In this work, in order to identify the most effective measure and combinations of several measures to control influenza spread, we propose an SVEIAR influenza model with imperfect vaccination, media coverage and antiv...In this work, in order to identify the most effective measure and combinations of several measures to control influenza spread, we propose an SVEIAR influenza model with imperfect vaccination, media coverage and antiviral treatment. The global dynamics of the model is explored. Sensitivity analysis of the basic reproduction number and the endemic equilibrium is conducted to evaluate the effectiveness of influenza control measures. Purthermore, an optimal control problem incorporating the three measures is formulated to design optimal control strategies for influenza. The cost-effectiveness analysis reveals that combining the three measures is the most cost-effective among the strategies considered. Numerical simulations show that media propaganda can play a dominant role in curbing influenza transmission.展开更多
A three-dimensional compartmental model with media coverage is proposed to describe the real characteristics of its impact in the spread of infectious diseases in a given region. A piecewise continuous transmission ra...A three-dimensional compartmental model with media coverage is proposed to describe the real characteristics of its impact in the spread of infectious diseases in a given region. A piecewise continuous transmission rate is introduced to describe that media coverage exhibits its effect only when the number of the infected exceeds a certain critical level. Further, it is assumed that the impact of media coverage on the contact transmission is described by an exponential decreasing factor. Stability analysis of the model shows that the disease-free equilibrium is globally asymptotically stable if the basic reproduction number is less than unity. On the other hand, when the basic reproduction number is greater than unity and media coverage impact is sufficiently small, a unique endemic equilibrium exists, which is globally asymptotically stable.展开更多
基金Acknowledgments The work was supported by National Natural Science Foundation of China （Nos. 11261017, 11371161）, and the key scientific research project of Education Department of Hubei Province of China （No. D20101902）.
文摘In this work, in order to identify the most effective measure and combinations of several measures to control influenza spread, we propose an SVEIAR influenza model with imperfect vaccination, media coverage and antiviral treatment. The global dynamics of the model is explored. Sensitivity analysis of the basic reproduction number and the endemic equilibrium is conducted to evaluate the effectiveness of influenza control measures. Purthermore, an optimal control problem incorporating the three measures is formulated to design optimal control strategies for influenza. The cost-effectiveness analysis reveals that combining the three measures is the most cost-effective among the strategies considered. Numerical simulations show that media propaganda can play a dominant role in curbing influenza transmission.
文摘A three-dimensional compartmental model with media coverage is proposed to describe the real characteristics of its impact in the spread of infectious diseases in a given region. A piecewise continuous transmission rate is introduced to describe that media coverage exhibits its effect only when the number of the infected exceeds a certain critical level. Further, it is assumed that the impact of media coverage on the contact transmission is described by an exponential decreasing factor. Stability analysis of the model shows that the disease-free equilibrium is globally asymptotically stable if the basic reproduction number is less than unity. On the other hand, when the basic reproduction number is greater than unity and media coverage impact is sufficiently small, a unique endemic equilibrium exists, which is globally asymptotically stable.
