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Optimal Control in Coupled Within-host and Between-host Models

Published online by Cambridge University Press:  20 June 2014

E. Numfor ,
S. Bhattacharya ,
S. Lenhart  and
M. Martcheva
E. Numfor
Affiliation:
Department of Mathematics, University of Tennessee, TN 37996, USA
S. Bhattacharya
Affiliation:
Department of Mathematics, University of Florida, FL 32611, USA
S. Lenhart*
Affiliation:
Department of Mathematics, University of Tennessee, TN 37996, USA
M. Martcheva
Affiliation:
Department of Mathematics, University of Florida, FL 32611, USA
*
⋆ Corresponding author. E-mail: lenhart@math.utk.edu
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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.

Keywords

within-host dynamicsbetween-host dynamicsequilibriastabilityoptimal control
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 9 , Issue 4: Optimal control , 2014 , pp. 171 - 203
Copyright
© EDP Sciences, 2014

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