Optimal control for SIRC epidemic outbreak

Computer Methods and Programs in Biomedicine

Volumn 110, Issue 3, 2013, Pages 333-342

  Iacoviello, Daniela ^a   Stasio, Nicolino ^a  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

Epidemic models; Optimal control; Optimization; SIRC model; System analysis

Indexed keywords

CONTROL STRATEGIES; EPIDEMIC DISEASE; EPIDEMIC MODELS; NUMERICAL RESULTS; OPTIMAL CONTROL STRATEGY; OPTIMAL CONTROLS; OPTIMAL SOLUTIONS; PONTRYAGIN'S MINIMUM PRINCIPLES;

CONTROL; OPTIMAL CONTROL SYSTEMS; OPTIMIZATION; SYSTEMS ANALYSIS;

DISEASE CONTROL;

ARTICLE; CONTROL STRATEGY; CONTROL SYSTEM; DISEASE PREDISPOSITION; EPIDEMIC; HEALTH CARE COST; HEALTH CARE UTILIZATION; HUMAN; INFECTION CONTROL; INFECTION RESISTANCE; INFECTION SENSITIVITY; OUTCOME ASSESSMENT; RISK REDUCTION; VACCINATION;

COMMUNICABLE DISEASES; COMPUTER SIMULATION; EPIDEMICS; HUMANS; INCIDENCE; INFECTION CONTROL; MATHEMATICAL CONCEPTS; MODELS, BIOLOGICAL;

EID: 84877059716     PISSN: 01692607     EISSN: 18727565     Source Type: Journal    
DOI: 10.1016/j.cmpb.2013.01.006     Document Type: Article

References (29)

1. Hethcote H., Zhien M., Shengbing L. Effects of quarantine in six endemic models for infectious diseases. Mathematical Biosciences 2002, 180:141-160.
2. Casagrandi R., Bolzoni L., Levin S.A., Andreasen V. The SIRC model and influenza A. Mathematical Biosciences 2006, 200:152-169.
3. Becker N.G., Starczak D.N. Optimal vaccination strategies for a community of household. Mathematical Biosciences 1997, 139:117-132.
4. Brandeau M., Zaric G.S., Richter A. Resource allocation for control of infectious diseases in multiple independent populations: beyond cost-effectiveness analysis. Journal of Health Economics 2003, 22:575-598.
5. Castilho C. Optimal control of an epidemic through educational campaign. Electronic Journal of Differential Equations 2006, 125:1-11.
6. Zaric G.S., Brandeau M. Dynamic resource allocation for epidemic control in multiple populations. Journal of Mathematics Applied in Medicine and Biology 2002, 19:235-255.
7. Verriest E., Delmotte F., Egerstedt M. Control of epidemics by vaccination. Proceedings of the American Control Conference 2005, 2:985-990.
8. Clancy D., Piunovskiy A.B. An explicit optimal isolation policy for a deterministic epidemic model. Applied Mathematics and Computation 2005, 163:1109-1121.
9. Behncke H. Optimal control of deterministic epidemics. Optimal Control, Applications and Methods 2000, 21:269-285.
10. Becker N.G., Glass K., Li Z., Aldis G.K. Controlling infectious diseases like SARS. Mathematical Biosciences 2005, 193:205-221.
11. Jiang C., Dong M. Optimal measures for SARS epidemics outbreaks. Proc. of the 6th World Congress on Intelligent Control and Automation 2006, 9331-9335.
12. Chang H., Astolfi A. Enhancement of the immune system in HIV dynamics by output feedback. Automatica 2009, 45:1765-1770.
13. Caetano M.A.L., Yoneyama T. Optimal and sub-optimal control in Dengue epidemics. Optimal Control, Applications and Methods 2001, 22:63-73.
14. Yan X., Zou Y. Optimal and suboptimal quarantine and isolation control in SARS epidemics. Mathematical and Computer Modelling 2008, 47:235-245.
15. Joshi H. Optimal control of an HIV immunology model. Optimal Control, Applications and Methods 2002, 23:199-213.
16. Iacoviello D., Liuzzi G. Fixed/free final time SIR epidemic models with multiple controls. International Journal of Simulation and Modelling 2008, 7:81-92.
17. Jung E., Lenhart S., Feng Z. Optimal control of treatment in a two strain tuberculosis model. Discrete and Continuous Dynamical Systems - Series B 2002, 2:473-482.
18. Blayneh K., Cao Y., Kwon H.D. Optimal control of vector-borne diseases: treatment and prevention. Discrete and Continuous Dynamical Systems - Series B 2009, 11:1-30.
19. Anderson R., May R. Population biology of infectious diseases: Part I. Nature 1979, 280-361.
20. Pease C. An evolutionary epidemiological mechanism, with applications to type A influenza. Theoretical Population Biology 1987, 31:422-452.
21. Zaman G., Kang Y.H., Jung I.H. Stability analysis and optimal vaccination of an SIR epidemic model. BioSystems 2008, 93:240-249.
22. Birkhoff G., Rota G.C.C. Ordinary Differential Equations 1989, John Wiley & Sons, New York. 4th ed.
23. Fleming W.H., Rishel R.W. Deterministic and Stochastic Optimal Control 1975, Springer Verlag, New York.
24. Lukes D.L. Differential Equations: Classical to Controlled. Mathematics in Science and Engineering 1982, vol. 162. Academic Press, New York.
25. Hartl R.F., Sethi S.P., Vickson R.G. A survey f the maximum principles for optimal control problems with state constraints. Society for Industrial and Applied Mathematics 1995, 37:181-218.
26. Fletcher R. Practical Methods of Optimization 1987, John Wiley and Sons, UK.
27. Gill P.E., Murray W., Wright M.H. Practical Optimization 1981, Academic Press, London.
28. Battiti R. First and second order methods for learning: between steepest descent and Newton's method. Neural Computation 1992, 4:141-166.
29. Lenhart S., Workman J.T. Optimal Control Applied to Biological Models, Mathematical and Computational Biology Series 2007, Chapman & Hall/CRC, London, UK.