**4.4 Parameter estimation**

For the simulation and conditional prediction of the process Eq. (6) MCMC was used, since this provides a solution to the impediment of direct calculation of the


#### **Table 2.**

*Estimation of parameters and their confidence intervals of the selected model.*

predictive distribution due to the high dimensionality of the integral Eq. (8) [36]. For this, 505000 simulations were performed, with a burn-in period of 5000 data and a thinning of chains of 100 data. Ordinary kriging was used for data interpolation. The initial values for the GLSM parameters were *<sup>σ</sup>*<sup>2</sup> <sup>¼</sup> 3, *<sup>ϕ</sup>* <sup>¼</sup> <sup>0</sup>*:*5 and *<sup>β</sup>* <sup>¼</sup> ð Þ 0*:*1, 0*:*1, 0*:*1, 0*:*1 . The estimation of *β* was carried out under the classical approach. Confidence intervals at 95% were obtained using 1000 Monte Carlo simulated samples [40].

For modeling the number of registered dengue cases in the 36 municipalities of Chiapas, *Yi*, *i* ¼ 1, … , 36. As for the 13 covariates considered, only the variables maximum environmental temperature, altitude above sea level in the municipality, average monthly rainfall, and patient age showed a relationship with the number of confirmed dengue cases. It was verified that the problem of multicollinearity did not exist in those included in the model: altitude and maximum environmental temperature (*r* ¼ �0*:*2231, *p* � *value* ¼ 0*:*191), average monthly rainfall and maximum temperature (*r* ¼ 0*:*243, *p* � *value* ¼ 0*:*1534), average monthly rainfall and altitude (*r* ¼ 0*:*1724, *p* � *value* ¼ 0*:*3147).

In **Table 2**, it is observed that the variables that have an effect on the cases of dengue observed are maximum environmental temperature, altitude of the municipalities, average monthly rainfall, and patient age. High temperatures and altitudes favor the presence of the disease, while young people will be preferred factors by the vector, as well as low rainfall because in seasons where there is no continuous flow of water in the rivers, stagnation causes an increase in the proliferation of *Aedes* mosquitoes.

### **4.5 Prediction of the model to the Chiapas map**

The projection of the model was carried out on a map of the state of Chiapas which was made based on the municipalities where the cases were registered, as can be seen in **Figure 2**, the prediction is divided by zones in shades of green to yellow with a contour delimited by contour lines that show the area in which the model predicts the number of cases for that area. As we can see, most of the predicted cases occur within the metropolitan area where the state capital Tuxtla Gutiérrez and the municipalities of Chiapa de Corzo, Berriozábal and Suchiapa are located, this corresponds to the observed data, since most of the cases occurred in the same area. On the other hand, it is observed that the prediction power is diminished in areas where no dengue cases were registered.

**Figure 2.** *Prediction of confirmed dengue cases.*
