| Summary: | In this paper, we study the bifurcation of an epidemic model with sub-optimal immunity and saturated treatment/recovery rate. Different from classical models, suboptimal models are more realistic to explain the microparasite infections disease such as Pertussis and Influenza A. By carrying out the bifurcation analysis of the model, we show that for certain values of the model parameters, Hopf bifurcation, Bogdonov-Takens bifurcation and its associated homoclinic bifurcation occur. By studying the bifurcation curves, we can predict the persistence or extinction of diseases.
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