Eric Numfor, Souvik Bhattacharya, Maia Martcheva, Suzanne Lenhart
Abstract:
We formulate and then analyze a multi-group coupled within-host model of ODEs
and between-host model of ODE and first-order PDEs, using the Human
Immunodeficiency Virus (HIV) for illustration. The basic reproduction
number of the multi-group coupled epidemiological model is derived, steady
states solutions are calculated and stability analysis of equilbria
is investigated. An optimal control problem for our model with drug treatment
on the multi-group within-host system is formulated and analyzed.
Ekeland's principle is used in proving existence and uniqueness of an
optimal control pair. Numerical simulations based on the semi-implicit
finite difference schemes and the forward-backward sweep iterative
method are obtained.
Published March 21, 2016.
Math Subject Classifications: 34D20, 35L02, 49K15, 49K15.
Key Words: Multi-group; within-host dynamics; between-host dynamics;
equilibria; basic reproduction number; stability; optimal control.
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| Eric Numfor Department of Mathematics Georgia Regents University Augusta, GA 30912, USA email: enumfor@gru.edu | |
| Souvik Bhattacharya Department of Mathematics University of Trento, Italy email: souvikb2005@gmail.com | |
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Maia Martcheva Department of Mathematics University of Florida Gainesville, FL 32611, USA email: maia@ufl.edu |
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Suzanne Lenhart Department of Mathematics University of Tennessee Knoxville, TN 37996, USA email: lenhart@math.utk.edu |
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