Accurateness and stability of delayed integral and differential equations and their discrete versions.

延迟积分和微分方程及其离散形式的准确性和稳定性。

• 批准号: 21540230
• 负责人: MUROYA Yoshiaki
• 金额: $ 1.33万
• 依托单位: Waseda University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2009
• 资助国家: 日本
• 起止时间: 2009 至 2011
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-21540230/
• 关键词: 関数方程式の大域理論; 数理モデル; 感染症モデル; 大域漸近安定性; Lyapunov関数法; 病理モデル

Applying the Lyapunov function techniques in MacCluskey(2010) which solve the open question on the global stability for delayed SIR epidemic models, we obtain results on sufficient condition of global stability, first by perturbation techniques, and second by extending the Lyapunov function techniques of MacCluskey which are corresponding to small loss rate of immunity recovery individuals. On the other hand, by modified monotone iterative techniques in Xu and Ma(2010), we improve results on the global stability for large loss rate of immunity recovery individuals.This monotone iterative techniques is a different techniques than that of Lyapunov function and we may hope to their applications to other models.Moreover, we find some natural extensions on global stability of continuous epidemic models to discrete models derived by the backward Euler method, by which we solve the open problem how to find the discrete version of the continuous model which keeps the global stability property.

利用Macrobinson key（2010）关于时滞SIR传染病模型全局稳定性的公开问题的李雅普诺夫函数技巧，首先利用扰动技巧，然后扩展Macrobinson key的李雅普诺夫函数技巧，得到了免疫恢复个体损失率小时全局稳定的充分条件.另一方面，通过对Xu和Ma（2010）的单调迭代技巧的改进，我们改进了免疫恢复个体大损失率下的全局稳定性结果，这种单调迭代技巧是一种不同于李雅普诺夫函数的技巧，我们希望将其应用于其他模型。我们发现连续传染病模型的全局稳定性到由向后欧拉方法导出的离散模型的一些自然推广，解决了如何找到连续模型的离散形式并保持全局稳定性的公开问题。

项目成果

Global stability of nonautonomous logistic equations with a piecewise constant delay

• DOI: 10.1016/j.nonrwa.2009.06.003
• 发表时间: 2010-06
• 期刊: Nonlinear Analysis-real World Applications
• 影响因子: 2
• 作者: Huaixing Li;Y. Muroya;Y. Nakata;R. Yuan

Global stability of a delayed SIRS epidemic model with a non-monotone incidence rate

具有非单调发生率的延迟 SIRS 流行病模型的全局稳定性

• 发表时间: 2011
• 期刊: J.Math.Anal.Appl.
• 作者: Y.Muroya. Y.Enatsu;Y.Nakata
• 通讯作者: Y.Nakata

Global stability of discrete SIR epidemic models with nonlinear incidence.

具有非线性发生率的离散 SIR 流行病模型的全局稳定性。

• 发表时间: 2011
• 期刊: J.Differ.Eq.Appl.
• 作者: Y.Enatsu;Y.Nakata;Y.Muroya;G.Izzo;A.Vecchio
• 通讯作者: A.Vecchio

離散グループSIRS病理モデルの大域漸近安定性

离散群 SIRS 病理模型的全局渐近稳定性

• 发表时间: 2010
• 作者: 室谷義昭;江夏洋一
• 通讯作者: 江夏洋一

Contractivity for nonautonomous logistic equation with piecewise constant delays

• DOI: 10.1063/1.3142940
• 发表时间: 2009-05
• 作者: Y. Nakata;Masataka Kuroda;Y. Muroya