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Analysis of an SIR model with bilinear incidence rate. (English) Zbl 1203.34136
Under the assumption that the susceptible of host population satisfies the logistic equation and the incidence rate is the simple mass action incidence, the authors study an SIR vector disease model with incubation time. The threshold quantity $R_0$ is derived which determines whether the disease dies out or remains endemic. Using the time delay (i.e., incubation time) as a bifurcation parameter, the local stability of the endemic equilibrium is investigated, and the conditions for Hopf bifurcation to occur are derived. Numerical simulations are presented to illustrate the main results.

##### MSC:
 34K60 Qualitative investigation and simulation of models 92D30 Epidemiology 34K18 Bifurcation theory of functional differential equations 34K20 Stability theory of functional-differential equations
##### Keywords:
SIR model; time delay; stability; Hopf bifurcation
Full Text:
##### References:
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