No Access

ANALYSIS OF A VECTOR-HOST MALARIA MODEL WITH IMPULSIVE EFFECT AND INFECTION-AGE

HELONG LIU

Department of Mathematics, Xinyang Teachers College, Xinyang, Henan, 464000, China

Beijing Institute of Information and Control, Beijing, 100037, China

Search for more papers by this author

JINGYUAN YU

Beijing Institute of Information and Control, Beijing, 100037, China

Search for more papers by this author

, and

GUANGTIAN ZHU

Academy of Mathematics and System Science, C.A.S., Beijing, 100080, China

Search for more papers by this author

https://doi.org/10.1142/S0219525906000720Cited by:7 (Source: Crossref)

Abstract

In this paper, we develop a mathematical model for malaria with impulsive effect and infection-age, and consider the effect of blood transfusion and infected vector transmission. We derive the condition under which malaria goes to extinction.

Keywords:

References

WHO, Malaria fact sheets, available from http://www.who.int/inf-fs/en/fact094.html (1998) . Google Scholar
Malaria foundation, Malaria: Background information, available from http://www.malaria.org/backgroundinfo.html (1998) . Google Scholar
J. H. Pollard , Mathematical Models for the Growth of Human Population ( Cambridge University Press , 1973 ) . Google Scholar
R. M. Anderson and R. M. May , Infectious Diseases of Humans ( Oxford University Press , 1991 ) . Crossref, Google Scholar
Bradley, T., Malaria and drug resistance, MBCHB Special Study Module Project Report, Department of Microbiology and Immunology, University of Leicester, avallable from http://www-micro.msb.le.ac.uk/224/Bradley/Bradely.html (1996) . Google Scholar
W. H. Wernsdorfer , Malaria, Vol. 1: Epidemiology, Chemotherapy, Morphology and Metabolism , ed. J. P. Kreier ( Academic Press , New York , 1980 ) . Google Scholar
H. Inaba and H. Sekine, Math. Biosci. 190(1), 39 (2004). Crossref, Web of Science, Google Scholar
Z. Fenget al., Math. Biosci 189, 1 (2004). Crossref, Web of Science, Google Scholar
Z. Aguret al., Proc. Natl. Acad. Sci. USA 90, 11698 (1993). Crossref, Web of Science, Google Scholar
B. Shugin, L. Stone and Z. Agur, Bull. Math. Biol. 60, 1 (1998). Web of Science, Google Scholar
A. D'Onofrio, Math. Biosci. 179, 57 (2002). Crossref, Web of Science, Google Scholar
Y. Zhou and H. Liu, Math. Comp. Model. 38, 299 (2003). Crossref, Web of Science, Google Scholar
M. Martcheva and H. R. Thieme, J. Math. Biol. 46, 385 (2003). Crossref, Web of Science, Google Scholar
G. F. Webb , Theory of Nonlinear Age-Dependent Population Dynamics ( Marcel Dekker , New York , 1985 ) . Google Scholar
Z. Feng, M. Iannelli and F. A. Milner, SIAM. Appl. Math. 62(5), 1634 (2002). Crossref, Web of Science, Google Scholar
H. W. Hethcote, SIAM Rev. 42(2), 599 (2000). Crossref, Web of Science, Google Scholar