Mutual interference and prey refuge are important drivers of predator–prey dynamics. The “exponent” or degree of mutual interference has been under much debate in theoretical ecology. In the present work, we investigate the interplay of the mutual interference exponent, and prey refuge, on the behavior of a predator–prey model with a generalized Holling type functional response — considering in particular the “non-smooth” case. This model can also be used to model an infectious disease where a susceptible population, moves to an infected class, after being infected by the disease. We investigate dynamical properties of the system and derive conditions for the occurrence of saddle–node, transcritical and Hopf-bifurcations. A sufficient condition for finite time extinction of the prey species has also been derived. In addition, we investigate the effect of a prey refuge on the population dynamics of the model and derive conditions such that the prey refuge would yield persistence of the population. We provide additional verification of our analytical results via numerical simulations. Our findings are in accordance with classical experimental results in ecology (Gause, 1934), that show that extinction of predator and prey populations is possible in a finite time period — but that bringing in refuge can effectively yield persistence.

相互干扰和避难所是捕食者-猎物动力学的重要驱动力。相互干扰的“指数”或程度在理论生态学中一直处于争论之中。在目前的工作中，我们研究了具有广义Holling型功能性反应的捕食者与被捕食者模型的行为之间的相互干扰指数和被捕食者的相互作用—特别是考虑到“非光滑”情况。该模型还可以用于对传染性疾病进行建模，在这种传染性疾病中，易感人群在被该疾病感染后移至感染类别。我们研究了系统的动力学特性，并推导了鞍节点，跨临界和Hopf分支发生的条件。还为猎物在有限时间内灭绝提供了充分的条件。此外，我们调查了避难所对模型种群动态的影响，并推导了条件，使得避难所将产生种群的持久性。我们通过数值模拟对分析结果进行其他验证。我们的发现与生态学中的经典实验结果一致（Gause，1934年），该研究表明捕食者和猎物种群在有限的时间内可能灭绝，但引入避难所可以有效地产生持久性。