Optimal control of vaccine distribution in a rabies metapopulation model

Mathematical Biosciences and Engineering

Volumn 5, Issue 2, 2008, Pages 219-238

  Asano, Erika ^a   Gross, Louis J ^b   Lenhart, Suzanne ^b   Real, Leslie A ^c  

^a UNIVERSITY OF SOUTH FLORIDA   (United States)

^b UNIVERSITY OF TENNESSEE   (United States)

^c EMORY UNIVERSITY   (United States)

Author keywords

Epidemiology; Mathematical model; Optimal control; Rabies in raccoons; Vaccine

Indexed keywords

PROCYON;

EID: 52049111883     PISSN: 15471063     EISSN: 15510018     Source Type: Journal    
DOI: 10.3934/mbe.2008.5.219     Document Type: Article

References (24)

1. L. J. S. Allen, D. A. Flores, R. K. Ratnayake, and J. R. Herbold. Discrete-time deterministic and stochastic models for the spread of rabies. Applied Mathematics and Computation, 132:271-92, 2002.
2. H. Behncke. Optimal control of deterministic dynamics. Optim. Control Appl. Meth., 21:269-85, 2000.
3. A. J. G. Cairns. Epidemics in heterogeneous populations: aspects of optimal vaccination policies. IMA J. of Math. Applied to Med. and Biology, 6:137-59, 1989.
4. J. E. Childs, A. T. Curns, M. E. Dey, L. A. Real, L. Feinstein, and O. N. Bjornstad. Predicting the local dynamics of epizootic rabies among raccoons in the United States. PNAS, 97(25):13666-71, 2000.
5. D. Clancy. Optimal intervention for epidemic models with general intervention and removal rate functions. J. Math. Biol., 39:309-31, 1999.
6. M. J. Coyne, G. Smith, and F. E. McAllister. Mathematic model for the population biology of rabies in raccoons in the mid-Atlantic states. American Journal of veterinary research, 50(12):2148-54, 1989.
7. N. D. Evans and A. J. Pritchard. A control theoretic approach to containing the spread of rabies. IMA Journal of Mathematics Applied in Medicine and Biology, 18:1-23, 2001.
8. R. Fister, S. Lenhart, and J. S. McNally. Optimizing chemotherapy in an HIV model. Electronic Journal of Differential Equations, 1998(32):1-12, 1998.
9. W. H. Fleming and R. W. Rishel. Deterministic and Stochastic Optimal Control. SpringerVerlag, New York, 2005.
10. P. J. Francis. Optimal tax/subsidy combinations for the flu season. J. of Econ. Dynamics and Control, 28:2037-54, 2004.
11. H. Gaff and E. Schaefer. Optimal control applied to vaccination and treatment strategies for various epidemiologic models, preprint.
12. D. Greenhalgh. Some results on optimal control applied to epidemics. Math. Biosci., 88:125-58, 1988.
13. M. I. Kamien and N. L. Schwarz. Dynamic Optimization: The Calculus of Variations and Optimal Control in Economics and Management. North-Holland, Amsterdam, 1991.
14. D. L. Lukes. Differential Equations: Classical to Controlled, Mathematics in Science and Engineering, volume 162. Academic press, New York, 1982.
15. C. Martin, L. Allen, M. Stamp, M. Jones, and R. Carpio. A model for the optimal control of a measles epidemic. In Computation and Control II, Proceedings of the Third Bozeman Conference, pages 265-83, Boston, 1992. Birkhauser.
16. R. Morton and K. H. Wickwire. On the optimal control of a deterministic epidemic. Advances in Appl. Probability, 6:622-35, 1974.
17. J. D. Murray, E. A. Stanley, and D. L. Brown. On the spatial spread of rabies among foxes. PTOC. R. Soc. London B, 229:111-50, 1986.
18. Division of Viral and Rickettsial Diseases (DVRD). Rabies. From National Center for Infectious Diseases (NCID) web site concerning rabies (http://www.cdc.gov/ncidod/dvrd/rabies/). Centers for Disease Control and Prevention.
19. P. Ögren and C. F. Martin. Vaccination strategies for epidemics in highly mobile populations. Applied Mathematics and Computation, 127:261-76, 2002.
20. L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelize, and E. F. Mishchenko. The Mathematical Theory of Optimal Processes. Wiley, New York, 1962.
21. L. A. Real, C. Russell, L. Waller, D. Smith, and J. Childs. Spatial dynamics and molecular ecology of north American rabies. Journal of Heredity, 96(3):253-60, 2005.
22. USDA Wildlife Services. National Rabies Management Program. From USDA Animal and Plant Health Inspection Service web site concerning the National Rabies Management Pro-gram (http://www.aphis.usda.gov/ws/rabies/). USDA Animla and Plant Health Inspection Service.
23. S. P. Sethi. Quantitative guidelines for communicable disease control program: a complete synthesis. Biometrics, 30:681-91, 1974.
24. K. Wickwire. Mathematical models for the control of pests and infectious diseases: a survey. Theoretical Population Biology, 11:182-238, 1977.