Abstract
In this paper we propose a model of HIV population through method of phases with non-Markovian evolution of immigration. The analysis leads to an explicit differential equations for the generating functions of the total population size. The detection process of antibodies (against the antigen of virus) is analysed and an explicit expression for the correlation functions are provided. A measure of bunching is also introduced for some particular choice of parameters.
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References
Anderson, R.M.,Population dynamics of infectious diseases, Chafman and Hall, London 1982.
Bailey, N.T.J.,The Mathematical theory of infectious diseases, Griffin: London, 1975.
Bailey, N.T.J.,The role of statistics in controlling and eradicating infectious diseases, Statistician 34 (1985), 3–17.
Bailey, N.T.J.,Macro modelling and predcition of epidemic spread at community level, Math Modelling, 7 (1986), 689–717.
Bartlett, M.S.,Stochastic Processes, 2nd edition (Cambridge University Press, Cambridge) 1966.
Dietz, K. and Schenzle, D.,Mathematical models for infectious disease statistics. In a celebration of statistics (Editors A.C. Atkinson and S.K. Fienberg), Springer, New York (1985), 167–204.
Harris, T.E.,Theory of Branching Process (Springer: Berlin) 1963.
Isham, V.,Mathematical modelling of the transmission dynamics of HIV infection and AIDS, a review, JRSS (1987), 5–23.
Kendall, D.G.,Stochastic Processes and Population Growth, J.R. Statistics Society, B-11, pp 230–264, 1949.
Sridharan, V. and Jayashree P.R.,A Model of HIV population to seropositivity. accepted in Korean J. Comput. and Appl. Math. (in press)
Srinivasan, S.K.,Stochastic point process and their applications, (Griffin: London), 1974.
Srinivasan, S.K.,Point process models of cavity radiation and detection, Charles Griffin and Co. Ltd., 1988.
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Sridharan, V., Jayashree, P.R. A non-Markovian evolution model of HIV population with bunching behaviour. Korean J. Comput. & Appl. Math. 5, 695–705 (1998). https://doi.org/10.1007/BF03008892
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DOI: https://doi.org/10.1007/BF03008892