| Epidemic models are vital for implementing, evaluating,
and optimizing control schemes in order to eradicate a disease. This
talk discusses some epidemic models with switching parameters. Both
constant control and pulse control schemes are examined, and, in
doing so, we hope to gain insight into the effects of a time-varying
contact rate on critical control levels required for eradication. By
introducing the notions of persistent limit set and persistent mode,
we extend the classical LaSalle's invariance principle to epidemic
models with switching parameters and pulse control. A weak
invariance principle is established for such systems, under a weak
dwell-time condition on the impulsive and switching signals. This
weak invariance principle is then applied to establish sufficient
conditions for the global asymptotic stability of the disease-free
solution, which may give some insight into the effects of a
time-varying contact rate on critical control levels required for
eradication of a disease. |