非线性疾病信息影响的随机传染病模型研究

Analysis of the Stochastic Epidemic Model Influenced by Random Noise and Nonlinear Awareness Program

提出并分析了非线性疾病信息影响的确定性模型和随机性模型,并研究了随机噪声对确定性模型的影响.将易感人群划分为两类,无疾病信息意识的易感者和有疾病信息意识的易感者,并求得确定性系统的无病平衡点和地方病平衡点,得出基本再生数的表达式和平衡点稳定的条件,进一步探讨了随机扰动如何来影响疾病的灭绝,得出新的阈值R_0~S.最后,选用合理的参数进行了数值模拟来论证结果的正确性.

In this paper,the deterministic and stochastic epidemic models which are influenced by random noise and nonlinear awareness program are proposed and analyzed.The influence of the stochastic noise is discussed.The susceptible class is divided into two subclasses,aware susceptible and unaware susceptible.The deterministic system has a disease-free equilibrium and an endemic equilibrium.The expression of the basic reproduction number and condition for the stability of the equilibria are derived.How the random perturbations affect the extinction of the disease is further explored.A new threshold R0S is proposed.Finally,The reasonable parameters are used to illustrate the analytical results with a series of numeral simulations.