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Transmission of Dengue hemorrhagic fever in an age structured population. (English) Zbl 1045.92040
Summary: The influence of age structure on the human population in the susceptible-infected recovered (SIR) model used to describe the transmission of Dengue hemorrhagic fever (DHF) is studied. The human population is separated into an adult and juvenile class with the transmission of the disease being different in the two classes. Two equilibrium states are found and conditions for stability of one of these states, the disease free state, is established. The stability of the endemic state of this model is discussed.
A simplified version of the model, one in which no adults become sick, is introduced. The conditions for the stability of the endemic state of this latter model are determined. Numerical calculations show that age structure in the simplified model reduces the periods of oscillations in the susceptible human population, the infected human population, and the infected mosquito population, and the tightness of the spiraling into the endemic equilibrium state.

##### MSC:
 92D30 Epidemiology 34D05 Asymptotic properties of solutions to ordinary differential equations 37N25 Dynamical systems in biology
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##### References:
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