SIS传染病模型中区域的空间扩散和周期演化
Spatial diffusion and periodic evolving of domain in an SIS epidemic model
摘要：
为了研究周期发展区域对疾病传播的影响，研究了周期发展区域上一类具有Logistic项的SIS反应扩散模型。基本再生数${\mathcal{R}}_0$由下一代感染算子给出，并依赖于周期性演化域的演化速率、感染个体的扩散系数$d_I$和空间的大小.导出了${\mathcal{R}}_0$关于$d_I$的单调性、演化速率$ρ(t)$和区间长度$L$，并讨论了一维空间中$d_I$或$L$足够小或足够大时${\mathcal{R}}_0$的渐近性质. ${\mathcal{R}}_0$作为阈值可以用来表征无病平衡点是否稳定。我们的理论结果和数值模拟表明，小的进化速率、小的感染个体扩散和小的间隔长度对疾病的预防和控制有积极的影响。
英文摘要：
In order to explore the impact of periodically evolving domain on the transmission of disease, we study a SIS reaction-diffusion model with logistic term on a periodically evolving domain. The basic reproduction number ${\mathcal{R}}_0$ is given by the next generation infection operator, and relies on the evolving rate of the periodically evolving domain, diffusion coefficient of infected individuals $d_I$ and size of the space. The monotonicity of ${\mathcal{R}}_0$ with respect to $d_I$, evolving rate $ρ(t)$ and interval length $L$ are derived, and asymptotic property of ${\mathcal{R}}_0$ if $d_I$ or $L$ is small enough or large enough in one-dimensional space are discussed. ${\mathcal{R}}_0$ as threshold can be used to characterize whether the disease-free equilibrium is stable or not. Our theoretical results and numerical simulations indicate that small evolving rate, small diffusion of infected individuals and small interval length have positive impact on prevention and control of disease.
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