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    Analysis and Optimization of Drug Resistant an Phase-Specific Cancer by Andrzej Swierniak, Jaroslaw Smieja

    Published 2005-07-01
    “…The methodology of analysis of such models, based on system decomposition, is discussed. The mathematical description is given by an infinite dimensional state equation with a system matrix, the form of which allows decomposing the model into two interacting subsystems. …”
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  14. 554

    Global stability of a multi-group model with vaccination age, distributed delay and random perturbation by Jinhu Xu, Yicang Zhou

    Published 2015-05-01
    “…A multi-group epidemic model withdistributed delay and vaccination age has been formulated and studied.Mathematical analysis shows that the global dynamics of the model is determinedby the basic reproduction number $\mathcal{R}_0$:the disease-free equilibrium is globally asymptotically stable if $\mathcal{R}_0\leq1$,and the endemic equilibrium is globally asymptotically stable if $\mathcal{R}_0>1$.Lyapunov functionals are constructed by the non-negative matrix theory and a novel grouping techniqueto establish the global stability.The stochastic perturbation of the model is studied and it is provedthat the endemic equilibrium of the stochastic model is stochastically asymptotically stablein the large under certain conditions.…”
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