### Mathematical Biosciences and Engineering

2015, Issue 3: 415-429. doi: 10.3934/mbe.2015.12.415

# An SIRS model with differential susceptibility and infectivity on uncorrelated networks

• Received: 01 July 2013 Accepted: 29 June 2018 Published: 01 January 2015
• MSC : Primary: 34C25, 92D30; Secondary: 34K25.

• We propose and study a model for sexually transmitted infections on uncorrelated networks, where both differential susceptibility and infectivity are considered. We first establish the spreading threshold, which exists even in the infinite networks. Moreover, it is possible to have backward bifurcation. Then for bounded hard-cutoff networks, the stability of the disease-free equilibrium and the permanence of infection are analyzed. Finally, the effects of two immunization strategies are compared. It turns out that, generally, the targeted immunization is better than the proportional immunization.

Citation: Maoxing Liu, Yuming Chen. An SIRS model with differential susceptibility and infectivity on uncorrelated networks[J]. Mathematical Biosciences and Engineering, 2015, 12(3): 415-429. doi: 10.3934/mbe.2015.12.415

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• We propose and study a model for sexually transmitted infections on uncorrelated networks, where both differential susceptibility and infectivity are considered. We first establish the spreading threshold, which exists even in the infinite networks. Moreover, it is possible to have backward bifurcation. Then for bounded hard-cutoff networks, the stability of the disease-free equilibrium and the permanence of infection are analyzed. Finally, the effects of two immunization strategies are compared. It turns out that, generally, the targeted immunization is better than the proportional immunization.

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沈阳化工大学材料科学与工程学院 沈阳 110142

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