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The dynamics of spreading and immune strategies of sexually transmitted diseases on scale-free network. (English) Zbl 1181.92074
Summary: We examine epidemic thresholds and dynamics for sexually transmitted diseases (STDs) spread using a multiple susceptible-infected-removed-susceptible ODE model on scale-free networks. We derive the threshold for the epidemic to be zero in infinite scale-free networks. For a hard cut off scale-free network, we also prove the stability of the disease-free equilibrium and the persistence of STDs infection. The effects of two immunization schemes, including a proportional scheme and targeted vaccination, are studied and compared. We find that the targeted strategy compares favorably to a proportional scheme in terms of effectiveness. Theory and simulations both prove that an appropriate condom use has a prominent effect to control STDs spread on scale-free networks.

MSC:
92D30 Epidemiology
34K20 Stability theory of functional-differential equations
34C60 Qualitative investigation and simulation of ordinary differential equation models
34C99 Qualitative theory for ordinary differential equations
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