| Issue |
ITM Web Conf.
Volume 31, 2020
International Conference “Mathematical Modelling in Biomedicine” 2019
|
|
|---|---|---|
| Article Number | 02003 | |
| Number of page(s) | 12 | |
| Section | Disease Modelling | |
| DOI | https://doi.org/10.1051/itmconf/20203102003 | |
| Published online | 09 March 2020 | |
Stochastic compartmental model of HIV-1 infection
Sobolev Institute of Mathematics, Siberian Branch of RAS, Omsk Department; 13 Pevtsova avenue, 644043, Omsk, Russia.
∗ e-mail: kloginov85@mail.ru
∗∗ e-mail: homlab@ya.ru
Stochastic model of the dynamics of HIV-1 infection describing the interaction of target cells and viral particles in the lymphatic nodes and their movement between the lymphatic nodes is constructed. The lymphatic system is represented as a graph, vertices of which are the lymphatic nodes and edges are the lymphatic vessels. The novelty of the model consists in the description of populations of cells and viral particles in terms of a multidimensional birth and death process with the random point-distributions. The random pointdistributions describe the duration of the transition of cells and viral particles between the lymph nodes and the duration of the stages of their development. The durations of transitions of viral particles and cells between the lymphatic nodes are not random and based on the rate of lymph flow. The durations of the developmental stages of infected target cells are assume to be constant. The graph theory for the formalization and compact representation of the model is used. An algorithm for modelling the dynamics of the studied populations is constructed basing on the Monte-Carlo method. The results of computational experiments for a system consisting of five lymphatic nodes are presented.
© The Authors, published by EDP Sciences, 2020
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