Stability Analysis of Susceptible-Infected-Recovered Epidemic Model_Journal of Biomedical Engineering

Authors：

 PANDuotao , SHIHongyan , HUANGMingzhong , YUANDecheng

Chemical Control Technology Key Laboratory of Liaoning Province, Shenyang University of Chemical Technology, Shenyang 110142, China;

Corresponding author：

PANDuotao, Email: panduotao@126.com

Keywords：

epidemic; systems biology; computational biology; biochemical systems theory; sensitivity analysis; nonlinear programming

DOI：

10.7507/1001-5515.20150180

Video：

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With the range of application of computational biology and systems biology gradually expanding, the complexity of the bioprocess models is also increased. To address this difficult problem, it is required to introduce positive alternative analysis method to cope with it. Taking the dynamic model of the epidemic control process as research object, we established an evaluation model in our laboratory. Firstly, the model was solved with nonlinear programming method. The results were shown to be good. Based on biochemical systems theory, the ODE dynamic model was transformed into S-system. The eigen values of the model showed that the system was stable and contained oscillation phenomenon. Next the sensitivities of rate constant and logarithmic gains of the three key parameters were analyzed, as well as the robust of the system. The result indicated that the biochemical systems theory could be applied in different fields more widely.

Citation： PANDuotao, SHIHongyan, HUANGMingzhong, YUANDecheng. Stability Analysis of Susceptible-Infected-Recovered Epidemic Model. Journal of Biomedical Engineering, 2015, 32(5): 1013-1018. doi: 10.7507/1001-5515.20150180 Copy

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14.	SHIVAKUMAR K, BIEGLER L T. Simultaneous dynamic optimization strategies:recent advances and challenges[J]. Computers and Chemical Engineering, 2006, 30(10):1560-1575.
15.	BIEGLER L T, CERVANTES A M, WÄCHTER A. Advances in simultaneous strategies for dynamic process optimization[J]. Chemical Engineering Science, 2002, 57(4):575-593.
16.	潘多涛,史洪岩,黄明忠,等.非线性规划在生物代谢仿真过程中的应用[J].控制工程,2014,21(6):896-899.
17.	VOIT E O. Biochemical systems theory:a review[J]. ISRN Biomathematics, 2013, 2013:1-53.
18.	VOIT E O. Computational analysis of biochemical systems:a practical guide for biochemists and molecular biologists[M]. UK Cambridge:Cambridge University Press, 2000:1-544.
19.	RESTIF O, GRENFELL B T. Vaccination and the dynamics of immune evasion[J]. J R Soc Interface. 2007, 4(12):143-153.
20.	TORRES N V, VOIT E O. Pathway analysis and optimization in metabolic engineering[M]. UK Cambridge:Cambridge University Press, 2002:1-324.
21.	VOIT E O. A first course in systems biology[M]. USA New York:Garland Science, 2013:1-496.

1. HEINZLE E, BIWER A P, COONEY C L. Development of sustainable bioprocesses:modeling and assessment[M]. Sussex:Wiley, 2007:1-316.
2. CHASSAGNOLE C, NOISOMMIT-RIZZI N, SCHMID J W, et al. Dynamic modeling of the central carbon metabolism of Escherichia coli[J]. Biotechnol Bioeng, 2002, 79(1):53-73.
3. TOHSATO Y, IKUTA K, SHIONOYA A, et al. Parameter optimization and sensitivity analysis for large kinetic models using a real-coded genetic algorithm[J]. Gene, 2013, 518(1):84-90.
4. KADIR T A, MANNAN A A, KIERZEK A M, et al. Modeling and simulation of the main metabolism in Escherichia coli and its several single-gene knockout mutants with experimental verification[J]. Microb Cell Fact, 2010, 9:88.
5. DALEY D J, GANI J. Epidemic modeling:an introduction[M]. New York:Cambridge University Press, 2001:1-213.
6. GRENFELL B T, PYBUS O G, GOG J R, et al. Unifying the epidemiological and evolutionary dynamics of pathogens[J]. Science, 2004, 303(5656):327-332.
7. MILLER J C. Epidemics on networks with large initial conditions or changing structure[J]. PLoS One, 2014, 9(7):e101421.
8. WAN X, LIU J, CHEUNG W K, et al. Inferring epidemic network topology from surveillance data[J]. PLoS One, 2014, 9(6):e100661.
9. 潘多涛,黄明忠,张学军,等.工程规划建模研究及流程优化的实现[J].北京工业大学学报,2012,38(10):1486-1490.
10. 潘多涛,史洪岩,黄明忠,等.复杂生物过程的仿真分析[J].系统仿真学报,2014,26(3):670-674.
11. HINDMARSH A C, BROWN P N, GRANT K E, et al. SUNDIALS:Suite of nonlinear and differential/algebraic equation solvers[J]. ACM Transactions on Mathematical Software, 2005, 31(3):363-396.
12. WÄCHTER A. An interior point algorithm for large-scale nonlinear optimization with applications in process engineering[D]. Pittsburgh:Carnegie Mellon University, 2002.
13. LI C, DONIZELLI M, RODRIGUEZ N, et al. BioModels Database:An enhanced, curated and annotated resource for published quantitative kinetic models[J]. BMC Syst Biol, 2010, 4:92.
14. SHIVAKUMAR K, BIEGLER L T. Simultaneous dynamic optimization strategies:recent advances and challenges[J]. Computers and Chemical Engineering, 2006, 30(10):1560-1575.
15. BIEGLER L T, CERVANTES A M, WÄCHTER A. Advances in simultaneous strategies for dynamic process optimization[J]. Chemical Engineering Science, 2002, 57(4):575-593.
16. 潘多涛,史洪岩,黄明忠,等.非线性规划在生物代谢仿真过程中的应用[J].控制工程,2014,21(6):896-899.
17. VOIT E O. Biochemical systems theory:a review[J]. ISRN Biomathematics, 2013, 2013:1-53.
18. VOIT E O. Computational analysis of biochemical systems:a practical guide for biochemists and molecular biologists[M]. UK Cambridge:Cambridge University Press, 2000:1-544.
19. RESTIF O, GRENFELL B T. Vaccination and the dynamics of immune evasion[J]. J R Soc Interface. 2007, 4(12):143-153.
20. TORRES N V, VOIT E O. Pathway analysis and optimization in metabolic engineering[M]. UK Cambridge:Cambridge University Press, 2002:1-324.
21. VOIT E O. A first course in systems biology[M]. USA New York:Garland Science, 2013:1-496.

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