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March  2017, 22(2): 507-536. doi: 10.3934/dcdsb.2017025

Lyapunov functionals for multistrain models with infinite delay

 Graduate School of Environmental and Life Science, Okayama University, Okayama, 700-8530, Japan

Received  February 2016 Revised  October 2016 Published  December 2016

We construct Lyapunov functionals for delay differential equation models of infectious diseases in vivo to analyze the stability of the equilibria. The Lyapunov functionals contain the terms that integrate over all previous states. An appropriate evaluation of the logarithm functions in those terms guarantees the existence of the integrals. We apply the rigorous analysis for the one-strain models to multistrain models by using mathematical induction.

Citation: Yoji Otani, Tsuyoshi Kajiwara, Toru Sasaki. Lyapunov functionals for multistrain models with infinite delay. Discrete & Continuous Dynamical Systems - B, 2017, 22 (2) : 507-536. doi: 10.3934/dcdsb.2017025
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$x^* \ne \hat{x}_i$ for all $i\in J$: in this case $K_J=\{1,2\}$
$x^* = \hat{x}_i$ for some $i\in J$: in this case $K_J=\{1,2,3\}, x^* = \hat{x}_3$
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