非自治耗散Schr\"odinger-Boussinesq 方程组紧致核截面的存在性$^$

讨论满足齐次Dirichlet边界条件的非自治耗散Schr\"odinger-Boussinesq 方程组解的长时间行为. 通过 对方程作适当的分解, 证明了方程组所生成的过程存在紧致核截面.     

Pattern selection in a predation model with self and cross diffusion

In this paper, we present the amplitude equations for the excited modes in a cross-diffusive predator--prey model with zero-flux boundary conditions. From these equations, the stability of patterns towards uniform and inhomogenous perturbations is determined. Furthermore, we present novel numerical evidence of six typical turing patterns, and find that the model dynamics exhibits complex pattern replications: for μ₁<μ≤μ₂, the steady state is the only stable solution of the model; for μ₂<μ≤μ₄, by increasing the control parameter μ, the sequence H_π-hexagons → H₀-hexagon-stripe mixtures rightarrow stripes → H_π-hexagon-stripe mixtures → H₀-hexagons is observed; for μ>μ₄, the stripe pattern emerges. This may enrich the pattern formation in the cross-diffusive predator--prey model.     

Turing pattern selection in a reactionben diffusion epidemic modelast

We present Turing pattern selection in a reaction—diffusion epidemic model under zero-flux boundary conditions. The value of this study is twofold. First, it establishes the amplitude equations for the excited modes, which determines the stability of amplitudes towards uniform and inhomogeneous perturbations. Second, it illustrates all five categories of Turing patterns close to the onset of Turing bifurcation via numerical simulations which indicates that the model dynamics exhibits complex pattern replication: on increasing the control parameter v, the sequence “H₀ hexagons → H₀-hexagon-stripe mixtures → stripes → H_π-hexagon-stripe mixtures → H_π hexagons” is observed. This may enrich the pattern dynamics in a diffusive epidemic model.     

温州市区手足口病SARIMA模型建立及应用

基于温州市区(鹿城区、瓯海区、龙湾区)2011年1月至2017年12月月报手足口病新发病人数统计数据,构建了季节求和自回归-移动平均模型(SARIMA).结果表明SARIMA(2,1,1)(0,1,1)_([12])模型平均绝对百分误差(MAPE)为6.002%,能较好的拟合出温州市区手足口新发病人数的季节性和趋势性特征.在对拟合值进行指数化和周期性还原后,预测2018年1-6月温州市区手足口新发病人数仍维持较高水平,其中6月份达到最高1094 (95%CI:321-3723)例.研究结果将可为相关部门制定手足口病防控措施提供决策依据.     

Turing pattern selection in a reaction-diffusion epidemic model

We present Turing pattern selection in a reaction-diffusion epidemic model under zero-flux boundary conditions.The value of this study is twofold.First,it establishes the amplitude equations for the excited modes,which determines the stability of amplitudes towards uniform and inhomogeneous perturbations.Second,it illustrates all five categories of Turing patterns close to the onset of Turing bifurcation via numerical simulations which indicates that the model dynamics exhibits complex pattern replication:on increasing the control parameter ν,the sequence "H 0 hexagons → H 0-hexagon-stripe mixtures → stripes → H π-hexagon-stripe mixtures → H π hexagons" is observed.This may enrich the pattern dynamics in a diffusive epidemic model.