Dynamics of a Stochastic SIS Epidemic Model with Birth Pulses and Pulse Treatments

Abstract

In this paper, a stochastic SIS epidemic model with birth pulses and pulse treatments is constructed and investigated. By applying Floquet theory and qualitative theory of stochastic differential equations, the existence and stability of trivial solution and infection-free periodic solution are discussed. A special endemic solution and the boundedness of infective individuals are investigated. Numerical results for phase portraits, which are illustrated with two examples, are in good agreement with the theoretical analysis.