A model for transmission of partial resistance to anti-malarial drugs

Mathematical Biosciences and Engineering

Volumn 6, Issue 3, 2009, Pages 649-661

  Tasman, Hengki ^a,d   Soewono, Edy ^a   Sidarto, Kuntjoro Adji ^a   Syafruddin, Din ^b   Rogers, William Oscar ^c  

^a BANDUNG INSTITUTE OF TECHNOLOGY   (Indonesia)

^b EIJKMAN INSTITUTE FOR MOLECULAR BIOLOGY   (Indonesia)

^c US Naval Medical Research Unit No 2 Jakarta   (Indonesia)

^d UNIVERSITY OF INDONESIA   (Indonesia)

Author keywords

Anti malarial drug resistance; Basic reproduction ratio; Dynamical system; Mathematical epidemiology; Treatment proportion

Indexed keywords

ANTIMALARIAL AGENT;

ARTICLE; BASIC REPRODUCTION NUMBER; BIOLOGICAL MODEL; COMPUTER SIMULATION; DEVELOPING COUNTRY; DISEASE TRANSMISSION; DRUG RESISTANCE; HUMAN; IMMUNOLOGY; MALARIA; PLASMODIUM; STANDARD;

ANTIMALARIALS; BASIC REPRODUCTION NUMBER; COMPUTER SIMULATION; DEVELOPING COUNTRIES; DRUG RESISTANCE; HUMANS; MALARIA; MODELS, IMMUNOLOGICAL; PLASMODIUM;

EID: 70349643230     PISSN: 15471063     EISSN: 15510018     Source Type: Journal    
DOI: 10.3934/mbe.2009.6.649     Document Type: Article

References (21)

1. R. M. Anderson and R. M. May, "Infectious Diseases of Humans: Dynamics and Control," Oxford University Press, Oxford, 1991.
2. S. J. Aneke, Mathematical modelling of drug resistant malaria parasites and vector populations, Math. Methods Appl. Sci., 25 (2002), 335-346.
3. N. T. J. Bailey, "The Biomathematics of Malaria," Charles Griffin & Co., Ltd., London, 1982.
4. A. Berman and R. J. Plemmons, "Nonnegative Matrices in the Mathematical Sciences," SIAM, Philadelphia, PA, 1994.
5. M. F. Boni, D. L. Smith and R. Laxminarayan, Benefits of using multiple first-line therapies against malaria, PNAS, 105 (2008), 14216-14221.
6. L. J. Bruce-Chwatt, R. H. Black, C. J. Canfield, D. F. Clyde, W. Peters and W. H. Werns- dorfer, "Chemotherapy of Malaria," 2nd Rev. Ed. WHO Monograph Series No. 27, WHO, Geneva, 1986.
7. C. Castillo-Chavez, Z. Feng and W. Huang, On the computation of Ro and its role on global stability, in "Mathematical Approaches for Emerging and Reemerging Infectious Diseases: An Introduction," IMA, 125 (2002), 229-250.
8. A. G. Clegg and P. C. Clegg, "Man Against Disease," Heinemann Educational Books, London, 1973.
9. C. F. Curtis and L. N. Otoo, A simple model of the build-up of resistance to mixtures of anti-malarial drugs, Trans. R. Soc. Trop. Med. Hyg., 80 (1986), 889-892.
10. O. Diekmann and j. A. P. Heesterbeek, "Mathematical Epidemiology of Infectious Diseases, Model Building, Analysis and Interpretation," John Wiley & Son, Chichester, 2000.
11. P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002), 29-48.
12. I. M. Hastings, A model for the origins and spread of drug-resistant malaria, Parasitology, 115 (1997), 133-141.
13. I. M. Hastings and W. M. Watkins, Tolerance is the key to understanding antimalarial drug resistance, TRENDS in Parasitology, 22 (2006), 71-77.
14. J. C. Koella and R. Antia, Epidemiological models for the spread of anti-malarial resistance, Malaria Journal, (2003) http://www.malariajoumal.eom/ content/2/l/3.
15. J. LaSalle and S. Lefschetz, "Stability by Liapunov's Direct Method with Applications," Academic Press, New York, 1961.
16. R. Laxminarayan, Act now or later? Economics of malaria resistance, Am. J. Trop. Med. Hyg., 71 (Suppl. 2) (2004), 187-197.
17. M. J. Mackinnon, Survival probability of drug resistant mutants in malaria parasites, Proc. R. Soc. Lond. B, 264 (1997), 53-59.
18. R. Ross, An application of the theory of probabilities to the study of a priori pathometry I, Proc. Roy. Soc. A, 92 (1916), 204-230.
19. H. C. Spencer, Epidemiology of malaria, in "Clinics in Tropical Medicine and Communicable Diseases," Vol.1, W. B. Saunders Company, (1986), 1-28.
20. W. H. Wernsdorfer, Epidemiology of drug resistance in malaria, Acta Tropica, 56 (1994), 143-156.
21. WHO, "World Malaria Report 2005," WHO & UNICEF, Geneva, 2005.