Incidence Rates and Deaths of Tuberculosis in HIV-Negative Patients in the United States and Germany as Analyzed by New Predictive Model for Infection

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+61.1639X2−60.104X3) 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.