In this article, an SIRS epidemic model spread by vectors （mosquitoes） which have an incubation time to become infectious is formulated. It is shown that a disease-free equilibrium point is globally stable if no end...In this article, an SIRS epidemic model spread by vectors （mosquitoes） which have an incubation time to become infectious is formulated. It is shown that a disease-free equilibrium point is globally stable if no endemic equilibrium point exists. Further, the endemic equilibrium point （if it exists） is globally stable with a respect ＂weak delay＂. Some known results are generalized.展开更多
In this article, we establish the global asymptotic stability of a disease-free equilibrium and an endemic equilibrium of an SIRS epidemic model with a class of nonlin- ear incidence rates and distributed delays. By u...In this article, we establish the global asymptotic stability of a disease-free equilibrium and an endemic equilibrium of an SIRS epidemic model with a class of nonlin- ear incidence rates and distributed delays. By using strict monotonicity of the incidence function and constructing a Lyapunov functional, we obtain sufficient conditions under which the endemic equilibrium is globally asymptotically stable. When the nonlinear inci- dence rate is a saturated incidence rate, our result provides a new global stability condition for a small rate of immunity loss.展开更多
Consider the discrete Lasota Wazewska modelN n+1 -N n =-μN n +pe -rN n-k , n=0,1,2,...(*)where μ∈(0,1),r,p∈(0,∞) and k ∈N.A sufficient condition for all positive solutions of (*) to...Consider the discrete Lasota Wazewska modelN n+1 -N n =-μN n +pe -rN n-k , n=0,1,2,...(*)where μ∈(0,1),r,p∈(0,∞) and k ∈N.A sufficient condition for all positive solutions of (*) to be attracted to its equilibrium N is obtained.It improves correspondent result obtained by Chen and Yu in 1999.展开更多
This note considers the model for the survival of the red blood ceels with several delays and establishes some new sufficient conditions which guarantee the positive equilibrium of the model being a global attractor. ...This note considers the model for the survival of the red blood ceels with several delays and establishes some new sufficient conditions which guarantee the positive equilibrium of the model being a global attractor. Our results generalize and improve the corre-spondently known results obtained in [1, 3], and solve a conjecture in [7].展开更多
In this paper, the asymptotic behavior of three types of population models with delays and diffusion is studied. The first represents one species growth in the patch Ω and periodic environment and with delays recruit...In this paper, the asymptotic behavior of three types of population models with delays and diffusion is studied. The first represents one species growth in the patch Ω and periodic environment and with delays recruitment, the second models a single species dispersal among the m patches of a heterogeneous environment, and the third models the spread of bacterial infections. Sufficient conditions for the global attractivity of periodic solution are obtained by the method of monotone theory and strongly concave operators. Some earlier results are extended to population models with delays and diffusion.展开更多
In this paper, we consider the following Logistic model where {rn}n=0 is a sequence of nonnegative real number, {kn} is a sequence of nonnegative integers satisfying lim (n-kn)= , lim sup kn=∞ , and K is a positive ...In this paper, we consider the following Logistic model where {rn}n=0 is a sequence of nonnegative real number, {kn} is a sequence of nonnegative integers satisfying lim (n-kn)= , lim sup kn=∞ , and K is a positive constant. We obtain a new sufficient condition for the positive equilibrium of Eq.() to be globally attractive, which improves some recent known results established in [3-4].展开更多
Consider the discrete delay logistic model where α∈(1,∞), β(0,∞), and k∈ {0,1,2,…}. We obtain new sufficient conditions for the positive equilibrium (α-1)/β of (1) to be a global attractor.
