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between-host dynamics

Mathematical Modelling of Natural Phenomena (1)

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Optimal Control in Coupled Within-host and Between-hostModels
E. Numfor, S. Bhattacharya, S. Lenhart, M. Martcheva
Journal:

Mathematical Modelling of Natural Phenomena / Volume 9 / Issue 4 / 2014

Published online by Cambridge University Press:

20 June 2014, pp. 171-203

Print publication:

2014
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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) forillustration. Existence and uniqueness of solution to the “between-host” model isestablished, and an explicit expression for the basic reproduction number of the“between-host” model derived. Stability of disease-free and endemic equilibria isinvestigated. An optimal control problem with drug-treatment control on the within-hostsystem is formulated and analyzed; these results are novel for optimal control of ODEslinked with such first order PDEs. Numerical simulations based on the forward-backwardsweep method are obtained.