Yoshiaki Muroya

Waseda University, Edo, Tōkyō, Japan

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Publications (91)90.49 Total impact

  • Yoichi Enatsu · Toshikazu Kuniya · Yoshiaki Muroya
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    ABSTRACT: In this paper, we investigate the global stability of a delayed multi-group SIRS epidemic model which includes not only nonlinear incidence rates but also rates of immunity loss and relapse of infection. The model analysis can be regarded as an extension to a multi-group epidemic analysis in [Muroya, Li and Kuniya, Complete global analysis of an SIRS epidemic model with graded cure rate and incomplete recovery rate, J. Math. Anal. Appl. 410 (2014) 719-732] is studied. Applying a Lyapunov functional approach, we prove that a disease-free equilibrium of the model, is globally asymptotically stable, if a threshold parameter R0 ≤ 1. For the global stability of an endemic equilibrium of the model, we establish a sufficient condition for small recovery rates δk ≥ 0, k = 1,2,⋯,n, if R0 > 1. Further, by a monotone iterative approach, we obtain another sufficient condition for large δk, k = 1, 2,⋯, n. Both results generalize several known results obtained for, e.g., SIS, SIR and SIRS models in the recent literature. We also offer a new proof on permanence which is applicable to other multi-group epidemic models.
    No preview · Article · Sep 2015 · Discrete and Continuous Dynamical Systems - Series B
  • Toshikazu Kuniya · Yoshiaki Muroya
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    ABSTRACT: In this paper, to analyze the effect of the cross patch infection between different groups to the spread of gonorrhea in a community, we establish the complete global dynamics of a multigroup SIS epidemic model with varying total population size by a threshold parameter. In the proof, we use special Lyapunov functional techniques, not only one proposed by the paper [Pruss et al., 2006], but also the other one for a varying total population size with some ideas specified to our model and no longer need a grouping technique derived from the graph theory which is commonly used for the global stability analysis of multi-group epidemic models.
    No preview · Article · Aug 2015 · Applied Mathematics and Computation
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    Yoshiaki Muroya
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    ABSTRACT: In this paper, for a Lotka-Volterra system with infinite delays and patch structure related to a multi-group SI epidemic model, applying Lyapunov functional techniques without using the form of diagonal dominance of the instantaneous negative terms over the infinite delay terms, we establish the complete global dynamics by a threshold parameter s(M(0)), that is, the trivial equilibrium is globally asymptotically stable if s(M(0)) ≤ 0 and the positive equilibrium is globally asymptotically stable if s(M(0)) ≥ 0, respectively. This offer new type condition of global stability for Lotka-Volterra systems with patch structure.
    Preview · Article · Jul 2015 · Discrete and Continuous Dynamical Systems - Series S
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    Yoshiaki Muroya · Toshikazu Kuniya · Jinliang Wang
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    ABSTRACT: In this paper, we focus on a delayed multi-group SIS epidemic model with nonlinear incidence rates and patch structure, in which the effects of time delay and population exchange between groups are considered. By using a Lyapunov functional approach, we establish that the global stability of the model is completely determined by a threshold parameter , that is, the disease-free equilibrium of the model is globally asymptotically stable if , while an endemic equilibrium of the model is such if . Moreover, in the analysis, we offer new techniques to prove the permanence and the existence of the endemic equilibrium of delayed nonlinear multi-group epidemic models. This result shows that the incidence delay and the migration delay do not alter the quality of the disease dynamics.
    Full-text · Article · May 2015 · Journal of Mathematical Analysis and Applications
  • Yoshiaki Muroya · Toshikazu Kuniya
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    ABSTRACT: In this paper, by applying Lyapunov functional approach, we establish a sufficient condition on the global stability of a "delayed" multi-group SIRS epidemic model with cure rate and incomplete recovery rate which does not depend on the delays and is an extension of the "light drug model" studied in the recent paper [Muroya, Li and Kuniya, Complete global analysis of an SIRS epidemic model with graded cure rate and incomplete recovery rate, J. Math. Anal. Appl.410 (2014) 719–732] to a multi-group model. Applying a Lyapunov functional on total population of each compartment, we offer new techniques for the delayed system, how to prove the permanence, the existence of the endemic equilibrium and the global stability of disease-free equilibrium for the reproduction number and endemic equilibrium for .
    No preview · Article · Feb 2015 · International Journal of Biomathematics
  • Yoshiaki Muroya · Toshikazu Kuniya
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    ABSTRACT: In this paper, applying Lyapunov functional techniques to nonresident computer virus models, we establish global dynamics of the model whose threshold parameter is the basic reproduction number R0 such that the virus-free equilibrium is globally asymptotically stable when R0 ≤ 1, and the infected equilibrium is globally asymptotically stable when R0 > 1 under the same restricted condition on a parameter, which appeared in the literature on delayed susceptible-infected-recovered-susceptible (SIRS) epidemic models. We use new techniques on permanence and global stability of this model for R0 > 1. Copyright © 2014 John Wiley & Sons, Ltd.
