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Mathematical Biosciences and Engineering (MBE)
 

Construction of Lyapunov functions for some models of infectious diseases in vivo: From simple models to complex models

Pages: 117 - 133, Volume 12, Issue 1, February 2015      doi:10.3934/mbe.2015.12.117

 
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Tsuyoshi Kajiwara - Graduate School of Environmental and Life Sciences, Okayama University, 3-1-1, Tsushima-Naka, Okayama, Japan (email)
Toru Sasaki - Graduate School of Environmental and Life Sciences, Okayama University, 3-1-1, Tsushima-Naka, Okayama, Japan (email)
Yasuhiro Takeuchi - College of Science and Engineering, Aoyama Gakuin University, 5-10-1, Fuchinobe, Sagamihara, Japan (email)

Abstract: We present a constructive method for Lyapunov functions for ordinary differential equation models of infectious diseases in vivo. We consider models derived from the Nowak-Bangham models. We construct Lyapunov functions for complex models using those of simpler models. Especially, we construct Lyapunov functions for models with an immune variable from those for models without an immune variable, a Lyapunov functions of a model with absorption effect from that for a model without absorption effect. We make the construction clear for Lyapunov functions proposed previously, and present new results with our method.

Keywords:  Lyapunov functions, infectious diseases, stability, ordinary differential equations, immunity.
Mathematics Subject Classification:  Primary: 92B05, 92D25; Secondary: 34D23.

Received: March 2014;      Accepted: September 2014;      Available Online: December 2014.

 References