HIV population is modelled as a point process with a time-dependent birth rate. A method of phases is introduced to analyse special types of time-dependencies. The conditional life time of HIV population is assumed to be hypothetical in phases, the life span of the process being distributed independently and exponentially. The analysis leads to an explicit differential equations for generating functions of the population size. The detection process of the antibodies (against the antigen of the virus) is analysed and an explicit expression for the correlation functions are also provided. The same model is attacked by using the product density approach which leads to the same result. Finally, some applications to the product density approach are given.
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Sridharan, V., Jayashree, P.R. A model of HIV population to seropositivity. Korean J. Comput. & Appl. Math. 5, 259–269 (1998). https://doi.org/10.1007/BF03008912
AMS Mathematics Subject Classification
Key word and phrases
- Detection process
- generating functions
- method of phases
- product densities