Influenza virus mutates frequently. This poses immense challenges to prevent the spread of influenza. This paper aims to investigate an influenza epidemic model in which influenza virus can mutate into a mutant influenza virus. We find a threshold condition that determines the stability of the disease-free equilibrium. Two equilibria may also exist: mutant-dominant equilibrium and endemic equilibrium. We show that the mutant-dominant equilibrium is globally asymptotically stable under some biological feasible conditions. Furthermore, the influenza is endemic in the sense of permanence if and only if the endemic equilibrium exists. Numerical simulations are also performed to illustrate theoretical results and demonstrate the effects of disease-induced death on the dynamics of the model.

中文翻译：

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具有病毒突变的流感流行模型的动态行为

流感病毒经常变异。这对预防流感的传播提出了巨大的挑战。本文旨在研究流感病毒可以变异为变异流感病毒的流感流行模型。我们找到了一个决定无病平衡稳定性的阈值条件。也可能存在两种平衡：突变主导平衡和地方性平衡。我们表明，在一些生物学可行的条件下，突变显性平衡是全局渐近稳定的。此外，当且仅当流行性平衡存在时，流感在持久性意义上是地方性的。还进行了数值模拟以说明理论结果并证明疾病引起的死亡对模型动力学的影响。