In order to explore the impact of periodically evolving domain on the transmission of disease, we study an 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 $\rho \left(t\right)$ and interval length $L$ is derived, and asymptotic property of ${\mathcal{R}}_0$ if $d_I$ or $L$ is small enough or large enough in one-dimensional space is 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.

为了探讨周期性演化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。基本复制数${\mathcal{[R}}_0$ 由下一代感染算子给出，并取决于周期性演化域的演化速率，被感染个体的扩散系数 $d_{\mathrm{一世}}$和空间的大小。的单调性${\mathcal{[R}}_0$ 关于 $d_{\mathrm{一世}}$，发展速度 $\rho （Ť）$ 和间隔长度 $\mathrm{大号}$ 导出，并且的渐近性质 ${\mathcal{[R}}_0$ 如果 $d_{\mathrm{一世}}$ 或者 $\mathrm{大号}$ 讨论在一维空间中足够小或足够大。 ${\mathcal{[R}}_0$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，较小的发展速度，较小的感染个体扩散和较小的间隔时间对疾病的预防和控制具有积极的影响。