MATHEMATICAL MODELLING AND ANALYSIS OF THE SPREAD OF AIDS CAUSED BY COINFECTION OF HIV WITH TB

Raghaw Shukla; Vivek Kumar

MATHEMATICAL MODELLING AND ANALYSIS OF THE SPREAD OF AIDS CAUSED BY COINFECTION OF HIV WITH TB

Raghaw Shukla¹*, Vivek Kumar²
¹Department of Applied Mathematics, Prabhat Engineering College, Kanpur
²Department of Applied Mathematics, Krishna Girls Engineering College, Kanpur
* Corresponding Author : raghawshukla79@gmail.com

Received : - Accepted : - Published : 21-12-2009
Volume : 1 Issue : 2 Pages : 1 - 14
Int J Syst Biol 1.2 (2009):1-14

Conflict of Interest : None declared

Cite - MLA : Raghaw Shukla and Vivek Kumar "MATHEMATICAL MODELLING AND ANALYSIS OF THE SPREAD OF AIDS CAUSED BY COINFECTION OF HIV WITH TB." International Journal of Systems Biology 1.2 (2009):1-14.

Cite - APA : Raghaw Shukla, Vivek Kumar (2009). MATHEMATICAL MODELLING AND ANALYSIS OF THE SPREAD OF AIDS CAUSED BY COINFECTION OF HIV WITH TB. International Journal of Systems Biology, 1 (2), 1-14.

Cite - Chicago : Raghaw Shukla and Vivek Kumar "MATHEMATICAL MODELLING AND ANALYSIS OF THE SPREAD OF AIDS CAUSED BY COINFECTION OF HIV WITH TB." International Journal of Systems Biology 1, no. 2 (2009):1-14.

Copyright : © 2009, Raghaw Shukla and Vivek Kumar, Published by Bioinfo Publications. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution and reproduction in any medium, provided the original author and source are credited.

Abstract

A combined SIS-SIRS model with migration for the spread of AIDS caused in co- infection involving TB and HIV is proposed in this manuscript. In mathematical modeling, the problem is assumed that an HIV infected individual intract with TB infected person (the former to have HIV & TB). It was assumed further that a fraction of this HIV class becomes AIDS patients. It is also considered that a certain fraction of TB interced person form a reservoir class, a part of which may recover and becomes susceptible again. The model is analysed by using stability theory of differential equation. It was found that AIDS epidemic spread faster due to co- infection of HIV with T.B.

References

[1] Fuzzi, et al. (1996) Journal of Biological Mathematics, 37, p 371-375
» CrossRef » Google Scholar » PubMed » DOAJ » CAS » Scopus

[2] Dufar (1982) Journal of Biological Mathematics, 37, 391-393.
» CrossRef » Google Scholar » PubMed » DOAJ » CAS » Scopus

[3] Waltman and Hethcote(1974) Journal of Biological Mathematics, 39, 381-398
» CrossRef » Google Scholar » PubMed » DOAJ » CAS » Scopus

[4] Shukla J.B. (1987) Journal of Biological Mathematics, 23, 121-131
» CrossRef » Google Scholar » PubMed » DOAJ » CAS » Scopus

[5] Cooke,1979,Marc and Hethcote,1976Gonzalez,Guzman,1989] Journal of Biological Mathematics
» CrossRef » Google Scholar » PubMed » DOAJ » CAS » Scopus

[6] Ramkrishnan and Chandrashekhar (1999) Journal of Biological Mathematics, p 232-238
» CrossRef » Google Scholar » PubMed » DOAJ » CAS » Scopus

[7] May Anderson (1987) Journal of Biological Mathematics, 54-65
» CrossRef » Google Scholar » PubMed » DOAJ » CAS » Scopus

[8] Anderson R.M., May R.M., Nature (1979) Journal of Biological Mathematics, 280, 361-367
» CrossRef » Google Scholar » PubMed » DOAJ » CAS » Scopus

[9] Anderson R.M., May R.M ., Trans. Roy. Phil. Soc. Series (1981) Journal of Biological Mathematics,B 291, 451-524
» CrossRef » Google Scholar » PubMed » DOAJ » CAS » Scopus

[10] Bailey N.T. (1980) Journal of Biological Mathematics, 38, 233-261
» CrossRef » Google Scholar » PubMed » DOAJ » CAS » Scopus

[11] Cooke K.L. and Yorke (1979) Journal of Biological Mathematics, 124-129
» CrossRef » Google Scholar » PubMed » DOAJ » CAS » Scopus

[12] Hethcote H.W35 (1973) Journal of Biological Mathematics, 607-614
» CrossRef » Google Scholar » PubMed » DOAJ » CAS » Scopus

[13] Blower Sally M. Mclean, Angela, Poroco, Travis C, Peterm Hpoewell, Philip C, sanchez, Melissa A, and Moss, Andrew R.Moss (1995) Journal of Biological Mathematics, 35 , 231-254
» CrossRef » Google Scholar » PubMed » DOAJ » CAS » Scopus

[14] Blower S.M ,Small P.M. and P.C. Hopewell P.C. (1996) Journal of Biological Mathematics, 43, 23-45
» CrossRef » Google Scholar » PubMed » DOAJ » CAS » Scopus

[15] Blower S.M ,Small P.M. and P.C. Hopewell P.C. (1996) Journal of Biological Mathematics, 43, 23-45
» CrossRef » Google Scholar » PubMed » DOAJ » CAS » Scopus

[16] Daley Z, and sally M.Blower (2001) Journal of Biological Mathematics, 67, 381-385
» CrossRef » Google Scholar » PubMed » DOAJ » CAS » Scopus

[17] Anderson R.M. and May R.M. (1986) Journal of Biological Mathematics, vol. 134, 533-570
» CrossRef » Google Scholar » PubMed » DOAJ » CAS » Scopus

[18] Anderson R.M. (1988a) Journal of Biological Mathematics, 151, 66-93
» CrossRef » Google Scholar » PubMed » DOAJ » CAS » Scopus

[19] Anderson R.M. (1988) Journal of Biological Mathematics, 1, 241-256
» CrossRef » Google Scholar » PubMed » DOAJ » CAS » Scopus

[20] Hethcote H.W. (1987) Journal of Biological Mathematics, 28, 54-78.
» CrossRef » Google Scholar » PubMed » DOAJ » CAS » Scopus

[21] May R.M. (1988) Journal of Biological Mathematics, l331, 665-66
» CrossRef » Google Scholar » PubMed » DOAJ » CAS » Scopus

[22] Pickering J.,Wiley-J Padion N.S.et al. (1986) Journal of Biological Mathematics, 7, 671-698.
» CrossRef » Google Scholar » PubMed » DOAJ » CAS » Scopus

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