A singularly perturbed HIV model with treatment and antigenic variation

Bobko, Nara; Zubelli, Jorge P.

doi:10.3934/mbe.2015.12.1

Cited by 6 publications

(8 citation statements)

References 32 publications

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“…I 1 > I 2 or s 1 < s 2 . Each epitope escape comes with a fitness cost as before, therefore the viral reproduction numbers satisfy 4 . We note that the fitness cost for resistance to z 1 may be greater than or equal to the fitness cost to z 2 , in other words the fitness of mutant y 2 is less than or equal to y 3 (R 2 ≤ R 3 ).…”

Section: Dynamics For Full Network On N = 2 Epitopesmentioning

confidence: 98%

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Dynamics of virus and immune response in multi-epitope network

Browne

Smith

2018

J. Math. Biol.

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The host immune response can often efficiently suppress a virus infection, which may lead to selection for immune-resistant viral variants within the host. For example, during HIV infection, an array of CTL immune response populations recognize specific epitopes (viral proteins) presented on the surface of infected cells to effectively mediate their killing. However HIV can rapidly evolve resistance to CTL attack at different epitopes, inducing a dynamic network of interacting viral and immune response variants. We consider models for the network of virus and immune response populations, consisting of Lotka-Volterra-like systems of ordinary differential equations. Stability of feasible equilibria and corresponding uniform persistence of distinct variants are characterized via a Lyapunov function. We specialize the model to a "binary sequence" setting, where for n epitopes there can be [Formula: see text] distinct viral variants mapped on a hypercube graph. The dynamics in several cases are analyzed and sharp polychotomies are derived characterizing persistent variants. In particular, we prove that if the viral fitness costs for gaining resistance to each epitope are equal, then the system of [Formula: see text] virus strains converges to a "perfectly nested network" with less than or equal to [Formula: see text] persistent virus strains. Overall, our results suggest that immunodominance, i.e. relative strength of immune response to an epitope, is the most important factor determining the persistent network structure.

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Section: Dynamics For Full Network On N = 2 Epitopesmentioning

confidence: 98%

“…, a n ) and a row of zeros. This particular assumption of a "one-to-one" interaction network, where each immune response population attacks a unique specific viral strain, has been considered in [34,20,4]. In this case, model (6) reduces to the following n + 1-strain and n-immune variant model:…”

Section: Strain-specific Networkmentioning

confidence: 99%

Dynamics of virus and immune response in multi-epitope network

Browne

Smith

2018

J. Math. Biol.

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“…For our virus-immune ecosystem, we are considering the situation where n immune response populations z j each targeting the corresponding epitope j in the virus strains at a rate solely dependent on the allele type of epitope j; (0) wild-type or (1) mutated form conferring full resistance to z j . The avidity of immune response z j and (wild-type) epitope j is described by the immune reproduction number I j given by (3), and are according to the immunodominance hierarchy (6). As opposed to this simple immune fitness ordering, the collection of virus reproduction numbers (fitnesses) in our model can have much more complex relationships among each other depending on the fitness landscape, formally defined below.…”

Section: Fitness and Epistasismentioning

confidence: 99%

“…, a n ) and a row of zeros. This subsystem of a "one-to-one" interaction network, where each immune response population attacks a unique specific viral strain, has been considered in [40,27,6]. Stability and persistence results, analogous to [8] for the nested subsystem, were proved in [40] for the one-to-one network under the assumption of decreasing reproduction numbers R i < R i+1 , i = 1, .…”

Section: One-to-one Network Determined By Epistasismentioning

confidence: 99%

Virus-immune dynamics determined by prey-predator interaction network and epistasis in viral fitness landscape

Browne¹,

Fadoua²

2021

Preprint

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Population dynamics and evolutionary genetics underly the structure of ecosystems, changing on the same timescale for interacting species with rapid turnover, such as virus (e.g. HIV) and immune response. Thus, an important problem in mathematical modeling is to connect ecology, evolution and genetics, which often have been treated separately. Here, extending analysis of multiple virus and immune response populations in a resource -prey (consumer) -predator model from Browne and Smith [9], we show that long term dynamics of viral mutants evolving resistance at distinct epitopes (viral proteins targeted by immune responses) are governed by epistasis in the virus fitness landscape. In particular, the stability of persistent equilibrium virus-immune (preypredator) network structures, such as nested and one-to-one, and bifurcations are determined by a collection of circuits defined by combinations of viral fitnesses that are minimally additive within a hypercube of binary sequences representing all possible viral epitope sequences ordered according to immunodominance hierarchy. Numerical solutions of our ordinary differential equation system, along with an extended stochastic version including random mutation, demonstrate how pairwise or multiplicative epistatic interactions shape viral evolution against concurrent immune responses and convergence to the multi-variant steady state predicted by theoretical results. Furthermore, simulations illustrate how periodic infusions of subdominant immune responses can induce a bifurcation in the persistent viral strains, offering superior host outcome over an alternative strategy of immunotherapy with strongest immune response.

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“…Mathematical modeling plays an important role in the study of biological systems. Mathematical models can provide a more typical, more refined, and more quantitative description of complex systems [6][7][8][9][10][11][12][13][14][15][16][17][18]. Due to the uncertainty of clinical measurement, the low quality of samples, and the high risk of repeated trials, the use of mathematical models to describe the infection process qualitatively and quantitatively, to study the mechanism of AIDS infection and the treatment of AIDS, is of great significance to the control of HIV infection [19][20][21].…”

Section: Introduction and Model Formulationmentioning

confidence: 99%

Dynamical Analysis of a Delayed HIV Virus Dynamic Model with Cell-to-Cell Transmission and Apoptosis of Bystander Cells

et al. 2020

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In this paper, a delayed viral dynamical model that considers two different transmission methods of the virus and apoptosis of bystander cells is proposed and investigated. The basic reproductive number R0 of the model is derived. Based on the basic reproductive number, we prove that the disease-free equilibrium E0 is globally asymptotically stable for R0<1 by constructing suitable Lyapunov functional. For R0>1, by regarding the time delay as bifurcation parameter, the existence of local Hopf bifurcation is investigated. The results show that time delay can change the stability of endemic equilibrium and cause periodic oscillations. Finally, we give some numerical simulations to illustrate the theoretical findings.

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A singularly perturbed HIV model with treatment and antigenic variation

Cited by 6 publications

References 32 publications

Dynamics of virus and immune response in multi-epitope network

Dynamics of virus and immune response in multi-epitope network

Virus-immune dynamics determined by prey-predator interaction network and epistasis in viral fitness landscape

Dynamical Analysis of a Delayed HIV Virus Dynamic Model with Cell-to-Cell Transmission and Apoptosis of Bystander Cells

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