TY - JOUR
T1 - Global stability of a population dynamics model with inhibition and negative feedback
AU - Vargas-de-leóon, Cruz
AU - Korobeinikov, Andrei
N1 - Funding Information:
A.K. is supported by the Mathematics Applications Consortium for Science and Industry (www.macsi. ul.ie) funded by the Science Foundation Ireland Mathematics Initiative Grant 06/MI/005.
PY - 2013/3
Y1 - 2013/3
N2 - Reactions or interactions with the rate which is inhibited by the product or a by-product of the reaction are fairly common in biology and chemical kinetics. Biological examples of such interactions include selfpoisoning of bacteria, the non-lytic immune response and the antiviral (and in particular antiretroviral) therapy. As a case study, in this notice, we consider global asymptotic properties for a simple model with negative feedback (the Wodarz model) where the interaction is inhibited by a by-product of the reaction. The objective of this notice is an extending of a technique that was developed during last decade for the global analysis of models with positive feedback to the systems, where the feedback is negative. Using the direct Lyapunov method with Volterra type Lyapunov functions, we establish conditions for the global stability of this model. This result enables us to evaluate the comparative impacts of the lytic and nonlytic components, the efficiency of the antiviral therapy and the possibility of self-poisoning for bacteria. The same approach can be successfully applied to more complex models with negative feedback.
AB - Reactions or interactions with the rate which is inhibited by the product or a by-product of the reaction are fairly common in biology and chemical kinetics. Biological examples of such interactions include selfpoisoning of bacteria, the non-lytic immune response and the antiviral (and in particular antiretroviral) therapy. As a case study, in this notice, we consider global asymptotic properties for a simple model with negative feedback (the Wodarz model) where the interaction is inhibited by a by-product of the reaction. The objective of this notice is an extending of a technique that was developed during last decade for the global analysis of models with positive feedback to the systems, where the feedback is negative. Using the direct Lyapunov method with Volterra type Lyapunov functions, we establish conditions for the global stability of this model. This result enables us to evaluate the comparative impacts of the lytic and nonlytic components, the efficiency of the antiviral therapy and the possibility of self-poisoning for bacteria. The same approach can be successfully applied to more complex models with negative feedback.
KW - Antiretroviral therapy
KW - Chemostat model
KW - Direct Lyapunov method
KW - Global stability
KW - Kinetics with inhibition
KW - Lyapunov function
KW - Negative feedback
KW - Non-lytic immune response
KW - Self-poisoning of bacteria
KW - The Wodarz model
KW - Virus dynamics
UR - http://www.scopus.com/inward/record.url?scp=84875026544&partnerID=8YFLogxK
U2 - 10.1093/imammb/dqr027
DO - 10.1093/imammb/dqr027
M3 - Artículo
SN - 1477-8599
VL - 30
SP - 65
EP - 72
JO - Mathematical Medicine and Biology
JF - Mathematical Medicine and Biology
IS - 1
ER -