## Stability analysis of an HIV/AIDS dynamics model with drug resistance.(English)Zbl 1257.92034

Summary: A mathematical model of HIV/AIDS transmission incorporating treatment and drug resistance is built in this study. We firstly calculate the threshold value of the basic reproductive number $$(R_0)$$ by the next generation matrix and then analyze the stability of two equilibria by constructing a Lyapunov function. When $$R_0 < 1$$, the system is globally asymptotically stable and converges to the disease-free equilibrium. Otherwise, the system has a unique endemic equilibrium which is also globally asymptotically stable. While an antiretroviral drug tries to reduce the infection rate and to prolong the patients’ survival, drug resistance is in fact neutralizing the effects of treatment.

### MSC:

 92C60 Medical epidemiology 34K60 Qualitative investigation and simulation of models involving functional-differential equations 34K20 Stability theory of functional-differential equations
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### References:

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