带接种和抗病毒治疗的流感传播模型  

Global Stability of an Influenza Model with Vaccination and Antiviral Treatment

作　　者：张丽娟[1] 赵宜宾[1] 庄需芹[1] 张鹤翔[1] 王福昌[1] 

机构地区：[1]中国地震局防灾科技学院,河北三河065201

出　　处：《数学的实践与认识》2013年第20期161-167,共7页Mathematics in Practice and Theory

基　　金：河北省高等学校科学技术研究指导项目(Z2012139);中央高校基本科研业务费专项资金创新团队资助计划项目(ZY20110101);中国地震局教师科研基金(20110116)

摘　　要：疫苗注射和抗病毒治疗是两种控制流感传播的重要途径,然而随着耐药菌株即抗药毒株的产生使得抗生素失效.2013年在中国新出现的人感染H7N9病例说明了病毒变异对人类造成的潜在威胁.建立数学模型,研究了抗病毒治疗和疫苗注射对流感传播的动力学行为的影响.模型中包括药物敏感感染群体和抗药性群体.通过分析传染性和抗药性个体的再生数Rsc和RRc得到了决定两者竞争结果的阈值.通过对各平衡点的稳定性分析,由Matlab模拟得到结论:高水平的抗病毒治疗有可能导致患病者的增加,增加程度要受到其他因素包括疫苗接种速率和抗药性的发展,所以抗病毒治疗应该适可而止.Vaccination and antiviral treatment are two important kinds of treatment and control the spread of the epidemic,however the benefit of antiviral use can be compromised if drug-resistant strains arise.The new case of infected people with varied H7N9 in China illustrates potential threat to the human healthy.In this paper we develop a mathematical model to explore the impact of vaccination and antiviral treatment on the transmission dynamics of influenza.The model includes both drug sensitive and resistant strains.We also add latent period in to the model.Analytical results of the model show that the quantities R_（Sc）andR_（Rc）,which represent the control reproduction numbers of the sensitive and resistant strains respectively,provide threshold conditions that determine the competitive outcomes of the two strains.These conditions can be used to gain important insights into the effect of vaccination and treatment on the prevention and control of influenza.The findings imply that higher level of treatment may lead to an increase of epidemic size,and extend to which this occurs depends on other factors such as the rates of vaccination and resistance development.This implies that antiviral treatment should be implemented appropriately.

关 键 词：流感传播模型 抗病毒治疗 疫苗接种 稳定性 抗药性 计算机模拟 H7N9 

分 类 号：R511.7[医药卫生—内科学]