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: firstname.lastname@example.org
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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.