    No preview · Article · Jan 2015 · Mathematical Methods in the Applied Sciences
  • Toshikazu Kuniya · Yoshiaki Muroya · Yoichi Enatsu
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    ABSTRACT: In this paper, we formulate an SIR epidemic model with hybrid of multigroup and patch structures, which can be regarded as a model for the geographical spread of infectious diseases or a multi-group model with perturbation. We show that if a threshold value, which corresponds to the well-known basic reproduction number R0, is less than or equal to unity, then the disease-free equilibrium of the model is globally asymptotically stable. We also show that if the threshold value is greater than unity, then the model is uniformly persistent and has an endemic equilibrium. Moreover, using a Lyapunov functional technique, we obtain a sufficient condition under which the endemic equilibrium is globally asymptotically stable. The sufficient condition is satisfied if the transmission coefficients in the same groups are large or the per capita recovery rates are small.
    No preview · Article · Dec 2014 · Mathematical biosciences and engineering: MBE
  • Yoshiaki Muroya · Toshikazu Kuniya
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    ABSTRACT: In this paper, we focus on a multi-group SIRS epidemic model with varying total population size and cross patch infection between different groups. By applying a monotone iterative approach to the model, we establish a new sufficient condition for large recovery rates δk,k=1,2,…,n on the global asymptotic stability of endemic equilibrium of the model. By combining the sufficient condition for small δk,k=1,2,…,n obtained by Lyapunov functional approach, we obtain new sufficient conditions which extend the known results in recent literature.
    No preview · Article · Dec 2014 · Applied Mathematics Letters
  • Yoshiaki Muroya · Yoichi Enatsu
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    ABSTRACT: In this paper, applying both Lyapunov function techniques and monotone iterative techniques, we establish new sufficient conditions under which the infected equilibrium of an HIV pathogenesis model with cure rate is globally asymptotically stable. By giving an explicit expression for eventual lower bound of the concentration of susceptible CD4+ T cells, we establish an affirmative partial answer to the numerical simulations investigated in the recent paper [Liu, Wang, Hu and Ma, Global stability of an HIV pathogenesis model with cure rate, Nonlinear Analysis RWA (2011) 12: 2947–2961]. Our monotone iterative techniques are applicable for the small and large growth rate in logistic functions for the proliferation rate of healthy and infected CD4+ T cells. Copyright © 2014 John Wiley & Sons, Ltd.
    No preview · Article · Nov 2014 · Mathematical Methods in the Applied Sciences
  • Yoshiaki Muroya · Huaixing Li · Toshikazu Kuniya
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    ABSTRACT: In this paper, we establish new sufficient conditions for the infected equilibrium of a nonresident computer virus model to be globally asymptotically stable. Our results extend two kind of known results in recent literature.
    No preview · Article · Sep 2014 · Acta Mathematica Scientia
  • Yoshiaki Muroya
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    ABSTRACT: In this paper, applying Lyapunov functional techniques to a nonlinear delayed Lotka–Volterra system with feedback controls and patch structure, we establish sufficient conditions of the global stability for a trivial equilibrium and a positive equilibrium, respectively. Moreover, we offer new techniques to prove the permanence and the existence of positive equilibrium of this system. The influence of the feedback controls can be essentially eliminated from the Lyapunov functional to prove the global stability, whereas feedback controls change the position of a unique positive equilibrium. These generalize the known results of recent literature.
    No preview · Article · Jul 2014 · Applied Mathematics and Computation
  • Yoshiaki Muroya · Toshikazu Kuniya
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    ABSTRACT: In this paper, using an approach of Lyapunov functional, we establish the complete global stability of a multi-group SIS epidemic model in which the effect of population migration among different regions is considered. We prove the global asymptotic stability of the disease-free equilibrium of the model for R-o <= 1, and that of an endemic equilibrium for Ro > 1. Here Ro denotes the well-known basic reproduction number defined by the spectral radius of an irreducible nonnegative matrix called the next generation matrix. We emphasize that the graph-theoretic approach, which is typically used for multi-group epidemic models, is not needed in our proof.
    No preview · Article · Apr 2014 · Discrete and Continuous Dynamical Systems - Series B
  • Yoshiaki Muroya · Yoichi Enatsu · Huaixing Li
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    ABSTRACT: We propose a delayed SIRS computer virus propagation model. Applying monotone iterative techniques and Lyapunov functional techniques, we establish sufficient conditions for the global asymptotic stability of both virus-free and virus equilibria of the model.
