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Modelling Stochastic and Deterministic Behaviours in Virus Infection Dynamics

I. Sazonov, D. Grebennikov, M. Kelbert, G. Bocharov, Igor Sazonov Orcid Logo

Mathematical Modelling of Natural Phenomena, Volume: 12, Issue: 5, Pages: 63 - 77

Swansea University Author: Igor Sazonov Orcid Logo

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DOI (Published version): 10.1051/mmnp/201712505

Abstract

Many human infections with viruses such as human immunodeficiency virus type 1 (HIV--1) are characterized by low numbers of founder viruses for which the random effects and discrete nature of populations have a strong effect on the dynamics, e.g., extinction versus spread. It remains to be establish...

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Published in: Mathematical Modelling of Natural Phenomena
ISSN: 1760-6101
Published: 2017
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URI: https://cronfa.swan.ac.uk/Record/cronfa36270
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last_indexed 2018-02-09T05:28:21Z
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spelling 2017-12-11T15:07:40.3526693 v2 36270 2017-10-26 Modelling Stochastic and Deterministic Behaviours in Virus Infection Dynamics 05a507952e26462561085fb6f62c8897 0000-0001-6685-2351 Igor Sazonov Igor Sazonov true false 2017-10-26 AERO Many human infections with viruses such as human immunodeficiency virus type 1 (HIV--1) are characterized by low numbers of founder viruses for which the random effects and discrete nature of populations have a strong effect on the dynamics, e.g., extinction versus spread. It remains to be established whether HIV transmission is a stochastic process on the whole. In this study, we consider the simplest (so-called, 'consensus') virus dynamics model and develop a computational methodology for building an equivalent stochastic model based on Markov Chain accounting for random interactions between the components. The model is used to study the evolution of the probability densities for the virus and target cell populations. It predicts the probability of infection spread as a function of the number of the transmitted viruses. A hybrid algorithm is suggested to compute efficiently the dynamics in state space domain characterized by a mix of small and large species densities. Journal Article Mathematical Modelling of Natural Phenomena 12 5 63 77 1760-6101 mathematical model, virus infection, stochastic dynamics, Markov Chain, hybrid modelling 31 12 2017 2017-12-31 10.1051/mmnp/201712505 COLLEGE NANME Aerospace Engineering COLLEGE CODE AERO Swansea University 2017-12-11T15:07:40.3526693 2017-10-26T09:41:12.1455122 College of Engineering Engineering I. Sazonov 1 D. Grebennikov 2 M. Kelbert 3 G. Bocharov 4 Igor Sazonov 0000-0001-6685-2351 5 0036270-31102017091719.pdf sazonov2017(4).pdf 2017-10-31T09:17:19.5400000 Output 897963 application/pdf Version of Record true 2017-10-31T00:00:00.0000000 true eng
title Modelling Stochastic and Deterministic Behaviours in Virus Infection Dynamics
spellingShingle Modelling Stochastic and Deterministic Behaviours in Virus Infection Dynamics
Igor Sazonov
title_short Modelling Stochastic and Deterministic Behaviours in Virus Infection Dynamics
title_full Modelling Stochastic and Deterministic Behaviours in Virus Infection Dynamics
title_fullStr Modelling Stochastic and Deterministic Behaviours in Virus Infection Dynamics
title_full_unstemmed Modelling Stochastic and Deterministic Behaviours in Virus Infection Dynamics
title_sort Modelling Stochastic and Deterministic Behaviours in Virus Infection Dynamics
author_id_str_mv 05a507952e26462561085fb6f62c8897
author_id_fullname_str_mv 05a507952e26462561085fb6f62c8897_***_Igor Sazonov
author Igor Sazonov
author2 I. Sazonov
D. Grebennikov
M. Kelbert
G. Bocharov
Igor Sazonov
format Journal article
container_title Mathematical Modelling of Natural Phenomena
container_volume 12
container_issue 5
container_start_page 63
publishDate 2017
institution Swansea University
issn 1760-6101
doi_str_mv 10.1051/mmnp/201712505
college_str College of Engineering
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hierarchy_top_title College of Engineering
hierarchy_parent_id collegeofengineering
hierarchy_parent_title College of Engineering
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description Many human infections with viruses such as human immunodeficiency virus type 1 (HIV--1) are characterized by low numbers of founder viruses for which the random effects and discrete nature of populations have a strong effect on the dynamics, e.g., extinction versus spread. It remains to be established whether HIV transmission is a stochastic process on the whole. In this study, we consider the simplest (so-called, 'consensus') virus dynamics model and develop a computational methodology for building an equivalent stochastic model based on Markov Chain accounting for random interactions between the components. The model is used to study the evolution of the probability densities for the virus and target cell populations. It predicts the probability of infection spread as a function of the number of the transmitted viruses. A hybrid algorithm is suggested to compute efficiently the dynamics in state space domain characterized by a mix of small and large species densities.
published_date 2017-12-31T03:49:18Z
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