Pr(>|z|) | Sig | |
---|---|---|---|---|---|---|

Teresina-PI | (Intercept) | 8.375 | 1. 659 | 5.047 | <0.001 | *** |

Teresina-PI | Lag 0 | −0.007 | 0.007 | −0. 920 | 0. 357 | |

Teresina-PI | Lag 1 | 0.029 | 0.007 | 3. 993 | <0.001 | *** |

Teresina-PI | Lag 2 | 0.040 | 0.006 | 6. 802 | <0.001 | *** |

Teresina-PI | Lag 3 | 0.014 | 0.005 | 2. 667 | 0.008 | ** |

Teresina-PI | Lag 4 | −0.044 | 0.005 | −8. 703 | <0.001 | *** |

Teresina-PI | Lag 5 | −0.051 | 0.005 | −10.068 | <0.001 | *** |

Teresina-PI | Lag 6 | −0.012 | 0.005 | −2. 465 | 0.014 | * |

Teresina-PI | Lag 7 | 0.000 | 0.005 | −0.085 | 0. 933 | |

Teresina-PI | Lag 8 | −0.008 | 0.006 | −1. 385 | 0. 166 | |

Teresina-PI | Lag 9 | −0.033 | 0.007 | −4. 462 | < 0.001 | *** |

Teresina-PI | Lag 10 | −0.020 | 0.008 | −2. 432 | 0.015 | * |

Teresina-PI | Lag 11 | −0.012 | 0.009 | −1. 238 | 0. 216 | |

Teresina-PI | Lag 12 | 0.020 | 0.008 | 2. 456 | 0.014 | * |

São Luís-MA | Intercept | −46.327 | 8.898 | −5.206 | <0.001 | *** |

São Luís-MA | Lag 0 | 0.114 | 0.022 | 5.235 | <0.001 | *** |

São Luís-MA | Lag 1 | 0.158 | 0.020 | 7.993 | <0.001 | *** |

São Luís-MA | Lag 2 | 0.115 | 0.016 | 7.135 | <0.001 | *** |

São Luís-MA | Lag 3 | 0.057 | 0.014 | 4.068 | <0.001 | *** |

São Luís-MA | Lag 4 | 0.040 | 0.015 | 2.758 | 0.006 | ** |

São Luís-MA | Lag 5 | −0.023 | 0.015 | −1.529 | 0.126 | |

São Luís-MA | Lag 6 | −0.003 | 0.018 | −0.195 | 0.846 | |

São Luís-MA | Lag 7 | 0.004 | 0.020 | 0.203 | 0.839 | |

São Luís-MA | Lag 8 | 0.002 | 0.020 | 0.104 | 0.917 | |

São Luís-MA | Lag 9 | 0.021 | 0.020 | 1.071 | 0.284 | |

São Luís-MA | Lag 10 | 0.011 | 0.020 | 0.566 | 0.571 | |

São Luís-MA | Lag 11 | 0.077 | 0.019 | 4.113 | <0.001 | *** |

São Luís-MA | Lag 12 | 0.009 | 0.017 | 0.516 | 0.606 |

SE = standard error; z = z-value score; Pr(>|z|) = significance score Z; Sig = significance level: considering “***” when z-value is ≤0.001 (result is “highly significant” with 99.9% of the hypothesis tested being true; that is, the probability (Pr) of the error was less than 0.1%); “**” ≤0.01 (99% of the hypothesis tested is true); and “*” ≤0.1 (9% of the hypothesis tested is true).

GAM shows high significant (p-value < 0.001) association between DF incidence and relative humidity over a range of time-lags 0 - 2, 4 - 5 and 9, being the lag 2 the most significant, with the largest z-value (z = 6.802). Already, in São Luis-MA, the simulated GAM presents high significant level (p-value < 0.001) association between DF incidence and relative humidity over a range of time-lags 0 - 3 and 11, being the lag 1 the most significant, with the largest z-value (z = 7.993).

offset | Intercept | |||||||||
---|---|---|---|---|---|---|---|---|---|---|

Model | Dengue | log (pop) | R-sq (adj) | DE (%) | edf | Chi.sq | Estimate | SE | z | |

Teresina | Lag 0 | Case | Yes | 0.714 | 77.3 | 8.991 | 22949.0 | 4.1331 | 0.0036 | 1159.0 |

