Optimal control of a vector borne disease with horizontal transmission

Nonlinear Analysis: Real World Applications

Volumn 13, Issue 1, 2012, Pages 203-212

  Lashari, Abid Ali ^a   Zaman, Gul ^b  

^a NATIONAL UNIVERSITY OF SCIENCES AND TECHNOLOGY   (Pakistan)

^b UNIVERSITY OF MALAKAND   (Pakistan)

Author keywords

Epidemic model; Numerical simulation; Optimal control; Pontryagin's Maximum Principle

Indexed keywords

CONTROL EFFORT; CONTROL FUNCTIONS; CONTROL PROBLEMS; COST EFFECTIVE; EPIDEMIC MODELS; NUMERICAL SOLUTION; NUMERICAL TECHNIQUES; OPTIMAL CONTROLS; OPTIMALITY SYSTEM; PONTRYAGIN'S MAXIMUM PRINCIPLE; VECTOR-BORNE DISEASE;

COMPUTER SIMULATION; CONTROL; ITERATIVE METHODS; NUMERICAL METHODS; OPTIMIZATION;

DISEASE CONTROL;

EID: 80052793577     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2011.07.026     Document Type: Article

References (21)

1. V. Wiwanitkit Unusual mode of transmission of dengue J. Infect. Dev. Ctries 30 2009 51 54
2. H. Wei, X.Z. Li, and M. Martcheva An epidemic model of a vector-borne disease with direct transmission and time delay J. Math. Anal. Appl. 342 2008 895 908
3. World Health Organization, Dengue and Dengue Haemorrhagic Fever, Geneva, Report, 2002.
4. R. Ross The Prevention of Malaria second ed. 1911 Murray London
5. G. Macdonald The analysis of equilibrium in malaria Trop. Dis. Bull. 49 1952 813 828
6. L. Esteva, and C. Vargas A model for dengue disease with variable human population J. Math. Biol. 38 1999 220 240
7. J. Tumwiine, J.Y.T. Mugisha, and L.S. Luboobi A host-vector model for malaria with infective immigrants J. Math. Anal. Appl. 361 2010 139 149
8. S. Lenhart, and John T. Workman Optimal Control Applied to Biological Models Mathematical and Computational Biology Series 2007 Chapman & Hall, CRC London, UK
9. K.W. Blayneh, Y. Cao, and H.D. Kwon Optimal control of vector-borne diseases: treatment and prevention Discrete Contin. Dyn. Syst. Ser. 11 2009 587 611
10. I.H. Jung, Y.H. Kang, and G. Zaman Optimal treatment of an SIR epidemic model with time delay Biosystems 98 2009 43 50
11. A.A. Lashari, and G. Zaman Global dynamics of vector borne disease with horizontal transmiion in host population Comput. Math. Appl. 61 2011 745 754
12. K.W. Blayneh, A.B. Gumel, S. Lenhart, and T. Clayton Backward bi-furcation and optimal control in transmission dynamics of west nile virus Bull. Math. Biol. 72 2010 1006 1028
13. World Health Organization Immunological correlates of protection induced by dengue vaccines Vaccine 25 2007 4130 4139
14. G. Birkhoff, and Gian-Carlo Rota Ordinary Differential Equations fourth ed. 1989 John Wiley & Sons New York
15. D.L. Lukes Differential Equations: Classical to Controlled Mathematics in Science and Engineering vol. 162 1982 Academic Press New York
16. M.I. Kamien, and N.L. Schwartz Dynamics Optimization: The Calculus of Variations and Optimal Control in Economics and Management 1991
17. Z. Feng Velasco-hernandez, competitive exclusion in a vector-host model for the dengue fever J. Math. Biol. 35 1997 523 544 (Pubitemid 127759099)
18. L. Esteva, and C. Vargas Analysis of a dengue disease transmission model Math. Biosci. 150 1998 131 151 (Pubitemid 28303363)
19. F.A.B. Coutinho, M.N. Burattini, L.F. Lopez, and E. Massad Threshold conditions for a non-autonomous epidemic system describing the population dynamics of dengue Bull. Math. Biol. 68 2006 2263 2282
20. O. Sharomi, C.N. Podder, A.B. Gumel, E.H. Elbasha, and J. Watmough Role of incidence function in vaccine-induced backward bifurcation in some HIV models Math. Biosci. 210 2007 436 463 (Pubitemid 350116899)
21. W.K. Hackbusch A numerical method for solving parabolic equations with opposite orientations Computing 20 1978 229 240