Math. Model. Nat. Phenom.
Volume 9, Number 4, 2014Optimal control
|Page(s)||171 - 203|
|Published online||20 June 2014|
Optimal Control in Coupled Within-host and Between-host Models
Department of Mathematics, University of Tennessee,
2 Department of Mathematics, University of Florida, FL 32611, USA
⋆ Corresponding author. E-mail: email@example.com
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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