IJTEEE
International Journal of Technology Enhancements and Emerging Engineering Research (ISSN 2347-4289)
PREVIOUS PUBLICATIONS



IJTEEE >> Volume 2 - Issue 7, July 2014 Edition



International Journal of Technology Enhancements and Emerging Engineering Research  
International Journal of Technology Enhancements and Emerging Engineering Research

Website: http://www.ijteee.org

ISSN 2347-4289



The Effect Of External Source Of Disease On The HIV\ Aids Model With Bifurcation

[Full Text]

 

AUTHOR(S)

Ahmed A. Muhseen

 

KEYWORDS

Keywords: Epidemic models, Stability, HIV\AIDS, external sources, Local bifurcation.

 

ABSTRACT

ABSTRACT: In this paper a mathematical model that describes the spread of sexual infectious disease in a population is proposed and studied. It is assumed that the disease divided the population into four classes: susceptible individuals of males (S), infected individuals of males (I), susceptible individuals of females and infected individuals of females . The impact of contact between of population and external sources of disease for example (blood and other), on the dynamics of epidemic model is investigated. The existence, uniqueness and boundedness of the solution of the model are discussed. The local and global stability of the model is studied. The occurrence of local bifurcation in the model is investigated. Finally the global dynamics of the proposed model is studied numerically.

 

REFERENCES

[1] Roxana Lopez, (May 2006). Structured SI Epidemic Model With Application To HIV Epidemic, Arizona State University.

[2] Cooke K.L. and Yorke J.A., (1973). Some equations modelling growth processes and gonorrhea epidemics, Math Biosciences 16, 75101.
[3] Lajmanovich A. and Yorke J.A., (1976). A deterministic model for gonorrhea in a nonhomogeneous population Math. Biosciences 28, 221-236.

[4] Knox, E. G., (1986). A transmission model for AIDS, European J. Epidemiol. 2:165-177.


[5] Anderson, R. M., Medley, G., May, F.R. M. and Johnson, A., (1986). M. A preliminary study of the transmission dynamics of the human immunodeficiency virus (HIV), the causative agent of AIDS, IMA J. Math. Appl. Med. Biol. 3 229-263.

[6] Anderson, R. M., (1988). The role of mathematical models in the study of HIV transmission and the epidemiology of AIDS, J. AIDS 1:214-256.

[7] Dietz, K., Heesterbeek, J. A. P., Tudor, D.W., (1993). The Basic Reproduction Ratio for Sexually Transmitted Diseases Part 2. Effects of Variable HIV Infectivity, Mathematical Biosciences 117:35-47.

[8] Dietz, K., (1988). On the Transmission Dynamics of HIV, Mathematical Biosciences 90:397-414.

[9] Brauer, F. and Castillo-Chavez, C., (2001). Mathematical Models in Population Biology and Epidemiology, Text in Applied Mathematics Vol 40, Springer Verlag.

[10] Levin, B.R., Bull, J.J. and Stewart, F.M., (2001). Epidemiology, Evolution, and Future of the HIV/AIDS Pandemic, Vol. 7, No. 3 Supplement, June.

[11] Hirsch, M. W. and Smale, S. (1974). Differential Equation, Dynamical System, and Linear Algebra. Academic Press, Inc., New York. p 169-170.

[12] Wiggins S., (1990). Introduction to applied nonlinear dynamical system and chaos, Springer-Verlag New York, Inc.

[13] Sotomayor, J., (1973). “Generic bifurcations of dynamical systems, in dynamical systems”, M., M., Peixoto, New York, academic press.