Qualitative Analysis of Delayed SIR Epidemic Model with a Saturated Incidence Rate | Zendy

Fathalla A. Rihan | Zendy; M. Naim Anwar | Zendy

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Qualitative Analysis of Delayed SIR Epidemic Model with a Saturated Incidence Rate

Author(s) -

Fathalla A. Rihan,

M. Naim Anwar

Publication year - 2012

Publication title -

international journal of differential equations

Language(s) - English

Resource type - Journals

eISSN - 1687-9651

pISSN - 1687-9643

DOI - 10.1155/2012/408637

Subject(s) - mathematics , hopf bifurcation , incidence (geometry) , epidemic model , stability (learning theory) , combinatorics , qualitative analysis , statistics , mathematical analysis , demography , bifurcation , nonlinear system , geometry , population , physics , computer science , qualitative research , social science , quantum mechanics , machine learning , sociology

We consider a delayed SIR epidemic model in which the susceptibles are assumed to satisfy the logistic equation and the incidence term is of saturated form with the susceptible. We investigate the qualitative behaviour of the model and find the conditions that guarantee the asymptotic stability of corresponding steady states. We present the conditions in the time lag in which the DDE model is stable. Hopf bifurcation analysis is also addressed. Numerical simulations are provided in order to illustrate the theoretical results and gain further insight into the behaviour of this system

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