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A stochastic  SIR  model with vertical transmission and vaccination is proposed and investigated in this paper. The threshold dynamics are explored when the noise is small. The conditions for the extinction or persistence of infectious diseases are deduced. Our results show that large noise can lead to the extinction of infectious diseases which is conducive to epidemic diseases control.

computational and mathematical methods in medicine

Threshold Dynamics of a Stochastic <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mi>S</mml:mi><mml:mi>I</mml:mi><mml:mi>R</mml:mi></mml:math> Model with Vertical Transmission and Vaccination

Threshold Dynamics of a Stochastic SIR Model with Vertical Transmission and Vaccination