Analysis of Transmission and Control of Tuberculosis in Mainland China, 2005–2016, Based on the Age-Structure Mathematical Model
Abstract
:1. Introduction
2. Materials and Methods
2.1. Data Collection
2.2. Model Formulation
2.3. Theoretical Results of Model (2)
- Model (2) has the following positively invariant set:
- Making use of the next generation matrix (see [29]), we obtained the basic reproduction number of Model (2) as follows:
- This model has a disease-free equilibrium , whereand the endemic equilibrium , which is determined by the following equations
- If , the disease-free equilibrium is globally asymptotically stable.
3. Numerical Simulations and Sensitivity Analysis
3.1. Parameter Estimation
3.2. Numerical Simulations from 2005 to 2016
3.3. Uncertainty and Sensitivity Analysis of
3.4. Feasibility Assessment of Reaching WHO End TB Strategy
4. Discussion
Acknowledgments
Author Contributions
Conflicts of Interest
Appendix A
Appendix A.1. Proof of the Positively Invariant Set
Appendix A.2. Proof of the Existence of Positive Steady State
Appendix A.3. Proof of the Global Stability of P0
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Year | 2005 | 2006 | 2007 | 2008 | 2009 | 2010 |
Cases | 1,259,308 | 1,127,571 | 1,163,959 | 1,169,540 | 953,275 | 951,508 |
Year | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 |
Cases | 1,076,938 | 991,350 | 889,381 | 864,015 | 864,015 | 836,236 |
Parameter | Value | Confidence Interval | Source |
---|---|---|---|
A | [32] | ||
d | (0.00688, 0.00702) | [32] | |
(0.0013, 0.0021) | [32] | ||
(0.0023, 0.0024) | [32] | ||
[32] | |||
− | Fitting | ||
− | Fitting | ||
− | [2] | ||
p | [10] | ||
− | [10] | ||
− | [3] | ||
v | 6 | − | [33] |
− | [30] | ||
− | [3] | ||
− | Fitting | ||
− | Fitting | ||
− | Fitting |
Parameters | PRCC | p-Value |
---|---|---|
A | 0.9961 | 0.0005 |
−0.7482 | 0.0009 | |
0.6141 | ||
−0.5265 | 0.0001 | |
0.5195 | ||
0.4820 | ||
0.1808 | 0.0036 | |
0.0175 | 0.0012 |
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Zhao, Y.; Li, M.; Yuan, S. Analysis of Transmission and Control of Tuberculosis in Mainland China, 2005–2016, Based on the Age-Structure Mathematical Model. Int. J. Environ. Res. Public Health 2017, 14, 1192. https://doi.org/10.3390/ijerph14101192
Zhao Y, Li M, Yuan S. Analysis of Transmission and Control of Tuberculosis in Mainland China, 2005–2016, Based on the Age-Structure Mathematical Model. International Journal of Environmental Research and Public Health. 2017; 14(10):1192. https://doi.org/10.3390/ijerph14101192
Chicago/Turabian StyleZhao, Yu, Mingtao Li, and Sanling Yuan. 2017. "Analysis of Transmission and Control of Tuberculosis in Mainland China, 2005–2016, Based on the Age-Structure Mathematical Model" International Journal of Environmental Research and Public Health 14, no. 10: 1192. https://doi.org/10.3390/ijerph14101192