Department of Applied Mathematics, School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, PR China.
Department of Mathematics & Statistics, York University, Toronto, Canada.
PLoS One. 2019 Mar 21;14(3):e0213898. doi: 10.1371/journal.pone.0213898. eCollection 2019.
Mass media reports can induce individual behaviour change during a disease outbreak, which has been found to be useful as it reduces the force of infection. We propose a compartmental model by including a new compartment of the intensity of the media reports, which extends existing models by considering a novel media function, which is dependent both on the number of infected individuals and on the intensity of mass media. The existence and stability of the equilibria are analyzed and an optimal control problem of minimizing the total number of cases and total cost is considered, using reduction or enhancement in the media reporting rate as the control. With the help of Pontryagin's Maximum Principle, we obtain the optimal media reporting intensity. Through parameterization of the model with the 2009 A/H1N1 influenza outbreak data in the 8th Hospital of Xi'an in Shaanxi Province of China, we obtain the basic reproduction number for the formulated model with two particular media functions. The optimal media reporting intensity obtained here indicates that during the early stage of an epidemic we should quickly enhance media reporting intensity, and keep it at a maximum level until it can finally weaken when epidemic cases have decreased significantly. Numerical simulations show that media impact reduces the number of cases during an epidemic, but that the number of cases is further mitigated under the optimal reporting intensity. Sensitivity analysis implies that the outbreak severity is more sensitive to the weight α1 (weight of media effect sensitive to infected individuals) than weight α2 (weight of media effect sensitive to media items).
大众媒体报道可以在疾病爆发期间诱导个体行为改变，这已经被证明是有用的，因为它可以降低感染的力度。我们提出了一个包含媒体报道强度的新 compartment 的 compartmental 模型，通过考虑一种新的媒体功能，该功能既依赖于感染个体的数量，也依赖于大众媒体的强度，从而扩展了现有的模型。分析了平衡点的存在性和稳定性，并考虑了一个最小化总病例数和总成本的最优控制问题，使用减少或增强媒体报告率作为控制。借助庞特里亚金极大值原理，我们得到了最优的媒体报道强度。通过对中国陕西省西安市第八医院 2009 年 A/H1N1 流感爆发数据的模型参数化，我们得到了两种特定媒体功能下所提出模型的基本繁殖数。这里得到的最优媒体报道强度表明，在疫情早期，我们应该迅速增强媒体报道强度，并将其保持在最高水平，直到疫情病例显著减少时才最终减弱。数值模拟表明，媒体的影响会减少疫情期间的病例数，但在最优报告强度下，病例数会进一步减少。敏感性分析表明，疫情严重程度对权重α1（对感染个体敏感的媒体效应权重）比权重α2（对媒体敏感的媒体效应权重）更敏感。
