Modeling viral coevolution: HIV multi-clonal persistence and competition dynamics

Abstract

The coexistence of different viral strains (quasispecies) within the same host are nowadays observed for a growing number of viruses, most notably HIV, Marburg and Ebola, but the conditions for the formation and survival of new strains have not yet been understood. We present a model of HIV quasispecies competition, which describes the conditions of viral quasispecies coexistence under different immune system conditions. Our model incorporates both T and B cells responses, and we show that the role of B cells is important and additive to that of T cells. Simulations of coinfection (simultaneous infection) and superinfection (delayed secondary infection) scenarios in the early stages (days) and in the late stages of the infection (years) are in agreement with emerging molecular biology findings. The immune response induces a competition among similar phenotypes, leading to differentiation (quasispeciation), escape dynamics and complex oscillations of viral strain abundance. We found that the quasispecies dynamics after superinfection or coinfection has time scales of several months and becomes even slower when the immune system response is weak. Our model represents a general framework to study the speed and distribution of HIV quasispecies during disease progression, vaccination and therapy. r

Bifurcations of a mathematical model for HIV dynamics

“…To illustrate the theoretical results, we select K = 10 12 , γ 1 = 5 × 10 −6 , γ 2 = 10 −5 , γ 3 = 5 × 10 −6 , δ 1 = 0.08, δ 2 = 0.9, β = 9 × 10 −7 , c = 2.3, N = 100 from [1,2,6,48]. When λ = 10 5 or λ = 1000, we have B < 0 and (C1) holds.…”

“…Let us illustrate interesting phenomena from this type of bifurcations. We take K = 10 12 , γ 2 = 10 −5 , c = 2.3 from [1,2,6,48] and fix γ 3 = 5 ×10 −6 , β = 9 ×10 −7 . By numerical simulations on the basis of MatCont package [9,10], we find that system (2.1) admits four patterns of equilibrium curves born from the infectionfree equilibrium and from the singularity of an infection equilibrium ( Fig.…”

“…All the other parameters in (1.2) have the same meaning as those in (1.1). Numerical simulations of model (1.2) in [2] found the case of asymptotic coexistence of immune system and virus, and found the case of virus eradication. The stability of infection-free equilibrium of (1.2) was examined in [48].…”

“…Indeed, biological studies indicate that CD4 + T cell activation plays a fundamental role in guiding CTL responses [11,26]. In papers [2,33,48], an HIV model is proposed that incorporates CTL responses to intracellular pathogens, CD4 + T cell proliferation due to stimulations of pathogens, and B cell responses to virus particles. The model admits only three state variables, which makes mathematical analysis tractable.…”

How the Mutational-Selection Interplay Organizes the Fitness Landscape

“…This model allows to investigate time scale of quasi species evolution during superinfection (multiple infections at different times) or coinfection (simultaneous infection by different strains). For further details see [39].…”