Applying optimal control theory to complex epidemiological models to inform real-world disease management

Philosophical Transactions of the Royal Society B: Biological Sciences

Volumn 374, Issue 1776, 2019, Pages

  Bussell, E H ^a   Dangerfield, C E ^a   Gilligan, C A ^a   Cunniffe, N J ^a  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

Disease management; Feedback; Model predictive control; Optimal control

Indexed keywords

CONTROL SYSTEM; DISEASE CONTROL; EPIDEMIOLOGY; FEEDBACK MECHANISM; NUMERICAL MODEL;

ANIMALIA;

EID: 85065442188     PISSN: 09628436     EISSN: 14712970     Source Type: Journal    
DOI: 10.1098/rstb.2018.0284     Document Type: Article

References (44)

1. Heesterbeek H et al. 2015 Modeling infectious disease dynamics in the complex landscape of global health. Science 347, aaa4339. (doi:10.1126/ science.aaa4339)
2. Metcalf CJE, Edmunds WJ, Lessler J. 2015 Six challenges in modelling for public health policy. Epidemics 10, 93 - 96. (doi:10.1016/j.epidem.2014.08.008)
3. Cunniffe NJ, Koskella B, Metcalf CJ, Parnell S, Gottwald TR, Gilligan CA. 2015 Thirteen challenges in modelling plant diseases. Epidemics 10, 6-10. (doi:10.1016/j.epidem.2014.06.002)
4. Lofgren ET et al. 2014 Opinion: mathematical models: a key tool for outbreak response. Proc. Natl Acad. Sci. USA 111, 18 095 - 18 096. (doi:10.1073/ pnas.1421551111)
5. Jit M, Choi YH, Edmunds WJ. 2008 Economic evaluation of human papillomavirus vaccination in the United Kingdom. Br. Med J. 337, a769. (doi:10. 1136/bmj.a769)
6. Choi YH, Jit M, Gay N, Cox A, Garnett GP, Edmunds WJ. 2010 Transmission dynamic modelling of the impact of human papillomavirus vaccination in the United Kingdom. Vaccine 28, 4091-4102. (doi:10. 1016/j.vaccine.2009.09.125)
7. Keeling MJ 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)
8. Keeling MJ. 2005 Models of foot-and-mouth disease. Proc. R. Soc. B 272, 1195-1202. (doi:10. 1098/rspb.2004.3046)
9. Keeling MJ, Woolhouse MEJ, May RM, Davies G, Grenfell BT. 2003 Modelling vaccination strategies against foot-and-mouth disease. Nature 421, 136-142. (doi:10.1038/nature01343)
10. Tildesley MJ, Savill NJ, Shaw DJ, Deardon R, Brooks SP, Woolhouse ME, Grenfell BT, Keeling MJ. 2006 Optimal reactive vaccination strategies for a foot- and-mouth outbreak in the UK. Nature 440, 83-86. (doi:10.1038/nature04324)
11. Cunniffe NJ, Stutt ROJH, DeSimone RE, Gottwald TR, Gilligan CA. 2015 Optimising and communicating options for the control of invasive plant disease when there is epidemiological uncertainty. PLoS Comput. Biol 11, e1004211. (doi:10.1371/journal. pcbi.1004211)
12. Hyatt-Twynam SR, Parnell S, Stutt ROJH, Gottwald TR, Gilligan CA, Cunniffe NJ. 2017 Risk-based management of invading plant disease. New Phytol. 214, 1317-1329. (doi:10.1111/nph.14488)
13. Adrakey HK, Streftaris G, Cunniffe NJ, Gottwald TR, Gilligan CA, Gibson GJ. 2017 Evidence-based controls for epidemics using spatio-temporal stochastic models in a Bayesian framework. J. R. Soc. Interface 14, 20170386. (doi:10.1098/rsif. 2017.0386)
14. Craig AP, Cunniffe NJ, Parry M, Laranjeira FF, Gilligan CA. 2018 Grower and regulator conflict in management of the citrus disease Huanglongbing in Brazil: a modelling study. J. Appl. Ecol. 55, 1956-1965. (doi:10.1111/1365-2664.13122)
15. Cunniffe NJ, Cobb RC, Meentemeyer RK, Rizzo DM, Gilligan CA. 2016 Modeling when, where, and how to manage a forest epidemic, motivated by sudden oak death in California. Proc. Natl Acad. Sci. USA 113, 5640-5645. (doi:10.1073/pnas.1602153113)
16. Keeling MJ, Rohani P. 2008 Modeling infectious diseases in humans and animals. Princeton, NJ: Princeton University Press.
17. Anderson RM, Medley GF, May RM, Johnson AM. 1986 A preliminary study of the transmission dynamics of the human immunodeficiency virus (HIV), the causative agent of AIDS. Math. Med. Biol. 3, 229-263. (doi:10.1093/imammb/3.4.229)
18. Smith DL, Lucey B, Waller LA, Childs JE, Real LA. 2002 Predicting the spatial dynamics of rabies epidemics on heterogeneous landscapes. Proc. Natl Acad. Sci. USA 99, 3668-3672. (doi:10.1073/pnas. 042400799)
19. Bellman R. 2013 Dynamic programming. New York, NY: Courier Corporation.
