Incorporating the environmental perturbations and available resources of the public health system, we construct both deterministic and stochastic models of SIRS type. The deterministic model exhibits very rich dynamics, such as Hopf bifurcation and backward bifurcation which leads to the co-existence of the stable disease-free state and a stable endemic equilibrium. For the stochastic model, we show that under mild extra conditions, if the basic reproduction number is less than one, then the disease will be eradicated almost surely, and if the basic reproduction number is greater than one, the stochastic model will admit a unique ergodic stationary distribution, which implies that the disease persists almost surely. Part of our numerical simulations indicate that: (i) The introduction of environmental perturbations may drift the endemic equilibrium to the disease-free equilibrium, or vice versa; (ii) Increasing available resources is necessary in order to mitigate the infections.

结合环境扰动和公共卫生系统的可用资源，我们构建了SIRS类型的确定性模型和随机模型。确定性模型表现出非常丰富的动力学，例如Hopf分叉和向后分叉，这导致稳定的无病状态和稳定的地方性平衡并存。对于随机模型，我们表明在温和的额外条件下，如果基本繁殖数小于1，则几乎可以肯定地根除疾病；如果基本繁殖数大于1，则随机模型将承认唯一遍历的平稳分布，这意味着该疾病几乎可以肯定地持续下去。我们的部分数值模拟表明：（i）引入环境扰动可能使地方性平衡向无病平衡转移，反之亦然；（ii）为了减轻感染，有必要增加可用资源。