论文标题
SIS流行模型中的空间扩散和周期性域的周期性发展
Spatial diffusion and periodic evolving of domain in an SIS epidemic model
论文作者
论文摘要
为了探索周期性发展的域对疾病传播的影响，我们研究了具有逻辑术语的SIS反应扩散模型，该模型在周期性发展的域上。基本的复制号$ {\ Mathcal {r}} _ 0 $由下一代感染操作员给出，并依赖于定期发展的域的不断发展的速率，受感染个体的扩散系数$ d_i $和空间的大小。 $ {\ Mathcal {r}} _ 0 $的单调性相对于$ d_i $，不断发展的速率$ρ（t）$和间隔长度$ l $是派生的，$ {\ nathcal {r}}} _ 0 $ d_i $ d_i $或$ l $的渐近属性是一个dim，一个dimens nimend，in Mathcal {r}} _ 0 $ d_i $ d_i $ lace。 $ {\ Mathcal {r}} _ 0 $作为阈值可以用来表征无病平衡是否稳定。我们的理论结果和数值模拟表明，较小的不断发展的速率，受感染个体的少量扩散和较小的间隔长度对预防和控制疾病具有积极影响。
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.
