Applied Mathematics Colloquium - Dr. Xinzhi Liu
Wednesday, August 20, 2014
10:00 am - 12:00 pm
Middlesex College (MC)
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.
Coffee and cookies will be provided.