A nonautonomous SIRS epidemic model with density dependence is proposed and studied. Threshold values R*0
R*1and R*2for the permanence and extinction of the disease are established. It is shown that the disease is extinct if R**0≤ 0 or R1< 0 and the disease is permanent if R*2> 0. As applications
the periodic and almost periodic models are discussed. The basic reproductive numbers R0 are obtained. It is shown that the disease is extinct if R0≤ 1 and the disease is permanent if R0> 1.
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references
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