In a polluted environment, considering the biological population infected with a kind of disease and hunted by human beings, we formulate a nonautonomous SIR population-epidemic model with time-varying impulsive relea...In a polluted environment, considering the biological population infected with a kind of disease and hunted by human beings, we formulate a nonautonomous SIR population-epidemic model with time-varying impulsive release and general nonlinear incidence rate and investigate dynamical behaviors of the model. Under the reasonable assumptions, the sufficient conditions which guarantee the globally attractive of the disease-free periodic solution and the permanence of the infected fish are established, that is, the infected fish dies out if , whereas the disease persists if . To substantiate our theoretical results, extensive numerical simulations are performed for a hypothetical set of parameter values.展开更多
In this paper, we consider the model for the survival of red blood ceels with several delaysdN(t)dt=-μ N(t)+m i=1 P ie -r iN(t-τ i) , t≥ 0 (*) and establish a sufficient condition under which the posit...In this paper, we consider the model for the survival of red blood ceels with several delaysdN(t)dt=-μ N(t)+m i=1 P ie -r iN(t-τ i) , t≥ 0 (*) and establish a sufficient condition under which the positive equilibrium N * of (*) is a global attractor. Our criteria generalize and improve the correspondent results obtained in .展开更多
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 d...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 R0 ≤ 1 and endemic equilibrium forR0 ≥ 1.展开更多
In this paper, we consider a SIRS epidemic model with impulsive vaccination and distributed time delays. By the discrete dynamical system determined by the stroboscopic map, we obtain the exact infection-free periodic...In this paper, we consider a SIRS epidemic model with impulsive vaccination and distributed time delays. By the discrete dynamical system determined by the stroboscopic map, we obtain the exact infection-free periodic solution to the system. Further, using the comparison theorem, we prove that the infection-free periodic solution is globally attractive under an assumption. A sufficient condition for the permanence of the model is investigated.展开更多
Pulse vaccination is an effective and important strategy to eradicate an infectious disease. The authors investigate an SEIRS epidemic model with two delays and pulse vaccination. By using the discrete dynamical syste...Pulse vaccination is an effective and important strategy to eradicate an infectious disease. The authors investigate an SEIRS epidemic model with two delays and pulse vaccination. By using the discrete dynamical system determined by stroboscopic map, the authors obtain that the infectious population dies out if R△ 〈 1, and the infectious population is uniformly persistent if R^△ 〉 1. The results indicate that a short period of pulse vaccination or a large pulse vaccination rate is a sufficient condition to eradicate the disease.展开更多
In this paper, the effect of delay on the asymptotic behavior of a Lasota-Wazewska model with multiple time-varying delays is investigated. By employing the fluctuation lemma and some differential inequality technique...In this paper, the effect of delay on the asymptotic behavior of a Lasota-Wazewska model with multiple time-varying delays is investigated. By employing the fluctuation lemma and some differential inequality techniques, delay-dependent criteria are obtained for the global attractivity of the considered model. An example is also given in the end of this paper to show the effectiveness of our results.展开更多
基金This work is supported by the National Sciences Foundation of China (10471040)the Youth Science Foundations of Shanxi Province (20021003).
文摘In this article, an SIRS epidemic model spread by vectors （mosquitoes） which have an incubation time to become infectious is formulated. It is shown that a disease-free equilibrium point is globally stable if no endemic equilibrium point exists. Further, the endemic equilibrium point （if it exists） is globally stable with a respect ＂weak delay＂. Some known results are generalized.
基金supported in part by JSPS Fellows,No.237213 of Japan Society for the Promotion of Science to the first authorthe Grant MTM2010-18318 of the MICINN,Spanish Ministry of Science and Innovation to the second authorScientific Research (c),No.21540230 of Japan Society for the Promotion of Science to the third author
文摘In this article, we establish the global asymptotic stability of a disease-free equilibrium and an endemic equilibrium of an SIRS epidemic model with a class of nonlin- ear incidence rates and distributed delays. By using strict monotonicity of the incidence function and constructing a Lyapunov functional, we obtain sufficient conditions under which the endemic equilibrium is globally asymptotically stable. When the nonlinear inci- dence rate is a saturated incidence rate, our result provides a new global stability condition for a small rate of immunity loss.
