×

Dynamics analysis of an impulsive stochastic SIS epidemic model with standard incidence. (Chinese. English summary) Zbl 1424.92051

Summary: In this paper, random disturbance, birth pulse and pulse treatments are simultaneously considered to build a class of SIS epidemic model with standard incidence. Using a stochastic differential equation, sufficient conditions for the stochastic stability of the trivial solution are obtained. Sufficient conditions for the existence of the disease free solution are obtained using a discrete map. The stochastic extinction of the disease is investigated using the Itô formula. Moreover, a numerical simulation is conducted to verify the theoretical analysis.

MSC:

92D30 Epidemiology
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
34D20 Stability of solutions to ordinary differential equations
PDFBibTeX XMLCite
Full Text: DOI