2010•Fuzhou daxue xuebao. Ziran kexue banRequires access

The analysis of SEIS epidemic model with nonlinear incidence rate

WU Cheng-qiang

Abstract

Change the incidence rate of SEIS epidemic model from βSI to nonlinear,and change the inflows A with the proportionality factor q:qA is the number of exposed individuals while(1-q)A is the number of susceptible individuals.It is showed that the global dynamics and the outcome of the disease are completely determined by the basic reproduction number R1;there is a unique endemic equilibrium if and only if R11.In addition,when 0q1 and R11,the unique endemic equilibrium is proved to be locally asymptotically stable by using Liapunov function.In the end,it is proved that there is no disease-free equilibrium.That is to say,the epidemic won't disappear but will become a local disease.Further,the influence of q on the epidemic model is analyzed.

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Key concepts: Epidemic model, Basic reproduction number, Nonlinear system, Mathematics, Nonlinear model, Incidence (geometry), Applied mathematics, Control theory (sociology)