Periodic solutions of an SIS epidemic model with fixed-time birth pulses and state feedback pulse treatments

Abstract

Fixed-time pulse and state pulse, which were discussed separately in previous works, are introduced in a susceptible-infected-susceptible (SIS) epidemic model in this paper. Periodic solutions of the SIS epidemic model with fixed-time birth pulses and state feedback pulse treatments are discussed by means of both theoretical and numerical ways. The conditions for the existence of epidemic period-(1, 1), period-(2, 1), and period-(3, 2) solution are investigated.

Keywords:

• epidemic model
• birth pulse
• pulse treatment
• periodic solution

2010 AMS Subject Classifications:

• 34C23
• 34C25
• 92B05

Acknowledgements

We would like to thank the anonymous referees very much for their valuable comments and suggestions. This work was supported by the National Natural Science Foundation of China (Nos. 11162004), the Science Foundation of Guangxi Province, China (No. 2012GXNSFAA053006), and the Innovation Project of Guangxi Graduate Education (No. YCSZ2012072)