Background Many studies have compared the performance of time series models in predicting pulmonary tuberculosis (PTB), but few have considered the role of meteorological factors in their prediction models. This study aims to explore whether incorporating meteorological factors can improve the performance of time series models in predicting PTB. Methods We collected the monthly reported number of PTB cases and records of six meteorological factors in three cities of China from 2005 to 2018. Based on this data, we constructed three time series models, including an autoregressive integrated moving average (ARIMA) model, the ARIMA with exogenous variables (ARIMAX) model, and a recurrent neural network (RNN) model. The ARIMAX and RNN models incorporated meteorological factors, while the ARIMA model did not. The mean absolute percentage error (MAPE) and root mean square error (RMSE) were used to evaluate the performance of the models in predicting PTB cases in 2018. Results Both the cross-correlation analysis and Spearman rank correlation test showed that PTB cases reported in the study areas were related to meteorological factors. The predictive performance of both the ARIMA and RNN models was improved after incorporating meteorological factors. The MAPEs of the ARIMA, ARIMAX, and RNN models were 12.54%, 11.96%, and 12.36% in Xuzhou, 15.57%, 11.16%, and 14.09% in Nantong, and 9.70%, 9.66%, and 12.50% in Wuxi, respectively. The RMSEs of the three models were 36.194, 33.956, and 34.785 in Xuzhou, 34.073, 25.884, and 31.828 in Nantong, and 19.545, 19.026, and 26.019 in Wuxi, respectively. Conclusions Our study revealed a possible link between PTB and meteorological factors. Taking meteorological factors into consideration increased the accuracy of time series models in predicting PTB, and the ARIMAX model was superior to the ARIMA and RNN models in study settings.

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In [10] (Y. Guo, Y. Wang, Decay of dissipative equations and negative Sobolev spaces, Commun. Partial Differ. Equ. 37 (2012) 2165-2208), Y. Guo and Y. Wang developed a general new energy method for proving the optimal time decay rates of the solutions to dissipative equations. In this paper, we generalize this method in the framework of homogeneous Besov spaces. Moreover, we apply this method to a model arising from electro-hydrodynamics, which is a strongly coupled system of the Navier-Stokes equations and the Poisson-Nernst-Planck equations through charge transport and external forcing terms. We show that the negative Besov norms are preserved along time evolution, and obtain the optimal time decay rates of the higher-order spatial derivatives of solutions by the Fourier splitting approach and the interpolation techniques.

This paper concerns the Cauchy problem of the two-dimensional (2D) nonhomogeneous incompressible nematic liquid crystal flows on the whole space R 2 with vacuum as far field density. It is proved that the 2D nonhomogeneous incompressible nematic liquid crystal flows admits a unique global strong solution provided the initial data density and the gradient of orientation decay not too slow at infinity, and the initial orientation satisfies a geometric condition (see (1.3)). In particular, the initial data can be arbitrarily large and the initial density may contain vacuum states and even have compact support. Furthermore, the large time behavior of the solution is also obtained. Remark 1.3 When d is a constant vector and |d| = 1, the system (1.1) turns to be the nonhomogeneous incompressible Navier-Stokes equations, and Theorem 1.2 is similar to the results of [36]. Roughly speaking, we generalize the results of [36] to the incompressible nematic liquid crystal flows.Remark 1.4 Our Theorem 1.2 holds for arbitrarily large data which is in sharp contrast to [9,21,42] where the smallness conditions on the initial data is needed in order to obtain the global existence of strong solutions.Moreover, the compatibility condition (1.4) on the initial data is also needed in [9,21,42]. It seems more involved to show the global existence of strong solutions with general initial data. This is the main reason for us to add an additional geometric condition (1.3).Remark 1.5 Compared with [22], there is no need to impose the absence of vacuum for the initial density.Furthermore, it should be pointed out that the large time asymptotic decay with rates of the global strong solution in (1.10) is completely new for the 2D nonhomogeneous nematic liquid crystal flows.We now make some comments on the analysis of the present paper. Using some key ideas due to [24,35], where the authors deal with the 2D incompressible Navier-Stokes and MHD equations, respectively, we first establish that if (̺ 0 , u 0 , d 0 ) satisfies (1.5)-(1.7), then there exists a small T 0 > 0 such that the Cauchy problem (1.1)-(1.2) admits a unique strong solution (̺, u, P, d) in R 2 × (0, T 0 ] satisfying (1.8) and (1.9) (see Theorem

We are concerned with the Cauchy problem of the two-dimensional (2D) nonhomogeneous incompressible nematic liquid crystal flows on the whole space R 2 with vacuum as far field density. It is proved that the 2D nonhomogeneous incompressible nematic liquid crystal flows admits a unique global strong solution provided the initial data density and the gradient of orientation decay not too slow at infinity, and the basic energyL 2 is small. In particular, the initial density may contain vacuum states and even have compact support. Moreover, the large time behavior of the solution is also investigated.