Yoshiaki Muroya

Waseda University, Edo, Tōkyō, Japan

Are you Yoshiaki Muroya?

Claim your profile

Publications (86)83.87 Total impact

  • Yoshiaki Muroya, Toshikazu Kuniya, Jinliang Wang
    [Show abstract] [Hide abstract]
    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.
    Journal of Mathematical Analysis and Applications 05/2015; 425(1). DOI:10.1016/j.jmaa.2014.12.019 · 1.12 Impact Factor
  • Yoshiaki Muroya, Toshikazu Kuniya
    International Journal of Biomathematics 02/2015; DOI:10.1142/S1793524515500485 · 0.65 Impact Factor
  • Yoshiaki Muroya, Toshikazu Kuniya
    [Show abstract] [Hide abstract]
    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 01/2015; 38(2). DOI:10.1002/mma.3068 · 0.88 Impact Factor
  • Toshikazu Kuniya, Yoshiaki Muroya, Yoichi Enatsu
    [Show abstract] [Hide abstract]
    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.
    Mathematical biosciences and engineering: MBE 12/2014; 11(6):1375-93. DOI:10.3934/mbe.2014.11.1375 · 0.87 Impact Factor
  • Yoshiaki Muroya, Toshikazu Kuniya
    [Show abstract] [Hide abstract]
    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 12/2014; 38:73–78. DOI:10.1016/j.aml.2014.07.005 · 1.48 Impact Factor
  • Yoshiaki Muroya, Yoichi Enatsu
    [Show abstract] [Hide abstract]
    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.
    Mathematical Methods in the Applied Sciences 11/2014; DOI:10.1002/mma.3334 · 0.88 Impact Factor
  • Yoshiaki Muroya
    [Show abstract] [Hide abstract]
    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. DOI:10.1016/j.amc.2014.04.036 · 1.60 Impact Factor
  • Yoshiaki Muroya, Toshikazu Kuniya
    [Show abstract] [Hide abstract]
    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.
    Discrete and Continuous Dynamical Systems - Series B 04/2014; 19(4):1105-1118. DOI:10.3934/dcdsb.2014.19.1105 · 0.63 Impact Factor
  • Yoshiaki Muroya, Yoichi Enatsu, Huaixing Li
    [Show abstract] [Hide abstract]
    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 03/2014; 91(3). DOI:10.1080/00207160.2013.790534 · 0.72 Impact Factor
  • Yoshiaki Muroya, Huaixing Li, Toshikazu Kuniya
    [Show abstract] [Hide abstract]
    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.
    Journal of Mathematical Analysis and Applications 02/2014; 410(2):719-732. DOI:10.1016/j.jmaa.2013.08.024 · 1.12 Impact Factor
  • Source
  • Yoshiaki Muroya, Yoichi Enatsu
    [Show abstract] [Hide abstract]
    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 09/2013; 19(9). DOI:10.1080/10236198.2012.757602 · 0.86 Impact Factor
  • Yoshiaki Muroya, Yoichi Enatsu, Huaixing Li
    [Show abstract] [Hide abstract]
    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. DOI:10.1016/j.amc.2013.03.081 · 1.60 Impact Factor
  • Yoshiaki Muroya, Yoichi Enatsu, Toshikazu Kuniya
    [Show abstract] [Hide abstract]
    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.
    Nonlinear Analysis Real World Applications 06/2013; 14(3):1693–1704. DOI:10.1016/j.nonrwa.2012.11.005 · 2.34 Impact Factor
  • Yoichi Enatsu, Yoshiaki Muroya
    [Show abstract] [Hide abstract]
    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). DOI:10.1142/S1793524513500010 · 0.65 Impact Factor
  • Yoshiaki MUROYA, Yoichi ENATSU, Toshikazu KUNIYA
    [Show abstract] [Hide abstract]
    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. DOI:10.1016/S0252-9602(13)60003-X · 0.62 Impact Factor
  • Yoshiaki Muroya, Yoichi Enatsu, Huaixing Li
    [Show abstract] [Hide abstract]
    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). DOI:10.3934/dcdsb.2013.18.173 · 0.63 Impact Factor
  • Yoichi Enatsu, Yukihiko Nakata, Yoshiaki Muroya
    [Show abstract] [Hide abstract]
    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. DOI:10.1016/j.nonrwa.2012.01.007 · 2.34 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    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(7-7):1163-1181. DOI:10.1080/10236198.2011.555405 · 0.86 Impact Factor
  • Source
    Yoichi Enatsu, Yukihiko Nakata, Yoshiaki Muroya
    [Show abstract] [Hide abstract]
    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). DOI:10.1016/S0252-9602(12)60066-6 · 0.62 Impact Factor