Geodesic
Stochastic analog of the dynamic model of HIV-1 infection described by delay differential equations
Sibirskij žurnal industrialʹnoj matematiki, Tome 22 (2019) no. 1, pp. 74-89

Voir la notice de l'article provenant de la source Math-Net.Ru

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 the coinciding and significantly different conditions of HIV-1 infection elimination in the framework of deterministic and stochastic models.
Mots-clés : HIV-1 infection
Keywords: delay differential equation, branching process with interaction and immigration of particles, Monte-Carlo method, basic reproductive number. 
@article{SJIM_2019_22_1_a7,
     author = {N. V. Pertsev and B. Yu. Pichugin and K. K. Loginov},
     title = {Stochastic analog of the dynamic model of {HIV-1} infection described by delay differential equations},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {74--89},
     publisher = {mathdoc},
     volume = {22},
     number = {1},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2019_22_1_a7/}
}
TY  - JOUR
AU  - N. V. Pertsev
AU  - B. Yu. Pichugin
AU  - K. K. Loginov
TI  - Stochastic analog of the dynamic model of HIV-1 infection described by delay differential equations
JO  - Sibirskij žurnal industrialʹnoj matematiki
PY  - 2019
SP  - 74
EP  - 89
VL  - 22
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJIM_2019_22_1_a7/
LA  - ru
ID  - SJIM_2019_22_1_a7
ER  - 
%0 Journal Article
%A N. V. Pertsev
%A B. Yu. Pichugin
%A K. K. Loginov
%T Stochastic analog of the dynamic model of HIV-1 infection described by delay differential equations
%J Sibirskij žurnal industrialʹnoj matematiki
%D 2019
%P 74-89
%V 22
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJIM_2019_22_1_a7/
%G ru
%F SJIM_2019_22_1_a7
N. V. Pertsev; B. Yu. Pichugin; K. K. Loginov. Stochastic analog of the dynamic model of HIV-1 infection described by delay differential equations. Sibirskij žurnal industrialʹnoj matematiki, Tome 22 (2019) no. 1, pp. 74-89. http://geodesic.mathdoc.fr/item/SJIM_2019_22_1_a7/