Abstract
With the consideration of mechanism of prevention and control for the spread of infectious diseases, we propose, in this paper, a state dependent pulse vaccination and medication control strategy for a SIRS type epidemic dynamic system. The sufficient conditions on the existence and orbital stability of positive order-1 or order-2 periodic solution are presented. Numerical simulations are carried out to illustrate the main results and compare numerically the state dependent vaccination strategy and the fixed time pulse vaccination strategy.
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Acknowledgements
The authors would like to thank antonymous referees for their constructive suggestions and comments that improve substantially the original manuscript.
This work was supported in part by the Natural Science Foundation of Xinjiang (Grant No. 2011211B08), the National Natural Science Foundation of China (Grant No. 11001235, 11271312, and 11261056), the China Postdoctoral Science Foundation (Grant No. 20110491750 and 2012T50836), the Scientific Research Programmes of Colleges in Xinjiang (Grant No. XJEDU2011S08), the National Basic Research Program of China (2011CB808002), and the National Research Foundation of South Africa.
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Nie, LF., Teng, ZD. & Guo, BZ. A State Dependent Pulse Control Strategy for a SIRS Epidemic System. Bull Math Biol 75, 1697–1715 (2013). https://doi.org/10.1007/s11538-013-9865-y
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DOI: https://doi.org/10.1007/s11538-013-9865-y