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Volume 18,     Number 1,     Spring 2010

 

STABILITY OF A DELAYED SYSTEM
MODELLING HOST-PARASITE ASSOCIATIONS
SÁNDOR KOVÁCS AND SHABAN A. H. ALY

Abstract. This paper deals with stability analysis of a delayed SIS epidemiological model with disease-induced mortality and nonlinear incidence rate. Conditions are derived under which there can be no change in stability. Using the discrete time delay as a bifurcation parameter it is found that Hopf bifurcation occurs when the delay passes through a critical value. In case of the single delay a formula for determining the stability of the periodic solutions is given by using the centre manifold theory and the normal form method. Results are verified by computer simulations.

 

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