A non-Markovian evolution model of HIV population with bunching behaviour
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.
AMS Mathematics Subject Classification60G55
Key word and phrasesBunching detection process generating functions immigrations methods of phases moments non-Markov evolution stationarity
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- 1.Anderson, R.M.,Population dynamics of infectious diseases, Chafman and Hall, London 1982.Google Scholar
- 6.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.Google Scholar
- 7.Harris, T.E.,Theory of Branching Process (Springer: Berlin) 1963.Google Scholar
- 8.Isham, V.,Mathematical modelling of the transmission dynamics of HIV infection and AIDS, a review, JRSS (1987), 5–23.Google Scholar
- 10.Sridharan, V. and Jayashree P.R.,A Model of HIV population to seropositivity. accepted in Korean J. Comput. and Appl. Math. (in press)Google Scholar
- 11.Srinivasan, S.K.,Stochastic point process and their applications, (Griffin: London), 1974.Google Scholar
- 12.Srinivasan, S.K.,Point process models of cavity radiation and detection, Charles Griffin and Co. Ltd., 1988.Google Scholar