• Journal of the Korean Statistical Society
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• v.35 no.4
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• pp.397-407
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• 2006

A new stochastic process is introduced for describing a mechanism of viruses. The process generalizes the $Bartoszy\'{n}ski's$ process ($Bartoszy\'{n}ski$, 1975a, 1975b, 1976) by allowing the stochastic perturbation between consecutive jumps to take into account the persistent infection (the infection without breaking infected cells). It is shown that the new process can be obtained by a weak limit of a sequence of Markov branching processes. Along with the construction of the new process, we study how the stochastic perturbation influences the risk of a symptom in an infected host. For this purpose, the quantal response model and the threshold model are investigated and compared through their induced survival functions.

• The Mathematical Education
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• v.27 no.1
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• pp.55-60
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• 1988