Optimal control of epidemics in metapopulations

Journal of the Royal Society Interface

Volumn 6, Issue 41, 2009, Pages 1135-1144

  Rowthorn, Robert E ^a   Laxminarayan, Ramanan ^b   Gilligan, Christopher A ^a  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

^b RESOURCES FOR THE FUTURE   (United States)

Author keywords

Control theory; Economic modelling; Epidemiological modelling; Quarantine; Spatio temporal epidemics

Indexed keywords

CONTROL THEORY; INTERCONNECTION NETWORKS; OPTIMIZATION; SYSTEM THEORY;

DISCOUNTED NUMBERS; EPIDEMIOLOGICAL MODELLING; METAPOPULATIONS; OPTIMAL CONTROL METHODS; OPTIMAL CONTROLS; QUARANTINE; SCARCE RESOURCES; SPATIO-TEMPORAL EPIDEMICS;

DISEASE CONTROL;

ARTICLE; BUDGET; DISEASE COURSE; DISEASE TRANSMISSION; EPIDEMIC; INFECTION CONTROL; INFECTION SENSITIVITY; METAPOPULATION; POPULATION SIZE; PREVALENCE; REINFECTION;

EID: 70350513290     PISSN: 17425689     EISSN: 17425662     Source Type: Journal    
DOI: 10.1098/rsif.2008.0402     Document Type: Article

References (34)

