Global analysis of the dynamics of a mathematical model to intermittent HIV treatment

Carvalho, Tiago; Cristiano, Rony; Gonçalves, Luiz Fernando; Tonon, Durval J.

doi:10.1007/s11071-020-05775-4

Cited by 22 publications

(12 citation statements)

References 27 publications

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“…It is clear that this numerical model is a two-step exponential discretization of the continuous problem (2). Indeed, using the discrete operators, it is an easy algebraic task to check that (7) can be equivalently rewritten as follows:…”

Section: Numerical Modelmentioning

confidence: 99%

“…This equivalent form is employed to propose an exponential-type discretization of the continuous problem under investigation. In particular, we provide a Bhattacharya-type discrete scheme to solve the mathematical model (2). The reason to follow this approach obeys the need to preserve some important features of the relevant solutions of this system and to provide an unconditionally stable and explicit numerical solution for our differential model.…”

Section: Introductionmentioning

confidence: 99%

“…It is worth pointing out that the mathematical investigation of the human immunodeficiency virus HIV-1 is an interesting avenue of research. In fact, some works investigate mathematical models to estimate HIV-1 virological failure and establish rigorously the role of lymph node drug penetration [1], the global analysis of the dynamics of predictive systems for intermittent HIV-1 treatment [2], mathematical models of cell-wise spread of HIV-1 which include temporal delays [3], models for patterns of the sexual behavior and their relation with the spread of HIV-1 [4], and the long-term dynamics in mathematical models of HIV-1 with temporal delay in various variants of the drug therapy [5]. Some of these models are based on ordinary differential equations, and their analytical study is followed by simulation experiments which assess the validity of the qualitative results.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A finite-difference discretization preserving the structure of solutions of a diffusive model of type-1 human immunodeficiency virus

Alba-Pérez

Macías‐Díaz

2021

Adv Differ Equ

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We investigate a model of spatio-temporal spreading of human immunodeficiency virus HIV-1. The mathematical model considers the presence of various components in a human tissue, including the uninfected CD4+T cells density, the density of infected CD4+T cells, and the density of free HIV infection particles in the blood. These three components are nonnegative and bounded variables. By expressing the original model in an equivalent exponential form, we propose a positive and bounded discrete model to estimate the solutions of the continuous system. We establish conditions under which the nonnegative and bounded features of the initial-boundary data are preserved under the scheme. Moreover, we show rigorously that the method is a consistent scheme for the differential model under study, with first and second orders of consistency in time and space, respectively. The scheme is an unconditionally stable and convergent technique which has first and second orders of convergence in time and space, respectively. An application to the spatio-temporal dynamics of HIV-1 is presented in this manuscript. For the sake of reproducibility, we provide a computer implementation of our method at the end of this work.

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Section: Numerical Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A finite-difference discretization preserving the structure of solutions of a diffusive model of type-1 human immunodeficiency virus

Alba-Pérez

Macías‐Díaz

2021

Adv Differ Equ

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“…In the present section we consider a tangential sliding vector that appears in the dynamics of a piecewise smooth system that models the intermittent treatment of the human immunodeficiency virus. For more details about the formal mathematical analysis for this model, see [2].…”

Section: Application In a Model Of Intermittent Treatment Of Hivmentioning

confidence: 99%

“…A non-exhaustive list of books concerning this theme includes [1,6,9,15,19,24]. Also, papers like [2,3,5,10,11,13,17,22,23] deals with applications of such theory to real world phenomena. Without doubts, the most valuable text concerning PSVFs is the book [9] of Filippov.…”

Section: Introductionmentioning

confidence: 99%

Sliding motion on tangential sets of Filippov systems

Carvalho¹,

Novaes²,

Tonon³

2021

Preprint

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We consider piecewise smooth vector fields Z = (Z + , Z − ) defined in R n where both vector fields are tangent to the switching manifold Σ along a manifold M . Our main purpose is to study the existence of an invariant vector field defined on M , that we call tangential sliding vector field. We provide necessary and sufficient conditions under Z to characterize the existence of this vector field. Considering a regularization process, we proved that this tangential sliding vector field is topological equivalent to an invariant dynamics under the slow manifold. The results are applied to study a Filippov model for intermittent treatment of HIV.

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Analysis and Bifurcations of Non-smooth Filippov Predator Prey System with Harvesting

Yadav,

Gakkhar,

Nayak

2024

NODYCON Conference Proceedings Series

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Global analysis of the dynamics of a mathematical model to intermittent HIV treatment

Cited by 22 publications

References 27 publications

A finite-difference discretization preserving the structure of solutions of a diffusive model of type-1 human immunodeficiency virus

A finite-difference discretization preserving the structure of solutions of a diffusive model of type-1 human immunodeficiency virus

Sliding motion on tangential sets of Filippov systems

Analysis and Bifurcations of Non-smooth Filippov Predator Prey System with Harvesting

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