基金Supported by the Science Foundation of Educational Committee of Hunan Province
文摘Consider the discrete Lasota Wazewska modelN n+1 -N n =-μN n +pe -rN n-k , n=0,1,2,...(*)where μ∈(0,1),r,p∈(0,∞) and k ∈N.A sufficient condition for all positive solutions of (*) to be attracted to its equilibrium N is obtained.It improves correspondent result obtained by Chen and Yu in 1999.
文摘This note considers the model for the survival of the red blood ceels with several delays and establishes some new sufficient conditions which guarantee the positive equilibrium of the model being a global attractor. Our results generalize and improve the corre-spondently known results obtained in [1, 3], and solve a conjecture in [7].
基金This research is supported by the Developing Fund of Nanjing University of Science and Technology.
文摘In this paper, the asymptotic behavior of three types of population models with delays and diffusion is studied. The first represents one species growth in the patch Ω and periodic environment and with delays recruitment, the second models a single species dispersal among the m patches of a heterogeneous environment, and the third models the spread of bacterial infections. Sufficient conditions for the global attractivity of periodic solution are obtained by the method of monotone theory and strongly concave operators. Some earlier results are extended to population models with delays and diffusion.
基金Mathematical Tianyuan Foundation of China, Scientific Researches Foundation of Educational Committee of Hunan Province and Spe
文摘In this paper, we consider the following Logistic model where {rn}n=0 is a sequence of nonnegative real number, {kn} is a sequence of nonnegative integers satisfying lim (n-kn)= , lim sup kn=∞ , and K is a positive constant. We obtain a new sufficient condition for the positive equilibrium of Eq.() to be globally attractive, which improves some recent known results established in [3-4].
文摘Consider the discrete delay logistic model where α∈(1,∞), β(0,∞), and k∈ {0,1,2,…}. We obtain new sufficient conditions for the positive equilibrium (α-1)/β of (1) to be a global attractor.
文摘In a polluted environment, considering the biological population infected with a kind of disease and hunted by human beings, we formulate a nonautonomous SIR population-epidemic model with time-varying impulsive release and general nonlinear incidence rate and investigate dynamical behaviors of the model. Under the reasonable assumptions, the sufficient conditions which guarantee the globally attractive of the disease-free periodic solution and the permanence of the infected fish are established, that is, the infected fish dies out if , whereas the disease persists if . To substantiate our theoretical results, extensive numerical simulations are performed for a hypothetical set of parameter values.
文摘In this paper, we consider the model for the survival of red blood ceels with several delaysdN(t)dt=-μ N(t)+m i=1 P ie -r iN(t-τ i) , t≥ 0 (*) and establish a sufficient condition under which the positive equilibrium N * of (*) is a global attractor. Our criteria generalize and improve the correspondent results obtained in .
文摘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 R0 ≤ 1 and endemic equilibrium forR0 ≥ 1.
基金supported by the National Natural Science Foundation of China (10471040)the Natural Science Foundation of Shanxi (2009011005-3)
文摘In this paper, we consider a SIRS epidemic model with impulsive vaccination and distributed time delays. By the discrete dynamical system determined by the stroboscopic map, we obtain the exact infection-free periodic solution to the system. Further, using the comparison theorem, we prove that the infection-free periodic solution is globally attractive under an assumption. A sufficient condition for the permanence of the model is investigated.
基金the National Natural Science Foundation of China under Grant No.10471117the Emphasis Subject of Guizhou College of Finance & Economics.
文摘Pulse vaccination is an effective and important strategy to eradicate an infectious disease. The authors investigate an SEIRS epidemic model with two delays and pulse vaccination. By using the discrete dynamical system determined by stroboscopic map, the authors obtain that the infectious population dies out if R△ 〈 1, and the infectious population is uniformly persistent if R^△ 〉 1. The results indicate that a short period of pulse vaccination or a large pulse vaccination rate is a sufficient condition to eradicate the disease.
文摘In this paper, the effect of delay on the asymptotic behavior of a Lasota-Wazewska model with multiple time-varying delays is investigated. By employing the fluctuation lemma and some differential inequality techniques, delay-dependent criteria are obtained for the global attractivity of the considered model. An example is also given in the end of this paper to show the effectiveness of our results.
