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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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. 潘多濤,黃明忠,張學軍,等.工程規劃建模研究及流程優化的實現[J].北京工業大學學報,2012,38(10):1486-1490.
10. 潘多濤,史洪巖,黃明忠,等.復雜生物過程的仿真分析[J].系統仿真學報,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. W?CHTER 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, W?CHTER A. Advances in simultaneous strategies for dynamic process optimization[J]. Chemical Engineering Science, 2002, 57(4):575-593.
16. 潘多濤,史洪巖,黃明忠,等.非線性規劃在生物代謝仿真過程中的應用[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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