随机噪声和媒体报道影响的传染病模型分析

Analysis the Epidemic Model Influenced by Random Noise and Media Coverage

媒体报道对疾病的预防和控制有着重要的作用，它可以减少人们感染疾病的机会。主要分析了随机噪声和媒体报道共同影响的传染病模型。首先计算出确定性模型的无病平衡点并验证了地方病平衡点的存在唯一性；其次，建立了随机性模型并通过Ito公式研究了系统的全局正解的存在唯一性，运用局部鞅的强大数定律分析了疾病灭绝和持久存在的条件；最后通过数值模拟验证了理论结果。

Media coverage plays an important role in the prevention and control of diseases, which can reduce the chance of contracting diseases. Random noise and media are analyzed in this paper. Firstly, the disease-free equilibrium of the deterministic model is calculated and the existence and uniqueness of the unique endemic equilibrium is proved; Secondly, a random model is established and the existence and uniqueness of the global positive solution of the system are studied by the Ito formula. The condition of extinction and persistence of the disease is analyzed by the strong number theorem of the local martingale; Finally, the results of analysis are verified by numerical simulation.