Yoshiaki Muroya

Waseda University, Edo, Tōkyō, Japan

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Publications (73)57.35 Total impact

  • 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.
    Applied Mathematics and Computation 07/2014; 239:60–73. · 1.35 Impact Factor
  • 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.
    Mathematical Methods in the Applied Sciences 01/2014; · 0.78 Impact Factor
  • 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.
    International Journal of Computer Mathematics 01/2014; 91(3). · 0.54 Impact Factor
  • 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.
    Applied Mathematics Letters 01/2014; 38:73–78. · 1.50 Impact Factor
  • 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.
    Applied Mathematics and Computation 07/2013; 219(21):10559–10573. · 1.35 Impact Factor
  • Yoshiaki Muroya, Yoichi Enatsu, Toshikazu Kuniya
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    ABSTRACT: In this paper, by extending well-known Lyapunov function techniques to SIRS epidemic models, we establish sufficient conditions for the global stability of an endemic equilibrium of a multi-group SIRS epidemic model with varying population sizes which has cross patch infection between different groups. Our proof no longer needs such a grouping technique by graph theory commonly used to analyze the multi-group SIR models.
    Nonlinear Analysis Real World Applications 06/2013; 14(3):1693–1704. · 2.20 Impact Factor
  • 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.
    International Journal of Biomathematics 04/2013; 06(02). · 0.63 Impact Factor
  • Yoshiaki MUROYA, Yoichi ENATSU, Toshikazu KUNIYA
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    ABSTRACT: In this article, we establish the global stability of an endemic equilibrium of multi-group SIR epidemic models, which have not only an exchange of individuals between patches through migration but also cross patch infection between different groups. As a result, we partially generalize the recent result in the article [16].
    Acta Mathematica Scientia 03/2013; 33(2):341–361. · 0.49 Impact Factor
  • Yoshiaki Muroya, Yoichi Enatsu, Huaixing Li
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    ABSTRACT: Applying modified monotone sequences, the authors establish the global asymptotic stability of the endemic equilibrium of an SEIR epidemic model.Reviewer: Hong Zhang (Zhenjiang)
    Discrete and Continuous Dynamical Systems. Series B. 01/2013; 1(1).
  • 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].
    Journal of Difference Equations and Applications 01/2013; 19(9). · 0.74 Impact Factor
  • Yoichi Enatsu, Yukihiko Nakata, Yoshiaki Muroya
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    ABSTRACT: In this paper, we study the global dynamics of a delayed SIRS epidemic model for transmission of disease with a class of nonlinear incidence rates of the form βS(t)∫0hf(τ)G(I(t−τ))dτ. Applying Lyapunov functional techniques in the recent paper [Y. Nakata, Y. Enatsu, Y. Muroya, On the global stability of an SIRS epidemic model with distributed delays, Discrete Contin. Dyn. Syst. Supplement (2011) 1119–1128], we establish sufficient conditions of the rate of immunity loss for the global asymptotic stability of an endemic equilibrium for the model. In particular, we offer a unified construction of Lyapunov functionals for both cases of R0≤1R0≤1 and R0>1R0>1, where R0R0 is the basic reproduction number.
    Nonlinear Analysis Real World Applications 10/2012; 13(5):2120–2133. · 2.20 Impact Factor
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    ABSTRACT: In this paper, by applying a variation of the backward Euler method, we propose a discrete-time SIR epidemic model whose discretization scheme preserves the global asymptotic stability of equilibria for a class of corresponding continuous-time SIR epidemic models. Using discrete-time analogue of Lyapunov functionals, the global asymptotic stability of the equilibria is fully determined by the basic reproduction number , when the infection incidence rate has a suitable monotone property.
    Journal of Difference Equations and Applications 07/2012; 18(7):1163-1181. · 0.74 Impact Factor
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    Yoichi Enatsu, Yukihiko Nakata, Yoshiaki Muroya
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    ABSTRACT: In this paper, we establish the global asymptotic stability of equi-libria for an SIR model of infectious diseases with distributed time delays gov-erned by a wide class of nonlinear incidence rates. We obtain the global prop-erties of the model by proving the permanence and constructing a suitable Lyapunov functional. Under some suitable assumptions on the nonlinear term in the incidence rate, the global dynamics of the model is completely deter-mined by the basic reproduction number R 0 and the distributed delays do not influence the global dynamics of the model.
    Acta Mathematica Scientia 05/2012; 32(3). · 0.49 Impact Factor
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    ABSTRACT: In this paper, we propose a discrete epidemic model for disease with immunity and latency spreading in a heterogeneous host population which is derived from the continuous case by using the well-known backward Euler method and ap-plying a Lyapunov functional technique which is a discrete version to that in the paper [Prüss, Pujo-Menjouet, Webb and Zacher, Analysis of a model for the dynamics of prions, Discrete and Continuous Dynamical Systems-Series B 6 (2006), 225-235]. It is shown that the global dynamics of this discrete epidemic model with latency are fully determined by a single threshold parameter.
    Nonlinear Analysis Real World Applications 02/2012; 13(1). · 2.20 Impact Factor