1. Anderson, R. M. & May, R. M. 1991 Infectious diseases of humans: dynamics and control. Oxford, UK: Oxford University Press.
2. Barrett, S. 2003 Global disease eradication. J. Eur. Econ. Assoc. 1, 591-600. (doi:10.1162/154247603322391224)
3. Barrett, S. & Hoel, M. 2007 Optimal disease eradication. Environ. Dev. Econ. 12, 627-652. (doi:10.1017/S1355770X07003816)
4. Dye, C. & Gay, N. 2003 Modeling the SARS epidemic. Science 300, 1884-1885. (doi:10.1126/science.1086925)
5. Ferguson, N. M., Donnelly, C. A. & Anderson, R. M. 2001 The foot-and-mouth epidemic in Great Britain: pattern of spread and impact of interventions. Science 292, 1155-1160. (doi:10.1126/science.1061020)
6. Forster, G. & Gilligan, C. A. 2007 Optimizing the control of disease infestations at the landscape scale. Proc. Natl Acad. Sci. USA 104, 4984-4989. (doi:10.1073/pnas.0607900104)
7. Gilligan, C. A. 2003 Economics of transgenic crops and pest resistance, an epidemiological perspective. In Battling resistance to antibiotics and pesticides: an economic approach (ed. R. Laxminarayan), pp. 221-243.Washington, DC: Resources for the Future.
8. Goldman, S. M. & Lightwood, J. 2002 Cost optimisation in the SIS model of infectious disease with treatment. In Topics in economic analysis and policy, vol.2, pp. 1-24. Berkeley, CA: Berkley Electronic Press.
9. Grenfell, B. T. & Bolker, B. M. 1998 Cities and villages: infection hierarchies in a measles metapopulation. Ecol. Lett. 1, 63-70. (doi:10.1046/j.1461-0248.1998.00016.x)
10. Gyllenberg, M., Hanski, I. & Hastings, A. 1997 Structured metapopulation models. In Metapopulation biology: ecology, genetics and evolution (ed. M. E. Gilpin), pp. 93-122. San Diego, CA: Academic Press.
11. Hanski, I. 1998 Metapopulation dynamics. Nature 396, 41-49. (doi:10.1038/23876)
12. Hanski, I. & Ovaskainen, O. 2002 The metapopulation capacity of a fragmented landscape. Nature 404, 755-758. (doi:10.1038/35008063)
13. Hethcote, H. W. 1980 Three basic epidemiological models. In Applied mathematical ecology (ed. L. J. Gross), pp. 19-144. Berlin, Germany: Springer-Verlag.
14. Keeling, M. J. & Gilligan, C. A. 2000a Bubonic plague: a metapopulation model of a zoonosis. Proc. R. Soc. B 267, 2219-2230. (doi:10.1098/rspb.2000.1013)
15. Keeling, M. J. & Gilligan, C. A. 2000b Metapopulation dynamics of bubonic plague. Nature 407, 903-906. (doi:10.1038/35038073)
16. Keeling, M. J. et al. 2001 Dynamics of the 2001 UK foot and mouth epidemic: stochastic dispersal in a heterogeneous landscape. Science 294, 813-817. (doi:10.1126/science.1065973)
17. Keeling, M. J., Bjørnstad, O. N. & Grenfell, B. T. 2004 Metapopulation dynamics of infectious disease. In Ecology, genetics and evolution of metapopulations (ed. O. E. Gaggiotti), pp. 415-445. Amsterdam, The Netherlands: Elsevier.
18. Klein, E., Laxminarayan, R., Smith, D. L. & Gilligan, C. A. 2007 Economic incentives and mathematical models of disease. Environ. Dev. Econ. 12, 707-732. (doi:10.1017/S1355770X0700383X)
19. Lajmanovich, A. & Yorke, J. A. 1976 A deterministic model for gonorrhea in a nonhomogeneous population. Math. Biosci. 28, 221-236. (doi:10.1016/0025-5564(76)90125-5)
20. Lipsitch, M., Bergstrom, C. T. & Levin, B. R. 2000 The epidemiology of antibiotic resistance in hospitals: paradoxes and prescriptions. Proc. Natl Acad. Sci. USA 97, 1938-1943. (doi:10.1073/pnas.97.4.1938)
21. Murray, J. D. 2002 Mathematical biology I: an introduction. Berlin, Germany: Springer-Verlag.
22. Murray, G. D. & Cliff, A. D. 1977 A stochastic model for measles epidemics in a multi-region setting. Trans. Inst. Br. Geogr. 2, 158-174. (doi:10.2307/621855)
23. Murray, C. J. L. & Lopez, A. D. 1996 The global burden of disease. Geneva, Switzerland: World Health Organisation, Harvard School of Public Health, World Bank.
24. Nold, A. 1980 Heterogeneity in disease-transmission modeling. Math. Biosci. 52, 227-240. (doi:10.1016/0025-5564(80)90069-3)
25. Park, A. W., Gubbins, S. & Gilligan, C. A. 2003 Extinction times for spatially-structured closed epidemics. Ecol. Lett. 5, 747-755. (doi:10.1046/j.1461-0248.2002.00378.x)
26. Pinch, E. 1993 Optimal control and the calculus of variations. Oxford, UK: Oxford University Press.
27. Pontryagin, L. S., Boltyanski, B., Gamkrelidze, R. & Mishchenko, E. 1962 The mathematical theory of optimal processes. New York, NY: Interscience.
28. Rowthorn, R. E. & Brown, G. M. 2003 Using antibiotoics when resistance is renewable. In Battling resistance to antibiotics and pesticides: an economic approach (ed. R. Laxminarayan), pp. 42-62. Washington, DC: Resources for the Future.
29. Seierstad, A. & Sydsaeter, K. 1987 Optimal control theory with economic applications. Amsterdam, The Netherlands: North Holland.
30. Sethi, S. 1974 Quantitative guidelines for communicable disease control program: a complete synthesis. Biometrics 30, 681-691. (doi:10.2307/2529232)
31. Sethi, S. 1978 Optimal control of some simple deterministic epidemic models. J. Oper. Res. Soc. 29, 129-136. (doi:10.1057/jors.1978.27)
32. Smith, D. L., Levin, S. A. & Laxminarayan, R. 2005 Strategic interactions in multi-institutional epidemics of antibiotic resistance. Proc. Natl Acad. Sci. USA 102, 3153-3158. (doi:10.1073/pnas.0409523102)
33. Stacey, A. J., Truscott, J. E., Asher, M. J. C. & Gilligan, C. A. 2004 A model for the invasion of rhizomania in the United Kingdom: implications for control strategies. Phytopathology 94, 209-215. (doi:10.1094/PHYTO.2004.94. 2.209)
34. Swinton, J., Harwood, J., Grenfell, B. T. & Gilligan, C. A. 1998 Persistence thresholds for phocine distemper virus infection in harbour seal Phoca vitulina metapopulations. J. Anim. Ecol. 67, 54-68. (doi:10.1046/j.1365- 2656.1998.00176.x)