Stability and bifurcation analysis of contact tracing HIV/AIDS models
A class of HIV/AIDS model with contact tracing is studied,the unique existence of disease-free equilibria and internal equilibria is demonstrated.The basic reproduction number is calculated by the next generation matrix method,the necessary and sufficient conditions for the stability of the equilibrium point are derived,that is,when the basic reproduction number is smaller than 1,the disease-free equilibrium point is asymptotical stable.When the basic reproductive number is bigger than 1,the internal equilibrium is asymptotically stable.Combined with the center manifold theorem,the bifurcation phenomenon of the model is discussed,and the biological explanation of the transcritical bifurcation of the system is given.Finally,the stability of the system is verified by using Matlab to carry out numerical simulation.At the same time,combined with the biological significance of the parameters,some suggestions for the control of HIV are proposed.
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