Optimal control in coupled within-host and between-host models
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. © EDP Sciences, 2014.
Anita, S., Hritonenko, N., Marinoschi, G., Swierniak, A., Numfor, E., Bhattacharya, S., Lenhart, S., & Martcheva, M. (2014). Optimal control in coupled within-host and between-host models. Retrieved from https://digitalcommons.pvamu.edu/mathematics-facpubs/27