Abstract
In this paper we present an SIR drug-resistant model on scale-free networks. The model has a disease-free equilibrium, which is globally asymptotically stable when a threshold quantity is less than one. The model has a wild strain equilibrium and a resistant strain equilibrium, which are asymptotically stable when their respective reproduction number is great than one. When treatment leads to resistance development, the model can have a unique coexistence equilibrium, and we also prove the persistence of infection. The effects of two immunization schemes, including proportional immunization scheme and targeted immunization scheme, are studied and compared. We find that targeted strategy compare favorably to a proportional immunization has prominent effect to control the disease spread on scale-free networks.
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