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Incidence and mortality due to tuberculosis (TB) have been decreasing worldwide. Given that TB is a cosmopolitan disease, proper surveillance and evaluation are critical for controlling dissemination. Herein, mathematical modeling was performed in order to: 1) demonstrate a correlation between the incidence of TB in HIV-free patients in the US and Germany, and their corresponding mortality rates; 2) show the utility of the newly developed D-R algorithm for analyzing and predicting the incidence of TB in both countries; and 3) inform us on population death rates due to TB in HIV-negative patients. Using data published by the World Health Organization between 1990 and 2009, the relationship between incidence and mortality that could not be ascribed to HIV infection was evaluated. Using linear, quadratic and cubic curves, we found that a cubic function provided the best fit with the data in both the US (Y = 2.3588 + 2.2459X + 61.1639X² - 60.104 X ³ ) and Germany (Y = 1.9271 + 9.4967X + 18.3824X² - 10.350X³) where the correlation coefficient (R) between incidence and mortality was 0.995 and 0.993, respectively. Second, we demonstrated that fitted curves using the D-R model were equal to or better than those generated using the GM(1,1) algorithm as exemplified in the relative values for Sum of Squares of Error, Relative Standard Error, Mean Absolute Deviation, Average Relative Error, and Mean Absolute Percentage Error. Finally, future trends using both the D-R and the classic GM(1,1) models predicted a continued decline in infection and mortality rates of TB in HIV-negative patients rates extending to 2015 assuming no changes to diagnosis or treatment regimens are enacted. [ABSTRACT FROM AUTHOR]

Objective: To assess the efficacy of the D-R model for defining trends in the appearance of Ceftazidime-resistant Escherichia coli. Methods: Actual data related to the manifestation of Ceftazidime-resistant E. coli spanning years 1996-2009 were collected from the China National Knowledge Internet. These data originated from 430 publications encompassing 1004 citations of resistance. The GM(1,1) and the novel D-R models were used to fit current data and from this, predict trends in the appearance of the drug-resistant phenotype. The results were evaluated by Relative Standard Error (RSE), Mean Absolute Deviation (MAD) and Mean Absolute Error (MAE). Results: Results from the D-R model showed a rapid increase in the appearance of Ceftazidime-resistant E. coli in this region of the world. These results were considered accurate based upon the minor values calculated for RSE, MAD and MAE, and were equivalent to or better than those generated by the GM(1,1) model. Conclusion: The D-R model which was originally created to define trends in the transmission of swine viral diseases can be adapted to evaluating trends in the appearance of Ceftazidime-resistant E. coli. Using only a limited amount of data to initiate the study, our predictions closely mirrored the changes in drug resistance rates which showed a steady increase through 2005, a decrease between 2005 and 2008, and a dramatic inflection point and abrupt increase beginning in 2008. This is consistent with a resistance profile where changes in drug intervention temporarily delayed the upward trend in the appearance of the resistant phenotype; however, resistance quickly resumed its upward momentum in 2008 and this change was better predicted using the D-R model. Additional work is needed to determine if this pattern of "increasecontrol- increase" is indicative of Ceftazidime-resistant E. coli or can be generally ascribed to bacteria acquiring resistance to drugs in the absence of alternative intervention. [ABSTRACT FROM AUTHOR]