| Issue |
Math. Model. Nat. Phenom.
Volume 9, Number 4, 2014
Optimal control
|
|
|---|---|---|
| Page(s) | 171 - 203 | |
| DOI | https://doi.org/10.1051/mmnp/20149411 | |
| Published online | 20 June 2014 | |
Optimal Control in Coupled Within-host and Between-host Models
1
Department of Mathematics, University of Tennessee,
TN 37996,
USA
2
Department of Mathematics, University of Florida,
FL 32611,
USA
⋆ Corresponding author. E-mail: lenhart@math.utk.edu
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.
Mathematics Subject Classification: 34D20 / 35L02 / 49K15 / 49K20
Key words: within-host dynamics / between-host dynamics / equilibria / stability / optimal control
© EDP Sciences, 2014
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