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**Dynamical behavior for a stage-structured SIR infectious disease model.**
*(English)*
Zbl 1007.92032

From the introduction: The SIR infectious disease model is an important population model and has been studied by many authors. It is assumed in the classical epidemiological disease model that each species has the same contact rates. We classify the species as belonging to either the immature or the mature, and suppose that the mature population does not contract the disease and the immature population is susceptible to the infection. The assumption corresponds to the fact that there are many kinds of diseases which are only spread or have more opportunities to be spread in children, for example measles, mumps, chickenpox and scarlet fever. In addition, according to the characteristics of these diseases, we know that an infectious period is much shorter than time \(\tau\), representing the time from birth to maturity, that is, it is impossible that the population with disease enters into the maturity. We believe that this is the first time such an epidemic model has appeared in the literature.

### MSC:

92D30 | Epidemiology |

34K20 | Stability theory of functional-differential equations |

34D23 | Global stability of solutions to ordinary differential equations |

34K60 | Qualitative investigation and simulation of models involving functional-differential equations |

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\textit{Y. Xiao} et al., Nonlinear Anal., Real World Appl. 3, No. 2, 175--190 (2002; Zbl 1007.92032)

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