In this paper, to characterize the limited availability of medical resources, we incorporate a saturated treatment rate into a network-based susceptible-infected-susceptible (SIS) epidemic model with time delay and nonlinear incidence rate. Analytical study shows the boundedness of solutions, the basic reproduction number $R_0$ and equilibrium points of the proposed system. For any infection delay, we perform both local and global stability analyses for the disease-free equilibrium point by analyzing the characteristic equation and using Lyapunov functional. Furthermore, this system exhibits bifurcation behavior at $R_0=1$ due to the introduction of saturated treatment. More precisely, a backward bifurcation takes place from the disease-free equilibrium point when the saturation constant $\beta$ is sufficiently large. Under the given conditions, the unique disease-spreading equilibrium point is also proved to be locally asymptotically stable. In addition, we analyze an optimal control problem with consideration of two time-dependent control measures. Several numerical simulations are presented to validate the obtained theoretical results.

在本文中，为了表征医疗资源的有限可用性，我们将饱和治疗率纳入基于网络的具有时间延迟和非线性发病率的易感感染易感（SIS）流行病模型。解析研究显示解的有界性，基本再生数${\mathrm{电阻}}_0$和建议系统的平衡点。对于任何感染延迟，我们通过分析特征方程并使用 Lyapunov 函数对无病平衡点进行局部和全局稳定性分析。此外，该系统在${\mathrm{电阻}}_0=1$由于引入了饱和处理。更准确地说，当饱和常数不变时，从无病平衡点发生向后分叉$\beta$足够大。在给定条件下，唯一的疾病传播平衡点也被证明是局部渐近稳定的。此外，我们分析了考虑两个时间相关控制措施的最优控制问题。提出了几个数值模拟来验证所获得的理论结果。