Jikan okure o motsu suri moderu ni okeru pamanensu to heikoten no taiiki zenkin anteisei

制度:新 ; 報告番号:甲3529号 ; 学位の種類:博士(理学) ; 授与年月日:2012/3/15 ; 早大学位記番号:新586

Global stability for a discrete SIS epidemic model with immigration of infectives

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 R 0 ≤ 1 and the endemic equilibrium for R 0 > 1, where R 0 is the basic reproduction number of the continuous-time model. This is just a discrete analogue of continuous SIS epidemic model with immigration of infectives

Global analysis of a multi-group SIR epidemic model with nonlinear incidence rates and distributed moving delays between patches

In this paper, applying Lyapunov functional approach, we establish sufficient conditions under which each equilibrium is globally asymptotically stable for a class of multi-group SIR epidemic models. The incidence rate is given by nonlinear incidence rates and distributed delays incorporating not only an exchange of individuals between patches through migration but also cross patch infection between different groups. We show that nonlinear incidence rates and distributed delays have no influence on the global stability, but patch structure has. Moreover, the present results generalize known results on the global stability of a heroin model with two delays considered in the recent literatures. We also offer new techniques to prove the boundedness of the solutions, the existence of the endemic equilibrium and permanence of the model

Permanence for multi-species nonautonomous Lotka-Volterra cooperative systems

Abstract. In this paper, we establish sufficient conditions under which Lotka-Volterra cooperative systems are permanent for the n-dimensional case. We improve the result of [G. Lu and Z. Lu, Permanence for two species LotkaVolterra systems with delays, Math. Biosci. Engi. 5 (2008), 477-484] for the 2-dimensional case in that no restrictions of the size of time delays are needed. When the interval of time delays is constant, we further show that the restriction of the size of time delays is not required for the case n = 2, but it is required for the case n ≥ 3 to obtain lower bounds of solutions. An example is offered to illustrate the feasibility of our results

Original article Global stability for a discrete SIS epidemic model with immigration of infectives

In this paper, we propose a discrete-time SIS epidemic model which is derived from continuoustime 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 R 0 ≤ 1 and the endemic equilibrium for R 0 > 1, where R 0 is the basic reproduction number of the continuous-time model. This is just a discrete analogue of continuous SIS epidemic model with immigration of infectives

Reconsideration of r/K Selection Theory Using Stochastic Control Theory and Nonlinear Structured Population Models.

Despite the fact that density effects and individual differences in life history are considered to be important for evolution, these factors lead to several difficulties in understanding the evolution of life history, especially when population sizes reach the carrying capacity. r/K selection theory explains what types of life strategies evolve in the presence of density effects and individual differences. However, the relationship between the life schedules of individuals and population size is still unclear, even if the theory can classify life strategies appropriately. To address this issue, we propose a few equations on adaptive life strategies in r/K selection where density effects are absent or present. The equations detail not only the adaptive life history but also the population dynamics. Furthermore, the equations can incorporate temporal individual differences, which are referred to as internal stochasticity. Our framework reveals that maximizing density effects is an evolutionarily stable strategy related to the carrying capacity. A significant consequence of our analysis is that adaptive strategies in both selections maximize an identical function, providing both population growth rate and carrying capacity. We apply our method to an optimal foraging problem in a semelparous species model and demonstrate that the adaptive strategy yields a lower intrinsic growth rate as well as a lower basic reproductive number than those obtained with other strategies. This study proposes that the diversity of life strategies arises due to the effects of density and internal stochasticity