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

Tsuyoshi Kajiwara; Toru Sasaki; Yasuhiro Takeuchi

doi:10.3934/mbe.2015.12.117

Article Contents

2015, Volume 12, Issue 1: 117-133. Doi: 10.3934/mbe.2015.12.117

This issue Previous Article Global dynamics of a general class of multi-group epidemic models with latency and relapse Next Article Analysis of SI models with multiple interacting populations using subpopulations

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

Received: March 2014

Revised: September 2014

Published: December 2014

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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.

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Mathematics Subject Classification: Primary: 92B05, 92D25; Secondary: 34D23.

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