20. Lenhart S, Workman JT. 2007 Optimal control applied to biological models. Boca Raton, FL: CRC Press.
21. Sethi SP, Staats PW. 1978 Optimal control of some simple deterministic epidemic models. J. Oper. Res. Soc. 29, 129-136. (doi:10.1057/jors.1978.27)
22. Behncke H. 2000 Optimal control of deterministic epidemics. Optim. Control Appl. Methods 21, 269-285. (doi:10.1002/oca.678)
23. Perrings C et al. 2014 Merging economics and epidemiology to improve the prediction and management of infectious disease. EcoHealth 11, 464-475. (doi:10.1007/s10393-014-0963-6)
24. Epanchin-Niell RS. 2017 Economics of invasive species policy and management. Biol. Invasions 19, 3333-3354. (doi:10.1007/s10530-017-1406-4)
25. Cunniffe NJ, Laranjeira FF, Neri FM, DeSimone RE, Gilligan CA. 2014 Cost-effective control of plant disease when epidemiological knowledge is incomplete: modelling Bahia bark scaling of citrus. PLoS Comput. Biol. 10, 1003753. (doi:10.1371/ journal.pcbi.1003753)
26. Ndeffo Mbah ML, Gilligan CA. 2010 Balancing detection and eradication for control of epidemics: sudden oak death in mixed-species stands. PLoS ONE 5, e12317. (doi:10.1371/journal.pone.0012317)
27. Brown VL, White KAJ. 2011 The role of optimal control in assessing the most cost-effective implementation of a vaccination programme: HPV as a case study. Math. Biosci. 231, 126-134. (doi:10.1016/j.mbs.2011.02.009)
28. Forster G, Gilligan CA. 2007 Optimizing the control of disease infestations at the landscape scale. Proc. Natl Acad. Sci. USA 104, 4984-4989. (doi:10.1073/ pnas.0607900104)
29. Rowthorn RE, Laxminarayan R, Gilligan CA. 2009 Optimal control of epidemics in metapopulations. J. R. Soc. Interface 6, 1135-1144. (doi:10.1098/rsif. 2008.0402)
30. Ndeffo Mbah ML, Gilligan CA. 2011 Resource allocation for epidemic control in metapopulations. PLoS ONE 6, e24577. (doi:10.1371/journal.pone. 0024577)
31. Neilan RM, Lenhart S. 2011 Optimal vaccine distribution in a spatiotemporal epidemic model with an application to rabies and raccoons. J. Math. Anal. Appl. 378, 603-619. (doi:10.1016/j.jmaa. 2010.12.035)
32. An G et al. 2017 Optimization and control of agent-based models in biology: a perspective. Bull. Math. Biol. 79, 63-87. (doi:10.1007/s11538-016-0225-6)
33. Clarke J, White KAJ, Turner K. 2013 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, 1747-1777. (doi:10. 1007/s11538-013-9867-9)
34. Camacho EF, Bordons C. 1995 Model predictive control in the process industry. London, UK: Springer.
35. Lee JH. 2011 Model predictive control: review of the three decades of development. Int. J. Control Autom. Syst. 9, 415-424. (doi:10.1007/s12555-011-0300-6)
36. Zurakowski R, Teel AR. 2006 A model predictive control based scheduling method for HIV therapy. J. Theor. Biol. 238, 368-382. (doi:10.1016/j.jtbi. 2005.05.004)
37. David J, Tran H, Banks HT. 2011 Receding horizon control of HIV. Optim. Control Appl. Meth. 32, 681-699. (doi:10.1002/oca.969)
38. Hovorka R et al. 2004 Nonlinear model predictive control of glucose concentration in subjects with type 1 diabetes. Physiol. Meas. 25, 905-920. (doi:10.1088/0967-3334/25/4/010)
39. Sélley F, Besenyei Á, Kiss IZ, Simon PL. 2015 Dynamic control of modern, network-based epidemic models. SIAM J. Appl. Dyn. Syst. 14, 168-187. (doi:10.1137/130947039)
40. Thompson RN, Hart WS. 2018 Effect of confusing symptoms and infectiousness on forecasting and control of Ebola outbreaks. Clin. Infect. Dis. 67, 1472-1474. (doi:10.1093/cid/ciy248)
41. Thompson RN, Gilligan CA, Cunniffe NJ. 2018 Control fast or control smart: when should invading pathogens be controlled? PLoS Comput. Biol. 14, e1006014. (doi:10.1371/journal.pcbi.1006014)
42. Whitehead SJ, Ali S. 2010 Health outcomes in economic evaluation: the QALY and utilities. Br. Med. Bull. 96, 5-21. (doi:10.1093/bmb/ldq033)
43. Savary S, Ficke A, Aubertot JN, Hollier C. 2012 Crop losses due to diseases and their implications for global food production losses and food security. Food Secur. 4, 519-537. (doi:10.1007/s12571-012-0200-5)
44. Boyd IL, Freer-Smith PH, Gilligan CA, Godfray HCJ. 2013 The consequence of tree pests and diseases for ecosystem services. Science 342, 1235773. (doi:10. 1126/science.1235773)