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

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.

Global dynamics of a general diffusive HBV infection model with capsids and adaptive immune response

“…Extending model (2) to include the effect of treatments and time delays will give a deeper insight into HBV infection. Another extension of model (2) is to incorporate stochastic interactions (see [48]). We leave these points as future works.…”

Global stability of discrete virus dynamics models with humoural immunity and latency

“…Looking ahead to further developments an interesting perspective would be introducing a stochastic internal variable, as in [24], to account for virus mutations.…”

A critical analysis towards research perspectives

“…2. The problem of looking for a mathematical structure appropriate to provide the conceptual framework towards the derivation of models for the class of systems under consideration has been discussed by various comments [1,6,45] referring either to the use of the mathematical theory of swarms or hybrid system mixing deterministic and stochastic dynamics [40]. 3.…”