Qualitative study of transmission dynamics of drug-resistant malaria

Mathematical and Computer Modelling

Volumn 50, Issue 3-4, 2009, Pages 611-630

  Esteva, Lourdes ^a   Gumel, Abba B ^b   de León, Cruz Vargas ^a  

^a UNIVERSIDAD NACIONAL AUTÓNOMA DE MÉXICO   (Mexico)

^b UNIVERSITY OF MANITOBA   (Canada)

Author keywords

Antimalarial drugs; Equilibria; Malaria; Reproduction number; Stability; Wild resistant strain

Indexed keywords

ANTIMALARIAL DRUGS; EQUILIBRIA; MALARIA; REPRODUCTION NUMBER; WILD/RESISTANT STRAIN;

ASYMPTOTIC ANALYSIS; DIFFERENTIAL EQUATIONS; DYNAMICS; IMPACT RESISTANCE; LYAPUNOV FUNCTIONS; STRUCTURES (BUILT OBJECTS);

STRAIN RATE;

EID: 67549106637     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mcm.2009.02.012     Document Type: Article

References (31)

1. World Health Organization, WHO Expert Committee on Malaria, 20th Report. WHO Regional Office of Africa, 2003
2. P.B. Bloland, Drug Resistance in Malaria. WHO/CDS/CSR/DRS/2001.4, Geneva, 2001
3. Schapira A., Beales P.F., and Halloran M.E. Malaria: Living with drug resistance. Parasitol. Today 9 (1993) 168-174
4. Abuako B.K., Koram K.A., and Binka F.N. Antimalarial drug use among caregivers in Ghana. African Health Sci. 4 (2004) 171-177
5. R. Ross, in: John Murray, (Ed.) The Prevention of Malaria, London, 1911
6. Aron J.L., and May R.M. The Population Dynamics of Malaria. In: Anderson R.M. (Ed). Population Dynamics of Infectious Diseases (1982), Chapman and Hall, London 139-179
7. Chitnis N., Cushing J.M., and Hyman J.M. Bifurcation analysis of a mathematical model for malaria transmission. SIAM J. Appl. Math. 67 (2006) 24-45
8. Chiyaca C., Garira W., and Dube S. Transmission model of endemic human malaria in a partially immune population. Math. Comput. Modelling 46 (2007) 806-822
9. Dietz K. Mathematical Models for Transmission and Control of Malaria. In: Wensdorfer W.H., and McGregor I. (Eds). Malaria (1988), Churchill Livingstone, Edinburgh 1091-1133
10. Feng Z., Yinfei Y., and Zhu H. Fast and slow dynamics of malaria and the s-gene frequency. J. Dynam. Differential Equations 16 (2004) 869-895
11. Smith T., Killen G.F., Maire N., Ross A., Molineaux L., Tediosi F., Hutton G., Utzinger J., Dietz K., and Tanner M. Mathematical modelling of the impact of malaria vaccines on the clinical epidemiology and natural history of Plasmodium falciparum malaria: Overview. Am. J. Trop. Med. Hyg. 75 (2006) 1-10
12. Hastings I.M. A model for the origins and spread of drug resistant malaria. Parasitol. 115 (1997) 133-141
13. Mackinnon M.J. Drug resistance models for malaria. Acta Trop. 94 (2005) 207-217
14. Aneke S.J. Mathematical modelling of drug resistant malaria parasites and vector populations. Math. Meth. Appl. Sci. 25 (2002) 335-346
15. Koella J.C., and Antia R. Epidemiological models for the spread of antimalarial resistance. Malaria J. 2 (2003) 3
16. Bacaer N., and Sokna C. A reaction-diffusion system modeling the spread of resistance to an antimalarial drug. Math. Biosci. Eng. 2 (2005) 227-238
17. Pan American Health Organization. Annual Malaria Cases and Deaths in the Americas 1998-2006. http://www.paho.org/English/AD/DPC/CD/mal-cases-deaths-1998-2006.pdf (accessed: December 2007)
18. Diekmann O., and Heesterbeek J.A.P. Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation (2000), Wiley, New York
19. van den Driessche P., and Watmough J. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math. Biosci. 180 (2002) 29-48
20. Hethcote H.W. The mathematics of infectious diseases. SIAM Rev. 42 4 (2000) 599-653
21. Lashmikantham V., Leela S., and Martynyuk A.A. Stability Analysis of Nonlinear Systems (1989), Marcel Dekker, Inc., New York and Basel
22. Dushoff J., Huang W., and Castillo-Chavez C. Backwards bifurcations and catastrophe in simple models of fatal diseases. J. Math. Biol. 36 (1998) 227-248
23. Garba S.M., Gumel A.B., and Abu Bakar M.R. Backward bifurcation in dengue transmission dynamics. Math. Biosci. 215 1 (2008) 11-25
24. Gumel A.B., and Song B. Existence of multiple-stable equilibria for a multi-drug-resistant model of mycobacterium tuberculosis. Math. Biosci. Eng. 5 3 (2008) 437-455
25. Sharomi O., Podder C.N., Gumel A.B., Elbasha E.H., and Watmough J. Role of incidence function in vaccine-induced backward bifurcation in some HIV models. Math. Biosci. 210 (2007) 436-463
26. C.L.J. Bruce, Chemotheraphy of Malaria. WHO Technical Report Series No. 27. World Health Organization, Geneva, 1986
27. Ishikawa H., Ishii A., Nagai N., Ohmae H., Harada M., Suguri S., and Leafasia J. A mathematical model for the transmission of Plasmodium vivax malaria. Parasitol. Internat. 52 (2003) 81-93
28. Hale J.K. Ordinary Differential Equations (1980), Krieger Publishing, Florida
29. Esteva L., and Vargas C. Influence of vertical and mechanical transmission on the dynamics of dengue disease. Math. Biosci. 167 (2000) 51-64
30. Hethcote H.W., and Thieme H.R. Stability of the endemic equilibrium in epidemic models with subpopulations. Math. Biosci. 75 (1985) 205-227
31. Thieme H.R. In: Capasso V., Grosso E., and Paveri-Fontana S.L. (Eds). Local Stability in Epidemic Models for Heterogenous Populations. Lecture Notes in Biomathematics vol. 57 (1985), Springer 185-189