    No preview · Article · Mar 2014 · International Journal of Computer Mathematics
  • Yoshiaki Muroya · Huaixing Li · Toshikazu Kuniya
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    ABSTRACT: In this paper, applying two types of Lyapunov functional techniques to an SIRS epidemic model with graded cure and incomplete recovery rates, we establish complete global dynamics of the model whose threshold parameter is the basic reproduction number R-0 such that the disease-free equilibrium is globally asymptotically stable when R-0 <= 1, and the endemic equilibrium is globally asymptotically stable when R-0 > 1.
    No preview · Article · Feb 2014 · Journal of Mathematical Analysis and Applications
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    ABSTRACT: SIRS type epidemiological model has a fundamental form to study the role of temporal immunity of recovered individuals in disease transmission dynamics and several variant models have been considered in the last century, but up to now dynamical aspects of the model are not fully elucidated. We here look over previous studies concerning qualitative analysis for a family of SIRS type epidemiological models. To this aim we construct a general model in a form of delay equation, a coupled system of a renewal equation and delay differential equations, structuring infected population by infection-age (time elapsed since infection). We re-examine the structure of equilibria and stability of the disease free equilibrium. We then introduce slightly improved stability conditions for an endemic equilibrium. Specifying modelling ingredients we derive two special cases where the model can be represented as a system of ordinary and delay differential equations that have appeared in the literature. For those models we have a powerful tool, namely Lyapunov function, to study global stability of the endemic equilibrium. Relating epidemic models are also discussed.
    Full-text · Article · Jan 2014 · SUT Journal of Mathematics
  • Yoshiaki Muroya · Yoichi Enatsu
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    ABSTRACT: In this paper, we show dynamical consistency between the continuous SEIS epidemic model and its discrete-time analogue, that is, both global dynamics of a continuous SEIS epidemic model ‘without delays’ and the positive solutions of the corresponding backward Euler discretization with mesh width are fully determined by the same single-threshold parameter which is the basic reproduction number of the continuous SEIS model. To prove this, we first obtain lower positive bounds for the permanence of this discrete-time analogue for and then apply a discrete version of Lyapunov function technique in the paper [12].
    No preview · Article · Sep 2013 · Journal of Difference Equations and Applications
  • Teresa Faria · Yoshiaki Muroya
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    ABSTRACT: The paper deals with a multiple species Lotka-Volterra model with infinite distributed delays and feedback controls, for which we assume a weak form of diagonal dominance of the instantaneous negative intra-specific terms over the infinite delay effect in both the population variables and controls. General sufficient conditions for the existence and attractivity of a saturated equilibrium are established. When the saturated equilibrium is on the boundary of $\R^n_+$, sharper criteria for the extinction of all or part of the populations are given. While the literature usually treats the case of competitive systems only, here no restrictions on the signs of the intra- and inter-specific delayed terms are imposed. Moreover, our technique does not require the construction of Lyapunov functionals.
    No preview · Article · Jul 2013 · Proceedings of the Royal Society of Edinburgh Section A Mathematics
  • Yoshiaki Muroya · Yoichi Enatsu · Huaixing Li
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    ABSTRACT: In this paper, applying new Lyapunov functional techniques to a delayed HTLV-I infection model with a class of nonlinear incidence rates and CTLs immune response, we establish that the global dynamics are completely determined by two basic reproduction numbers R0>R0∗, as follows. If R0⩽1R0⩽1, then a viral-free equilibrium is globally asymptotically stable, if R0∗⩽1<R0, then there exists a unique no-immune response equilibrium is globally asymptotically stable, and if R0∗>1, then there exists a unique endemic equilibrium which is globally asymptotically stable. In particular, to obtain concrete eventual lower bounds for positive solutions of the model we offer some new techniques.
    No preview · Article · Jul 2013 · Applied Mathematics and Computation
  • Yoshiaki Muroya · Yoichi Enatsu · Toshikazu Kuniya
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    ABSTRACT: In this paper, to analyze the effect of the cross patch infection between different groups to the spread of gonorrhea in a community, we establish the complete global dynamics of a multi-group SIS epidemic model with varying total population size by a threshold parameter. In the proof, we use special Lyapunov functional techniques, not only one proposed by the paper [Prüss et al., 2006], but also the other one for a varying total population size with some ideas specified to our model and no longer need a grouping technique derived from the graph theory which is commonly used for the global stability analysis of multi-group epidemic models.
    No preview · Article · Jun 2013 · Nonlinear Analysis Real World Applications
  • Yoichi Enatsu · Yoshiaki Muroya
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    ABSTRACT: In this paper, we consider the backward Euler discretization derived from a continuous SIRS epidemic model, which contains a remaining problem that our discrete model has two solutions for infected population; one is positive and the other is negative. Under an additional positiveness condition on infected population, we show that the backward Euler discretization is one of simple discrete-time analogue which preserves the global asymptotic stability of equilibria of the corresponding continuous model.
    No preview · Article · Apr 2013 · International Journal of Biomathematics