Dynamic control of modern, network-based epidemic models

SIAM Journal on Applied Dynamical Systems

Volumn 14, Issue 1, 2015, Pages 168-187

  Sélley, Fanni ^a   Besenyei, Ádám ^a   Kiss, Istvan Z ^b   Simon, Péter L ^a  

^a EÖTVÖS LORÁND UNIVERSITY   (Hungary)

^b UNIVERSITY OF SUSSEX   (United Kingdom)

Author keywords

Adaptive network; Nonlinear model predictive control; Pairwise model; SIS epidemic

Indexed keywords

ADAPTIVE CONTROL SYSTEMS; DIAGNOSIS; EPIDEMIOLOGY; MODEL PREDICTIVE CONTROL; NONLINEAR SYSTEMS; PREDICTIVE CONTROL SYSTEMS;

ADAPTIVE NETWORKS; CONTACT STRUCTURE; CONTROL PARAMETERS; NONLINEAR MODEL PREDICTIVE CONTROL; NUMERICAL INVESTIGATIONS; REAL WORLD SITUATIONS; SIMULATION-BASED MODELS; SIS EPIDEMIC;

DISEASE CONTROL;

EID: 84925335151     PISSN: None     EISSN: 15360040     Source Type: Journal    
DOI: 10.1137/130947039     Document Type: Article

References (20)

1. R. ALBERT, H. JEONG, AND A.-L. BARABÁSI, Error and attack tolerance of complex networks, Nature, 406 (2000), pp. 378-382.
2. R. M. ANDERSON AND R. M. MAY, Infectious Diseases of Humans, Oxford University Press, Oxford, UK, 1991.
3. D. CLANCY AND A. B. PIUNOVSKIY, An explicit optimal isolation policy for a deterministic epidemic model, Appl. Math. Comput., 163 (2005), pp. 1109-1121.
4. J. CLARKE, K. A. J. WHITE, AND K. TURNER, Approximating optimal controls for networks when there are combinations of population-level and targeted measures available: Chlamydia infection as a case-study, Bull. Math. Biol., 75 (2013), pp. 1747-1777.
5. R. COHEN, S. HAVLIN, AND D. BEN-AVRAHAM, Efficient immunization strategies for computer networks and populations, Phys. Rev. Lett., 91 (2003), 247901-1.
6. R. F. CURTAIN AND H. ZWART, An Introduction to Infinite-Dimensional Linear Systems Theory, Texts Appl. Math. 21, Springer-Verlag, New York, 1995.
7. L. DANON, A. P. FORD, T. HOUSE, C. P. JEWELL, M. J. KEELING, G. O. ROBERTS, J. V. ROSS, AND M. C. VERNON, Networks and the epidemiology of infectious disease, Interdisciplinary Perspectives on Infectious Diseases, 2011 (2011), 284909; special issue on "Network Perspectives on Infectious Disease Dynamics."
8. L. GRÜNE AND J. PANNEK, Nonlinear Model Predictive Control, Springer, New York, 2011.
9. E. HANSEN AND T. DAY, Optimal control of epidemics with limited resources, J. Math. Biol., 62 (2011), pp. 423-451.
10. P. HOLME, B. J. KIM, C. N. YOON, AND S. K. HAN, Attack vulnerability of complex networks, Phys. Rev. E, 65 (2002), 056109.
11. T. HOUSE AND M. J. KEELING, Insights from unifying modern approximations to infections on networks, J. Roy. Soc. Interface, 8 (2011), pp. 67-73.
12. M. J. KEELING, The effects of local spatial structure on epidemiological invasions, Proc. R. Soc. Lond. B, 266 (1999), pp. 859-867.
13. M. J. KEELING AND K. T. D. EAMES, Networks and epidemic models, J. Roy. Soc. Interface, 2 (2005), pp. 295-307.
14. I. Z. KISS, D. M. GREEN, AND R. R. KAO, Disease contact tracing in random and clustered networks, Proc. R. Soc. Lond. B, 272 (2005), pp. 1407-1414.
15. Y. Y. LIU, J. J. SLOTINE, AND A. L. BARABÁSI, Controllability of complex networks, Nature, 473 (2011), pp. 167-173.
16. L. MAGNI, D. RAIMONDO, AND F. ALLGÖWER, EDS., Nonlinear Model Predictive Control: Towards New Challenging Applications, Lecture Notes in Control and Inform. Sci. 384, Springer-Verlag, Berlin, 2009.
17. R. MORTON AND K. H. WICKWIRE, On the optimal control of a deterministic epidemic, Adv. Appl. Probab., 6 (1974), pp. 622-635.
18. nd ed., Texts Appl. Math. 6, Springer-Verlag, New York, 1998.
19. A. SZABÓ, P. SIMON, AND I. Z. KISS, Detailed study of bifurcations in an epidemic model on a dynamic network, Differ. Equ. Appl., 4 (2012), pp. 277-296.
20. M. YOUSSEF AND C. SCOGLIO, Mitigation of epidemics in contact networks through optimal contact adaptation, Math. Biosci. Engrg., 10 (2013), pp. 1227-1251.