Optimal Control and Analysis of a Coupled ODE/PDE Immuno-epidemiological Model.

Eric Numfor (April 7, 2014)

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Abstract

Optimal control can be used to design intervention strategies for the management of infectious diseases, and has been applied in immunological and epidemiological models separately. We formulate an immuno-epidemiological model of coupled within-host model of ODEs and between-host model of ODE and PDE. 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 is derived. Stability of disease-free and endemic equilibria of the between-host model is investigated. An optimal control problem with drug-treatment control on the within-host system is formulated and analyzed. Numerical simulations based on the forward-backward sweep method are obtained.