Teresina | Lag 0 | Incidence | No | 0.699 | 76.3 | 7.887 | 154.9 | 1.8642 | 0.0409 | 45.6 |

Teresina | Lag 2 | Case | Yes | 0.750 | 79.3 | 8.989 | 30581.0 | 4.1376 | 0.0036 | 1162.0 |

Teresina | Lag 2 | Incidence | No | 0.754 | 82.3 | 6.067 | 118.2 | 2.5199 | 0.0356 | 70.81 |

São Luís | Lag 0 | Case | Yes | 0.714 | 77.3 | 8.991 | 22949.0 | 4.1331 | 0.0036 | 1159.0 |

São Luís | Lag 0 | Incidence | No | 0.699 | 76.3 | 7.887 | 154.9 | 1.8642 | 0.0409 | 45.6 |

São Luís | Lag 1 | Case | Yes | 0.750 | 79.3 | 8.989 | 30581.0 | 4.1376 | 0.0036 | 1162.0 |

São Luís | Lag 1 | Incidence | No | 0.726 | 78.0 | 7.276 | 210.2 | 1.8726 | 0.0408 | 45.9 |

R-sq = R square adjusted; DE = explained deviance; edf = effective degree freedom, chi.sq = quadratic mean error; SE = standard error; z = z-value score.

time function, in Teresina-PI and São Luis-MA. The seasonal trend of that incidence over monthly and annual time-frequency was observed.

In relation to Teresina-PI,

In relation to São Luis-MA,

All numerical output of GAM and respective intercepts in the capitals of the NEB have obtained setting on p-value of 0.001. The capital of João Pessoa-PB is the one with the smaller values of mean squared error (Chi.sq); in other words, the values of the estimated parameters of climatic variables around the true value of DF cases present a greater accuracy and precision in the quality of response by GAM. According Bolker (2008) [

We found a high correlation of DF incidence with relative humidity is lagged in 1 and 2 months, respectively, in São Luis and Teresina cities. Wu et al. (2007) [

Ehelepola and Ariyaratne (2016) [

The formulation of GAM model is nearly exactly the same as for GLM. These models use all the same families and link functions; but GAM is wrapping the predictors in a non-parametric smoother function, in this paper, specifically, the s spline. The GAM fit is more sensitive to minimizing deviance (higher wiggliness) than the default fit of the loess function. This model is also able to minimize deviance based on the logit transformation. The model output shows that an overall (parametric) intercept is fitted (the mean) on the scale of the logit transformation (logarithmic population of the capitals studied).

Modeling by GAM, assuming a Poisson distribution, explained 82.3% of the deviance of DF incidences, and significant effects were found in the estimates of all climatic variables on dengue; however, the high values of the effective degrees of freedom (edf) of smooth functions indicate that the association between dengue and climate is highly nonlinear. The estimate initially found, by the GLM and GEEGLM models for these studied variables, was too high, indicating the overdispersion data, however regressions by GAM reduced significantly excess dispersion presented in the proportion of deviations from the response shown in simulations by GLM and GEEGLM, i.e., not shown here. Our results were robust to other model specifications with different controls for long-term and seasonal trends. It is suggested that the models proposed in this paper are used by surveillance agencies for planning, prevention and control of Dengue Incidence.

From 12 climatic variables, it was verified that the relative humidity was the one that obtained the highest correlation to dengue in six of nine capitals of the NEB, with high significance (p < 0.001) in Teresina-PI, Fortaleza-CE, Natal-RN and Maceió-AL. Afterwards, GAM associated with visreg was applied to understand the effects between them. March and April months show the sensibility of the use of GAM for the analysis of that correlation. Relative humidity explains the dengue at an adjusted rate of 78.0% (in São Luis-MA) and 82.3% (in Teresina-PI) delayed in, respectively, −1 and −2 months.

The authors declare no conflicts of interest regarding the publication of this paper.

da Silva, J.C.B., Karam, H.A. and Machado, C.J.S. (2018) Visualizing Fit between Dengue and Climatic Variables on Capitals of the Brazilian Northeast Region by Generalized Additive Models. Open Journal of Epidemiology, 8, 259-275. https://doi.org/10.4236/ojepi.2018.84020