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Abstract：
Preventive treatment for people with latent Tuberculosis infection (LTBI) has aroused our great interest. In this paper, we propose and analyze a novel mathematical model of TB considering preventive treatment with media impact. The basic reproduction number R0 is defined by the next generation matrix method. In the case without media impact, we prove that the disease-free equilibrium is globally asymptotically stable (unstable) if R0<1(R0>1). Furthermore, we obtain that a unique endemic equilibrium exists when R0>1, which is globally asymptotically stable in the case of permanent immunity and no media impact. We fit the model to the newly reported TB cases data from 2009 to 2019 of four regions in China and estimate the parameters. And we estimated R0=0.5013<1 in Hubei indicating that TB in Hubei will be eliminated in the future. However, the estimated R0=1.015>1 in Henan, R0=1.282>1 in Jiangxi and R0=1.930>1 in Xinjiang imply that TB will continue to persist in these three regions without further prevention and control measures. Besides, sensitivity analysis is carried out to illustrate the role of model parameters for TB control. Our finding reveals that appropriately improving the rate of timely treatment for actively infected people and increasing the rate of individuals with LTBI seeking preventive treatment could achieve the goal of TB elimination. In addition, another interesting finding shows that media impact can only reduce the number of active infections to a limited extent, but cannot change the prevalence of TB.
摘要：
对潜伏性结核感染（LTBI）患者的预防性治疗引起了我们的极大兴趣。在本文中,我们提出并分析了一种新的结核病数学模型,该模型考虑了有媒体影响的预防性治疗.基本再现数R0由下一代矩阵方法定义。在没有媒体影响的情况下，我们证明了如果R0<1(R0>1)，无病平衡是全局渐近稳定(不稳定)的。此外，我们得到，当R0>1时，存在一个唯一的地方性均衡，在永久免疫和无媒体影响的情况下，它是全局渐近稳定的。我们将模型与中国四个地区2009-2019年新报告的结核病例数据进行拟合，并估计参数。我们估计湖北的R0=0.5013<1，表明湖北的结核病将在未来被消除。然而,河南估计R0=1.015>1，江西的R0=1.282>1和新疆的R0=1.930>1意味着结核病将在这三个地区继续存在，而没有进一步的预防和控制措施。此外,进行了敏感性分析，以说明模型参数在结核病控制中的作用。我们的发现表明，适当提高积极感染者的及时治疗率和增加LTBI患者寻求预防性治疗的比例可以实现消除结核病的目标。此外,另一个有趣的发现表明，媒体的影响只能在有限的程度上减少活动性感染的数量，但不能改变结核病的患病率。
