Prof. Dr. Horst R. Thieme (Arizona State University) Dynamics of a differential delay system modeling bluetongue,
Mittwoch, 10.07.2013 15:00 im Raum M5
Uniform disease persistence is investigated for the time
evolution of bluetongue, a viral disease in sheep and
cattle that is spread by midges as vectors. The model
is a system of several delay differential equations.
As in many other infectious disease models, uniform
disease persistence occurs if the basic disease reproduction
number for the whole system, R_0, exceeds one. However,
since bluetongue affects sheep much more severely than
cattle, uniform disease persistence can occur in two
different scenarios which are distinguished by the
disease reproduction number for the cattle-midge-bluetongue
system without sheep, ~ R_0.
If R_0 > 1 and ~ R_0 >1, bluetongue
persists in cattle and midges even though it may
eradicate the sheep relying on cattle as a reservoir. If R_0 > 1 > ~ R_0,
bluetongue and all host and vector species coexist, and bluetongue does
not eradicate the sheep because it cannot persist on midges and cattle alone.
The two scenarios require different use of dynamical systems persistence theory.