Abstract
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.
Original language | English (US) |
---|---|
Pages (from-to) | 171-203 |
Number of pages | 33 |
Journal | Mathematical Modelling of Natural Phenomena |
Volume | 9 |
Issue number | 4 |
DOIs | |
State | Published - 2014 |
Externally published | Yes |
Keywords
- Between-host dynamics
- Equilibria
- Optimal control
- Stability
- Within-host dynamics
ASJC Scopus subject areas
- Modeling and Simulation
- Applied Mathematics