STABILITY OF DELAYED S I R MODEL WITH VITAL DYNAMICS


Oleh: Rubono Setiawan

Abstract: An SIR epidemic model with vital dinamics, incubation time and also with bilinear incidence rate is formulated, where incubation time length as time delay. The total host population is assumed constant. The threshold value R0 determining whether the disease dies out found. The result obtained show that the global dynamics are completely determined by the values of the threshold value R0 and time delay. If R0 less than or equal to one, the disease-free equilibrium is globally asymptotically stable (GAS) and the disease always dies out, while if it exceeds one there will be endemic. Then, by using incubation time length as constant time delay, the local stability for endemic equilibrium is investigated. The result obtained that the endemic equilibrium is locally asymptotically stable (LAS) for R0 exceeds one and for all positive time delay, or it can be called absolutely locally asymptoticaly stable (ALAS) when R0 exceeds one.

Keywords : SIR model with vital dynamics, delayed SIR model , bilinear incidence rate , time delay

(Makalah ini telah dipresentasikan pada IndoMS International Conference on Mathematics and Its Applications 2009 (IICMA2009) di UGM pada tanggal 12-13 Oktober 2009)

STABILITY OF DELAYED S I R MODEL WITH VITAL DYNAMICS

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