Abstract
In this paper, we analyse the bifurcation of epidemic models. Those model is waning immunity. First, the stability of those system is analyzed by analyzing the stability of critical points. The threshold number that associated with the stability was determined. Later, the existence of bifurcation was analyzed. The result show that bifurcation exist and threshold number is considered as bifurcation parameter. Numerical simulation is given to confirm the analytical results by showing the graphic solutions and phase portrait.
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