Stability of an Age-Since-Infection Structured Epidemic Model

Many transmitted diseases have latent period,and the length of the latent period affects the disease incidence in general.So it considered an age-since-infection epidemic model,the model constructed by two ordinary differential equations and one partial differential equation.Disease-free steady state and epidemic steady state of the model was given,linked by a transcritical bifurcation.A local stability analysis of the equilibria was performed.It is shown that the dynamics of the model is determined by the threshold of the parameters,that is,the basic reproductive number R0.If the threshold value is less than one,i.e.R01,only the disease-free equilibrium exist and it is stable.While the threshold value is greater than one,i.e.R01,there is a unique endemic equilibrium,and it is stable.