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 journalArticle

13 Scopus citations


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
Issue number4
StatePublished - 2014
Externally publishedYes


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

ASJC Scopus subject areas

  • Modeling and Simulation
  • Applied Mathematics

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  • Cite this

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