Optimal control in coupled within-host and between-host models

S. Anita; N. Hritonenko; G. Marinoschi; A. Swierniak; E. Numfor; S. Bhattacharya; S. Lenhart; M. Martcheva

doi:10.1051/mmnp/20149411

Optimal control in coupled within-host and between-host models

S. Anita, N. Hritonenko, G. Marinoschi, A. Swierniak, E. Numfor, S. Bhattacharya, S. Lenhart, M. Martcheva

Research output: Contribution to journal › Article › peer-review

28 Scopus citations

Abstract

We formulate an immuno-epidemiological model of coupled "within-host" model of ODEs and "between-host" model of ODE and PDE, using the Human Immunodeficiency Virus (HIV) for illustration. Existence and uniqueness of solution to the "between-host" model is established, and an explicit expression for the basic reproduction number of the "between-host" model derived. Stability of disease-free and endemic equilibria is investigated. An optimal control problem with drug-treatment control on the within-host system is formulated and analyzed; these results are novel for optimal control of ODEs linked with such first order PDEs. Numerical simulations based on the forward-backward sweep method are obtained.

Original language	English (US)
Pages (from-to)	171-203
Number of pages	33
Journal	Mathematical Modelling of Natural Phenomena
Volume	9
Issue number	4
DOIs	https://doi.org/10.1051/mmnp/20149411
State	Published - 2014
Externally published	Yes

Keywords

Between-host dynamics
Equilibria
Optimal control
Stability
Within-host dynamics

ASJC Scopus subject areas

Modeling and Simulation
Applied Mathematics

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

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10.1051/mmnp/20149411

Cite this

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abstract = "We formulate an immuno-epidemiological model of coupled {"}within-host{"} model of ODEs and {"}between-host{"} model of ODE and PDE, using the Human Immunodeficiency Virus (HIV) for illustration. Existence and uniqueness of solution to the {"}between-host{"} model is established, and an explicit expression for the basic reproduction number of the {"}between-host{"} model derived. Stability of disease-free and endemic equilibria is investigated. An optimal control problem with drug-treatment control on the within-host system is formulated and analyzed; these results are novel for optimal control of ODEs linked with such first order PDEs. Numerical simulations based on the forward-backward sweep method are obtained.",

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T1 - Optimal control in coupled within-host and between-host models

AU - Anita, S.

AU - Hritonenko, N.

AU - Marinoschi, G.

AU - Swierniak, A.

AU - Numfor, E.

AU - Bhattacharya, S.

AU - Lenhart, S.

AU - Martcheva, M.

PY - 2014

Y1 - 2014

N2 - We formulate an immuno-epidemiological model of coupled "within-host" model of ODEs and "between-host" model of ODE and PDE, using the Human Immunodeficiency Virus (HIV) for illustration. Existence and uniqueness of solution to the "between-host" model is established, and an explicit expression for the basic reproduction number of the "between-host" model derived. Stability of disease-free and endemic equilibria is investigated. An optimal control problem with drug-treatment control on the within-host system is formulated and analyzed; these results are novel for optimal control of ODEs linked with such first order PDEs. Numerical simulations based on the forward-backward sweep method are obtained.

AB - We formulate an immuno-epidemiological model of coupled "within-host" model of ODEs and "between-host" model of ODE and PDE, using the Human Immunodeficiency Virus (HIV) for illustration. Existence and uniqueness of solution to the "between-host" model is established, and an explicit expression for the basic reproduction number of the "between-host" model derived. Stability of disease-free and endemic equilibria is investigated. An optimal control problem with drug-treatment control on the within-host system is formulated and analyzed; these results are novel for optimal control of ODEs linked with such first order PDEs. Numerical simulations based on the forward-backward sweep method are obtained.

KW - Between-host dynamics

KW - Equilibria

KW - Optimal control

KW - Stability

KW - Within-host dynamics

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Optimal control in coupled within-host and between-host models

Abstract

Keywords

ASJC Scopus subject areas

UN SDGs

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