AIDS Epidemic Modeling With Different Demographic Structures
Subject Areas : linear ProgrammingAgraj Tripathi 1 , Ram Naresh 2
1 - Department of Mathematics, Bhabha Institute of Technology,
Kanpur-209204, India
2 - Department of Mathematics, Harcourt Butler Technological Institute,
Kanpur-208002, India
Keywords:
Abstract :
[1] Anderson R. M., and May R. M., Population biology of infectious diseases I, Nature,180, 361-379, 1979.
[2] Anderson R. M., Jackson H. C., May R.M., and Smith A. D. M., Population dynamics of fox rabies in Europe. Nature, 289, 765-777, 1981.
[3] Bailey N. T.J., The mathematical theory of infectious diseases (2nd ed.). Macmillan, New York, 1975.
[4] Birkhoff G., and Rota G. C., Ordinary differential equations, Ginn (1982).
[5] Brauer F., and van den Driessche P., Models for transmission of disease with immigration of infectives. Math. Biosci., 171, 143-154, 2001.
[6] Brauer F., Models for the spread of universally fatal diseases. J. Math. Biol., 28, 451-462, 1990.
[7] Bremermann H. J., and Thieme H. R., A competitive exclusion principle for pathogen virulence. J. Math. Biol., 27, 179-190, 1989.
[8] Busenberg S. N., and Hadeler K.P., Demography and epidemics. Math. Biosci., 101, 41-62, 1990.
[9] Busenberg S. N., and van den Driessche P., Analysis of a disease transmission model in a population with varying size. J. Math. Biol., 28, 257-270, 1990.
[10] Fan M., Li M. Y., and Wang K., Global stability of an SEIS epidemic model with recruitment and varying total population size. Math. Biosci., 170, 199-208, 2001.
[11] Gao L. Q., and Hethcote H. W., Disease transmission models with density dependent demographics. J. Math. Biol., 30, 717-731, 1992.
[12] Hyman J. M., and Stanley E. A., Using mathematical models to understand the AIDS epidemic. Math. Biosci., 90, 415-473, 1988.
[13] Jacquez J. A., Simon C. P., Koopman J., Sattenspiel L., and Perry T., Modeling and analyzing HIV transmission: The effect of contact patterns. Math. Biosci., 92, 119-199, 1988.
[14] Kribs-Zaleta C. M., Lee M., Roman C., Wiley S., and Hernandez-Suarez C. M., The effect of the HIV/AIDS epidemic on Africa’s truck drivers. Math. Biosci. Eng., 2, 771-788, 2005.
[15] Massad E., A homogeneously mixing population model for the AIDS epidemic. Math. Comp. Model., 12, 89-96, 1989.
[16] May R. M., and Anderson R. M., Population biology of infectious diseases II. Nature, 280, 455-461, 1979.
[17] May R. M., and Anderson R. M., Transmission dynamics of HIV infection. Nature, 3426, 137-142, 1987.
[18] May R. M., Anderson R. M., and McLean A. R., Possible demographic consequences of HIV/AIDS epidemics. Math. Biosci., (1988), 90, 475-505.
[19] Mena-Lorca J., and Hethcote H. W., Dynamic models of infectious diseases as regulators of population size. J. Math. Biol., 30, 693-716, 1992.
[20] Naresh R., and Tripathi A., Modeling and analysis of HIV-TB co-infection in a variable size population. Math. Model. Anal., 10, 275-286, 2005.
[21] Naresh R., Omar S., and Tripathi A., Modelling and analysis of HIV/AIDS in a variable size population. Far East J. Appl. Math., 18, 345-360, 2005.
[22] Naresh R., Tripathi A., and Omar S., Modelling the spread of AIDS epidemic with vertical transmission. Appl. Math. Comp., 178, 262-272, 2006.
[23] National AIDS Control Organisation: Country Scenario AIDS, Published by NACO, Ministry of Health, Govt. of India, New Delhi, 2006.
[24] Pugliese A., Population models for disease with no recovery. J. Math. Biol., 28, 65-82, 1990.
[25] Tripathi A., Naresh R., and Sharma D., Modelling the effect of screening of unaware infectives on the spread of HIV infection. Appl. Math. Comp., 184, 1053-1068, 2007.