The following information was submitted:
Transactions: INTERNATIONAL JOURNAL of MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES
Transactions ID Number: 19-597
Full Name: Yongwimon Lenbury
Position: Professor
Age: ON
Sex: Female
Address: Department of Mathematics, Faculty of Science, Mahidol University, Bangkok
Country: THAILAND
Tel: 02-201-5448
Tel prefix: 66
Fax: 02-201-5343
E-mail address: scylb@mahidol.ac.th
Other E-mails: scylb@yahoo.com
Title of the Paper: Stability, Permanence and Positive Periodicity in a Model of Bone Remodeling under Impulsive PTH Control
Authors as they appear in the Paper: Mantana Chudtong, Yongwimon Lenbury and Chontita Rattanakul
Email addresses of all the authors: fiffy_fub111@hotmail.com, scylb@mahidol.ac.th, sccrt@mahidol.ac.th
Number of paper pages: 10
Abstract: In this paper, a mathematical model of bone remodeling process, which incorporates the effect of impulsive hormone supplementary treatments, is investigated both numerically and theoretically. A three dimensional model proposed in our earlier work in 2003 is first extended to incorporate impulsive treatment of estrogen supplement. It is illustrated that it is possible for the treatment to be interrupted with no apparent drop in its desirable effect on maintaining a normal bone mass. When the parathyroid hormone is assumed to have a very fast dynamics, the model in its reduced two dimensional form is then analyzed in terms of the boundedness, asymptotic stability, permanence, and oscillatory behavior. We show that there is a stable periodic solution, at the vanishing level of osteoclastic cells, when the impulsive period is less than some critical value. The conditions for permanence of the system are then given. Finally, it is shown that as the impulsive period inc!
reases beyond a certain critical value, the emergence of stable positive periodic solution may be observed under appropriate conditions on the system parameters. Thus, dynamic behavior of the system is sensitive to the period and amplitude of the hormone supplements so that the variation of these parameters are crucial for the proper management and control of this complex system.
Keywords: asymptotic stability, bone remodeling, impulsive differential equation models, permanence
EXTENSION of the file: .pdf
Special (Invited) Session: Stability and Periodicity in a Model of Bone Remodeling under Impulsive PTH Control
Organizer of the Session: 635-211
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