Tenth MSU Conference on Differential Equations and Computational Simulations. Electron. J. Diff. Eqns., Conference 23 (2016), pp. 87-117.

Optimal control in multi-group coupled within-host and between-host models

Eric Numfor, Souvik Bhattacharya, Maia Martcheva, Suzanne Lenhart

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
Maia Martcheva
Department of Mathematics
University of Florida
Gainesville, FL 32611, USA
email: maia@ufl.edu
Suzanne Lenhart
Department of Mathematics
University of Tennessee
Knoxville, TN 37996, USA
email: lenhart@math.utk.edu

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