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Heterogeneous population dynamics of active particles: Progression, mutations, and selection dynamics

L. Gibelli

Department of Mathematical Sciences, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Turin, Italy

E-mail Address: livio.gibelli@polito.it

Present address: School of Engineering, University of Warwick, Coventry CV4 7AL, UK.

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A. Ełaiw

Department of Mathematics, Faculty Sciences, King Abdulaziz University, Jeddah, Saudi Arabia

E-mail Address: aelaiwksu.edu.sa@kau.edu.sa

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M. A. Alghamdi

Department of Mathematics, Faculty Sciences, King Abdulaziz University, Jeddah, Saudi Arabia

E-mail Address: Proff-malghamdi@hotmail.com

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, and

A. M. Althiabi

Department of Mathematics, Faculty Sciences, King Abdulaziz University, Jeddah, Saudi Arabia

E-mail Address: aalroqi@kau.edu.sa

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https://doi.org/10.1142/S0218202517500117Cited by:71 (Source: Crossref)

Abstract

This paper proposes a conceptual revisiting of population dynamics to include heterogeneous behaviors of individuals, mutations, and selection. The first part of the paper focuses on the derivation of a general mathematical structure which permits to describe systems composed of individuals whose interactions are stochastic. Hybrid models where some of the populations follow a deterministic dynamics are also discussed. The second part deals with two specific applications, namely the effect of the cellular aging in the virus infection process and the dynamics of virus mutation and competition with the immune system. Sample simulations are presented and classical models of population dynamics are critically analyzed in light of the proposed approach.

Communicated by N. Bellomo

Keywords:

AMSC: 82D99, 91A15

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