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

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

Research output: Contribution to journalArticle

11 Citations (Scopus)

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 languageEnglish (US)
Pages (from-to)171-203
Number of pages33
JournalMathematical Modelling of Natural Phenomena
Volume9
Issue number4
DOIs
StatePublished - Jan 1 2014

Fingerprint

Optimal Control
Epidemiological Model
Basic Reproduction number
Endemic Equilibrium
Drug therapy
Existence and Uniqueness of Solutions
Sweep
Model
Virus
Optimal Control Problem
Drugs
Viruses
First-order
Numerical Simulation
Computer simulation

Keywords

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

ASJC Scopus subject areas

  • Modeling and Simulation

Cite this

Anita, S., Hritonenko, N., Marinoschi, G., Swierniak, A., Numfor, E. S., Bhattacharya, S., ... Martcheva, M. (2014). Optimal control in coupled within-host and between-host models. Mathematical Modelling of Natural Phenomena, 9(4), 171-203. https://doi.org/10.1051/mmnp/20149411

Optimal control in coupled within-host and between-host models. / Anita, S.; Hritonenko, N.; Marinoschi, G.; Swierniak, A.; Numfor, Eric Shu; Bhattacharya, S.; Lenhart, S.; Martcheva, M.

In: Mathematical Modelling of Natural Phenomena, Vol. 9, No. 4, 01.01.2014, p. 171-203.

Research output: Contribution to journalArticle

Anita, S, Hritonenko, N, Marinoschi, G, Swierniak, A, Numfor, ES, Bhattacharya, S, Lenhart, S & Martcheva, M 2014, 'Optimal control in coupled within-host and between-host models', Mathematical Modelling of Natural Phenomena, vol. 9, no. 4, pp. 171-203. https://doi.org/10.1051/mmnp/20149411
Anita, S. ; Hritonenko, N. ; Marinoschi, G. ; Swierniak, A. ; Numfor, Eric Shu ; Bhattacharya, S. ; Lenhart, S. ; Martcheva, M. / Optimal control in coupled within-host and between-host models. In: Mathematical Modelling of Natural Phenomena. 2014 ; Vol. 9, No. 4. pp. 171-203.
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