Considering the sudden change of environmental disturbance, a stochastic susceptible infectious recovered (SIR) model with Markov jump and the limited medical resources is proposed. Firstly, by a bifurcation analysis of the deterministic SIR model, the maximal medical resource tipping point can be detected to adjust and optimize the medical resource allocation. Then, the impact of environmental disturbance on the basin stability is explored via the first escape probability(FEP). Based on the stochastic averaging of Markov jump process, the SIR epidemic system with switching random excitation is transferred into a probability-weighted Itô stochastic differential equation. Furthermore, the theoretical FEP is solved by the finite difference method and the validity is verified by numerical simulation. It is worth noting that the increase of noise intensity can decrease the basin stability of SIR model, and the existence of switching noise makes a difference in the basin stability compared with the epidemic system without switching intensity.

考虑到环境干扰的突然变化，提出了一种具有马尔可夫跳跃和有限医疗资源的随机易感感染恢复（SIR）模型。首先，通过确定性SIR模型的分叉分析，可以检测到最大医疗资源临界点，从而调整和优化医疗资源配置。然后，通过首次逃逸概率（FEP）探讨环境扰动对盆地稳定性的影响。基于马尔可夫跳跃过程的随机平均，将具有切换随机激励的SIR流行系统转化为概率加权的Itô随机微分方程。此外，通过有限差分法求解了理论FEP，并通过数值模拟验证了其有效性。