A mathematical model for the dynamics of malaria in a human host and mosquito vector with temporary immunity

Applied Mathematics and Computation

Volumn 189, Issue 2, 2007, Pages 1953-1965

  Tumwiine, J ^a   Mugisha, J Y T ^b   Luboobi, L S ^b  

^a MBARARA UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Uganda)

^b MAKERERE UNIVERSITY   (Uganda)

Author keywords

Compound matrices; Immunity; Reproduction number; Stability

Indexed keywords

ASYMPTOTIC STABILITY; IMMUNIZATION; MATHEMATICAL MODELS; SYSTEM STABILITY;

COMPOUND MATRICES; DISEASE-FREE EQUILIBRIUM POINT; ENDEMIC EQUILIBRIUM; REPRODUCTION NUMBER; VERTICAL TRANSMISSION;

MALARIA CONTROL;

EID: 34249096551     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2006.12.084     Document Type: Article

References (30)

1. Anderson R.M., and May R.M. Infectious Diseases of Humans: Dynamics and Control (1991), Oxford University Press, Oxford
2. Aron J.L., and May R.M. The population dynamics of malaria. In: Anderson R.M. (Ed). The Population Dynamics of Infectious Diseases: The Theory and Applications (1982), Chapman and Hall, London 139-179
3. Aron J.L. Acquired immunity dependent upon exposure in an SIRS epidemic model. Mathematical Biosciences 88 (1988) 37-47
4. Aron J.L. Mathematical modelling of immunity to malaria. Mathematical Biosciences 90 (1988) 385-396
5. Bailey N.T.J. The Biomathematics of Malaria (1982), Charles Griff, London
6. Ghosh A.K., Chattopadhyay J., and Tapaswi P.K. Immunity boosted by low exposure to infection in an SIRS model. Ecological Modelling 87 (1996) 227-233
7. Hale J.K. Ordinary Differential Equations (1969), John Wiley, New York
8. Hethcote H.W. The Mathematics of Infectious diseases (2000), SIAM
9. Hethcote H.W. Qualitative analysis of communicable disease models. Mathematical Biosciences 28 (1976) 335-356
10. Hirsch M.W. Systems of differential equations that are competitive or cooperative. V. Convergence in 3-dimensional systems. Journal of Differential Equations 80 (1989) 94-106
11. Hirsch M.W. Systems of differential equations which are competitive or cooperative. IV. Structural stability in 3-dimensional systems. SIAM Journal on Mathematical Analysis 21 (1990) 1225-1234
12. Hviid P. Natural acquired immunity to Plasmodium falciparum malaria in Africa. Acta Tropica 95 (2005) 265-269
13. Levins R., Awerbuch T., Eckardt U., Brinkman I., Epstein P., Makhoul N., Albuquerque de Posas C., Puccia C., Spielman A., and Wilson M. The emergence of new diseases. American Scientist 82 (1994) 85-118
14. Li M.Y., Graef J.R., Wang L., and Karsai J. Global stability for the SEIR model with varying total population size. Mathematical Biosciences 160 (1999) 191-213
15. Li M.Y., and Mouldowney J.S. Global stability for the SEIR model in epidemiology. Mathematical Biosciences 125 (1995) 155-164
16. Macdonald G. The Epidemiology and Control of Malaria (1957), Oxford university press, Oxford
17. Marsh K., Otoo L., and Hayes R.H. Antibodies to blood stages antigens of Plasmodium falciparum in rural Gambians and their relationship to protection against infection. Transactions of the Royal Society of Tropical Medicine and Hygiene 83 (1989) 293-303
18. McCluskey C.C., and van den Driessche P. Global analysis of tuberclosis models. Journal of Differential Equations 16 (2004) 139-166
19. Mouldowney J.S. Compound matrices and ordinary differential equations. Rocky Mountain Journal of Mathematics 20 (1990) 857-872
20. Ngwa G.A., and Shu W.S. A mathematical model for endemic malaria with variable human and mosquito populations. Mathematics and Computer Modelling 32 (2000) 747-763
21. Olumese P. Epidemiology and surveillance: changing the global picture of malaria-myth or reality?. Acta Tropica 95 (2005) 265-269
22. Ross R. The Prevention of Malaria (1911), Murry, London
23. Sachs J.D. A new global effort to control malaria. Science 298 (2002) 122-124
24. Smith H.L. Monotone dynamical systems. An introduction to the theory of competitive and cooperative systems. Mathematical surveys and Monographs vol. 104 (1995), American Mathematical Society 231-240
25. Smith H.L. Systems of differential equations which generate an order preserving flow. SIAM Review 30 (1988) 87-113
26. Snow R.W., Guerra C.A., Noor A.M., Myint H.Y., and Hay S.I. The global distribution of clinical episodes of Plasmodium falciparum. Nature 434 (2005) 214-217
27. Tumwiine J., Luboobi L.S., and Mugisha J.Y.T. Modelling the effect of treatment and mosquitoes control on malaria transmission. International Journal of Management and Systems 21 2 (2005) 107-124
28. World Health Organization, World malaria report 2005. Geneva. World Health Organization. WHO/HAM/MAL/2005.1102, 2005.
29. World Health Organization. Malaria - A global crisis, Geneva, 2000.
30. Gratz N.G. Emerging and resulting vector-borne diseases. Annual Review of Entomology 44 (1999) 51-75