School of Mathematics and Statistics, Hubei Minzu University, Enshi, Hubei 445000, China.
College of Computer Science and Engineering, Chongqing Three Gorges University, Chongqing 404020, China.
Math Biosci Eng. 2022 Jan 13;19(3):2835-2852. doi: 10.3934/mbe.2022130.
In the process of spreading infectious diseases, the media accelerates the dissemination of information, and people have a deeper understanding of the disease, which will significantly change their behavior and reduce the disease transmission; it is very beneficial for people to prevent and control diseases effectively. We propose a Filippov epidemic model with nonlinear incidence to describe media's influence in the epidemic transmission process. Our proposed model extends existing models by introducing a threshold strategy to describe the effects of media coverage once the number of infected individuals exceeds a threshold. Meanwhile, we perform the stability of the equilibriua, boundary equilibrium bifurcation, and global dynamics. The system shows complex dynamical behaviors and eventually stabilizes at the equilibrium points of the subsystem or pseudo equilibrium. In addition, numerical simulation results show that choosing appropriate thresholds and control intensity can stop infectious disease outbreaks, and media coverage can reduce the burden of disease outbreaks and shorten the duration of disease eruptions.
在传染病传播过程中，媒体加速了信息的传播，人们对疾病有了更深入的了解，这将显著改变他们的行为，降低疾病传播；这对人们有效预防和控制疾病非常有利。我们提出了一个具有非线性发病率的 Filippov 传染病模型来描述媒体在传染病传播过程中的影响。我们的模型通过引入一个阈值策略来描述媒体报道的影响，一旦感染人数超过阈值。同时，我们对平衡点的稳定性、边界平衡点分岔和全局动力学进行了研究。该系统表现出复杂的动态行为，最终在子系统或伪平衡点处稳定。此外，数值模拟结果表明，选择适当的阈值和控制强度可以阻止传染病的爆发，媒体报道可以减轻疾病爆发的负担，并缩短疾病爆发的持续时间。
