## 3 The Model Processing and Analysis Forecasting Result
### Analysis of the Modeling Result for Tuberculosis Prevalence Rate in Each Income Group  
According to the above analysis, in this part, we further analyze the tuberculosis prevalence rate forecasting results of four different income groups. Note that the corresponding inverse transformations are implemented to obtain final forecasting values. The coefficients of each regression model are estimated by the least-squares method, and the adjusted \(R\)-square (A-R2) of each regression model is calculated. Finally, the combination model is formed based on the six individual regression models, whose weights are optimized by the cuckoo search algorithm, which is denoted as \"CS-Combined\". The reason why the aforementioned six regression models are chosen in our combined approach, is that these models have higher adjusted \(R\)-square values than other competing models. Appendix C plots the fit curves of all seven types of forecasting models while including details of the regression equations and adjusted \(R\)-squares. Combined models which integrate the results of six individual regression models are often utilized in the forecasting field. In order to obtain the optimal weight coefficients of the individual models, a novel deciding weight method based on the cuckoo search is developed to determine the optimal combination weights. The optimization is as follows. According to the cuckoo's process of hatching bird eggs, the CS algorithm is described as follows:  
**Step 1** Defines the objective function \(\hat{y}=\omega_{1}y_{1}+\omega_{2}y_{2}+\ldots+\omega_{6}y_{6}\), initializes the function, and randomly generates the initial position of \(n\) nests \(\omega=[\omega_{1i},\omega_{2i},\cdots,\omega_{6i}]\) (\(i=1\), \(2\), \(\ldots\), \(n\)) to set parameters such as population size, problem dimension, maximum discovery probability \(P\), and maximum iterative times;  
**Step 2** Chooses the fitness function and calculates the objective function value of each bird's nest position, and obtains the current optimal function value;  
**Step 3** Records the optimal function value of the previous generation, and uses the formula (5.10) to update the position and state of the other nests;  
**Step 4** The existing position function value is compared with the previous generation optimal function value and, if it is better, the current optimal value is changed;  
**Step 5** After the location update, compare the random number \(\gamma\in[0,1]\) with \(P\). If \(\gamma>P\), randomly change \(x_{i}^{(t+1)}\), otherwise, it will not change. Finally, keep the best of a group of nest positions \(y_{i}^{(t+1)}\);  
**Step 6** If the maximum number of iterations or the minimum error requirement is not reached, return to step 2, otherwise, continue to the next step;  
**Step 7** Output the global optimal combination weight. As demonstrated in Appendix C (Figure A1), all six individual regression models provide remarkable goodness-of-fit, with adjusted \(R\)-squares all above 0.93. Thus, the selection of regression models is proper and effective. From Appendix C (Figure A1), there are clearly significant improvements for combined model forecasts compared with the results of other forecasting models for high income group. The annual high income group tuberculosis prevalence rate from 2013 to 2016 years was forecasted by CS-combined model. The forecasting results show that the SSE (sum square error), RMSE (root mean square error) are 3.38 and 0.9587, respectively. The forecasting values are close to the actual value. It is indicated that the CS-combined model has better forecasting performance,which has high popularization and application in forecasting the tuberculosis prevalence rate. It can provide a reference basis for the prevention and control measures of TB in the world. Appendix C (Figure A2) plots the fitting and forecasting curves and presents related regression equations and goodness-of-fit for the upper-middle income group.