The analysis of an epidemic model on networks. (English) Zbl 1211.92053
Summary: This paper considers an epidemic model with birth and death on networks. We derive the epidemic threshold \(R_{0}\) dependent on the birth rate \(b\), the death rate \(d\) (natural death) and \(\mu \) from the infectious disease and natural death, and the cure rate \(\gamma \). The stability of the equilibriums (the disease-free equilibrium and endemic equilibrium) are analysed. Finally, the effects of various immunization schemes are studied and compared. We show that both targeted, and acquaintance immunization strategies compare favorably to a proportional scheme in terms of effectiveness. For active immunization, the threshold is easier to apply practically. To illustrate our theoretical analysis, some numerical simulations are also included.
MSC:
| 92D30 | Epidemiology |
| 92C42 | Systems biology, networks |
| 34D05 | Asymptotic properties of solutions to ordinary differential equations |
| 65C20 | Probabilistic models, generic numerical methods in probability and statistics |
| 34C60 | Qualitative investigation and simulation of ordinary differential equation models |
| 34D23 | Global stability of solutions to ordinary differential equations |
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