Modelling Stochastic and Deterministic Behaviours in Virus Infection Dynamics

• Published in: Mathematical modelling of natural phenomena Vol. 12; no. 5; pp. 63 - 77
• Main Authors: Sazonov, I., Grebennikov, D., Kelbert, M., Bocharov, G.
• Format: Journal Article
• Language: English
• Published: Les Ulis EDP Sciences 01.01.2017
• Subjects: 34B20; 35G31; 35Q53; Algorithms; Biological evolution; Computer applications; Disease transmission; Dynamics; HIV; Human behavior; Human immunodeficiency virus; hybrid modelling; Infections; Markov Chain; Markov chains; mathematical model; Populations; Probability theory; Species extinction; stochastic dynamics; Stochastic models; Stochastic processes; Stochasticity; virus infection; Viruses
• ISSN: 1760-6101; 0973-5348; 1760-6101
• DOI: 10.1051/mmnp/201712505

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.