Kinetic Analysis of a Transmission Model of a Group of Avian Influenza Infectious Diseases
In this paper,taking avian influenza H7N9 as an example,according to its incubation period,the transmission of H7N9 avian influenza virus with human-bird interaction is studied,and a kinetic model for the spread of SI-SEIR avian influenza is established.Then using the interaction among viruses in human,animal and environment,the stability of the disease free equilibrium and endemic equilibrium is analyzed,and the basic reproductive number R0 is obtained by kinetic analysis.Through the stability theory of Lyapunov and the principle of LaSalle invariant set,the global stability of the model is analyzed and the following conclusions are drawn:when R0 is less than 1,the disease free equilibrium is globally asymptotically stable;when R0 is greater than 1,the endemic equilibrium is globally asymptotically stable.Therefore,in areas where avian influenza outbreaks have already occurred,measures such as culling birds and reducing the circulation of birds in the market are key to stopping the spread of such infectious diseases.
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