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Pertsev, N. V.; Pichugin, B. Yu.; Loginov, K. K.

Stochastic analog of the dynamic model of HIV-1 infection described by delay differential equations. (Russian, English) Zbl 1438.34305

Sib. Zh. Ind. Mat. 22, No. 1, 74-89 (2019); translation in J. Appl. Ind. Math. 13, No. 1, 103-117 (2019).
Summary: Some deterministic and stochastic models are constructed basing on the same assumptions about the dynamics of HIV-1 infection. The deterministic model has the form of a system of differential equations with three delays. The stochastic model is based on a branching process with the interaction of particles and takes into account the stages of maturation of cells and virions. The durations of these stages correspond to the parameters describing the delays in the deterministic model. The influence of discreteness of stochastic model variables on the dynamics of HIV-1 infection is demonstrated. We find coinciding and significantly different conditions of HIV-1 infection elimination in the framework of deterministic and stochastic models.

Cited in 5 Documents

MSC:

34K60 Qualitative investigation and simulation of models involving functional-differential equations
92C60 Medical epidemiology
34K50 Stochastic functional-differential equations

Keywords:

HIV-1 infection; delay differential equation; branching process with interaction and immigration of particles; Monte Carlo method; basic reproductive number
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References:

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