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    Yukihiko Nakata, Yoichi Enatsu, Yoshiaki Muroya
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    ABSTRACT: We study global asymptotic stability for an SIS epidemic model with maturation delay proposed by Cooke et al. [1]. It is assumed that the population has a nonlinear birth term and disease causes death of infective individuals. By using a monotone iterative method, we establish sufficient conditions for the global stability of an endemic equilibrium when it exists dependently on the monotone property of the birth rate function. Based on the analysis, we, further, study the model with two specific birth rate functions B 1 (N) = be −aN and B 3 (N) = A/N + c, where N denotes the total population. For each model, the disease induced death rate which guarantees the global stability of the endemic equilibrium is established and this gives a positive answer for an open problem by Zhao and Zou [5].
    01/2012;
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    ABSTRACT: We analyze stability of equilibria for a delayed SIR epidemic model, in which population growth is subject to logistic growth in absence of disease, with a nonlinear incidence rate satisfying suitable monotonicity conditions. The model admits a unique endemic equilibrium if and only if the basic reproduction number R0 exceeds one, while the trivial equilibrium and the disease-free equilibrium always exist. First we show that the disease-free equilibrium is globally asymptotically stable if and only if R0⩽1. Second we show that the model is permanent and it has a unique endemic equilibrium if and only if R0>1. Moreover, using a threshold parameter R¯0 characterized by the nonlinear incidence function, we establish that the endemic equilibrium is locally asymptotically stable for 1R0⩽R¯0 and it loses stability as the length of the delay increases past a critical value for 1R¯0R0. Our result is an extension of the stability results in [J-J. Wang, J-Z. Zhang, Z. Jin, Analysis of an SIR model with bilinear incidence rate, Nonl. Anal. RWA.11 (2009) 2390-2402].
    Applied Mathematics and Computation 01/2012; 218:5327-5336. · 1.35 Impact Factor
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    ABSTRACT: In this paper, by constructing Lyapunov functionals, we consider the global dynamics of an SIRS epidemic model with a wide class of nonlinear incidence rates and distributed delays $\int^{h}_{0} p(\tau)f(S(t),I(t-\tau)) \mathrm{d}\tau$ under the condition that the total population converges to 1. By using a technical lemma which is derived from strong condition of strict monotonicity of functions f(S,I) and f(S,I)/I with respect to S≥0 and I>0, we extend the global stability result for an SIR epidemic model if R 0>1, where R 0 is the basic reproduction number. By using a limit system of the model, we also show that the disease-free equilibrium is globally asymptotically stable if R 0=1.
    Journal of Applied Mathematics and Computing 01/2012; 39(1-2).
  • Yoichi Enatsu, Yukihiko Nakata, Yoshiaki Muroya
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    ABSTRACT: In this paper, we propose a discrete-time SIS epidemic model which is derived from continuous-time SIS epidemic models with immigration of infectives by the backward Euler method. For the discretized model, by applying new Lyapunov function techniques, we establish the global asymptotic stability of the disease-free equilibrium for and the endemic equilibrium for , where R 0 is the basic reproduction number of the continuous-time model. This is just a discrete analogue of a continuous SIS epidemic model with immigration of infectives.
    Journal of Difference Equations and Applications 08/2011; iFirst article(2011). · 0.74 Impact Factor
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    Yoshiaki Muroya, Yoichi Enatsu, Yukihiko Nakata
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    ABSTRACT: In this paper, we investigate a disease transmission model of SIRS type with latent period τ 0 and the specific nonmonotone incidence rate, namely, k exp(−dτ)S(t)I(t−τ) 1+α I 2 (t−τ) . For the basic reproduction number R 0 > 1, applying monotone iterative techniques, we establish sufficient conditions for the global asymptotic stability of endemic equilibrium of system which become partial answers to the open problem in [Hai-Feng Huo, Zhan-Ping Ma, Dynamics of a delayed epidemic model with non-monotonic incidence rate, Commun. Nonlinear Sci. Numer. Simul. 15 (2010) 459–468]. Moreover, combining both monotone iterative techniques and the Lyapunov functional techniques to an SIR model by perturbation, we derive another type of sufficient conditions for the global asymptotic stability of the endemic equilibrium.
    Journal of Mathematical Analysis and Applications 01/2011; · 1.05 Impact Factor
  • Masataka Kuroda, Yoshiaki Muroya
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    ABSTRACT: In this paper, applying a method of energy estimation similar to that of Seong-A. Shim [Seong-A. Shim, Uniform boundedness and convergence of solutions to the systems with cross-diffusions dominated by self-diffusions, Nonlinear Anal. RWA 4 (2003) 65–86], which used Gagliardo–Nirenberg-type inequalities in the estimates of solutions in order to establish W21-bounds uniform in time, we extend the result to the case of time delays, and establish conditions for the uniform boundedness of solutions and global asymptotic stability for the constant steady state of a quasilinear parabolic “delay” system with cross-diffusions dominated by self-diffusions and large diffusion coefficients in population dynamics.
    Nonlinear Analysis-real World Applications - NONLINEAR ANAL-REAL WORLD APP. 01/2011; 12(2):990-1001.