Mathematical Biosciences and Engineering, 2015, 12(1): 117-133. doi: 10.3934/mbe.2015.12.117.

Primary: 92B05, 92D25; Secondary: 34D23.

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

1. Graduate School of Environmental and Life Sciences, Okayama University, 3-1-1, Tsushima-Naka, Okayama
2. College of Science and Engineering, Aoyama Gakuin University, 5-10-1, Fuchinobe, Sagamihara

We present a constructive method for Lyapunov functions forordinary 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 thoseof simpler models. Especially, we construct Lyapunov functions for modelswith an immune variable from those for models without an immunevariable, a Lyapunov functions of a model with absorption effectfrom that for a model without absorption effect. We make theconstruction clear for Lyapunov functions proposed previously, andpresent new results with our method.
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Keywords stability; Lyapunov functions; immunity.; ordinary differential equations; infectious diseases

Citation: Tsuyoshi Kajiwara, Toru Sasaki, Yasuhiro Takeuchi. Construction of Lyapunov functions for some models of infectious diseases in vivo: From simple models to complex models. Mathematical Biosciences and Engineering, 2015, 12(1): 117-133. doi: 10.3934/mbe.2015.12.117

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