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

References

• D. D. Bainov, P. S. Simeonov, Impulsive Differential Equations: Periodic Solutions and Applications, Longman Scientific and Technical, New York, 1993
   Google Scholar
• P. Boissy, T. L. Andersen, T. Lund, K. Kupisiewicz, T. Plesner, J. M. Delaissé, Pulse treatment with the proteasome inhibitor bortezomib inhibits osteoclast resorptive activity in clinically relevant conditions, Leuk. Res. 32 (2008), pp. 1661–1668 doi: 10.1016/j.leukres.2008.02.019
   PubMed Web of Science ®Google Scholar
• G. Caughley, Analysis of Vertebrate Population, John Wiley & Sons, New York, 1977
   Google Scholar
• M. Choisy, J. F. Guégan, P. Rohani, Dynamics of infectious diseases and pulse vaccination: Teasing apart the embedded resonance effects, Phys. D 223 (2006), pp. 26–35 doi: 10.1016/j.physd.2006.08.006
   Web of Science ®Google Scholar
• D. J. Daley, J. Gani, Epidemic Modeling: An Introduction, Cambridge University Press, New York, 2005
   Google Scholar
• P. Georgescu, H. Zhang, L. Chen, Bifurcation of nontrivial periodic solutions for an impulsively controlled pest management model, Appl. Math. Comput. 202 (2008), pp. 675–687 doi: 10.1016/j.amc.2008.03.012
   Web of Science ®Google Scholar
• A. Gray, D. Greenhalgh, X. Mao, J. Pan, The SIS epidemic model with Markovian switching, J. Math. Anal. Appl. 394 (2012), pp. 496–516 doi: 10.1016/j.jmaa.2012.05.029
   Web of Science ®Google Scholar
• D. Greenhalgh, Control of an epidemic spreading in a heterogeneously mixing population, Math. Biosci. 80 (1986), pp. 23–45 doi: 10.1016/0025-5564(86)90065-9
   Web of Science ®Google Scholar
• G. Jiang, Q. Lu, Impulsive state feedback control of a prey-predator Model, J. Comput. Appl. Math. 200 (2007), pp. 193–207 doi: 10.1016/j.cam.2005.12.013
   Web of Science ®Google Scholar
• G. Jiang, Q. Yang, Periodic solutions and bifurcation in an SIS epidemic model with birth pulse, Math. Comput. Modelling 50 (2009), pp. 498–508 doi: 10.1016/j.mcm.2009.04.021
   Web of Science ®Google Scholar
• J. Jiao, S. Cai, L. Chen, Analysis of a stage-structured predator-prey system with birth pulse and impulsive harvesting at different moments, Nonlinear Anal. Real 12 (2011), pp. 2232–2244 doi: 10.1016/j.nonrwa.2011.01.005
   Web of Science ®Google Scholar
• W. O. Kermack, A. G. McKendrick, Contributions to the mathematical theory of epidemics, Proc. R. Soc. Lond. 138 (1932), pp. 55–83 doi: 10.1098/rspa.1932.0171
   Google Scholar
• A. Lakmeche, O. Arino, Bifurcation of non trivial periodic solutions of impulsive differential equations arising chemotherapeutic treatment, Dyn. Contin. Discrete Impuls. 7 (2000), pp. 265–287
   Web of Science ®Google Scholar
• Y. Li, J. Cui, The effect of constant and pulse vaccination on SIS epidemic models incorporating media coverage, Commun. Nonlinear Sci. 14 (2009), pp. 2353–2365 doi: 10.1016/j.cnsns.2008.06.024
   Web of Science ®Google Scholar
• H. Liang, M. Liu, M. Song, Extinction and permanence of the numerical solution of a two-prey one-predator system with impulsive effect, Int. J. Comput. Math. 88 (2011), pp. 1305–1325 doi: 10.1080/00207160.2010.504829
   Web of Science ®Google Scholar
• X. Liu, P. Stechlinski, Pulse and constant control schemes for epidemic models with seasonality, Nonlinear Anal. Real 12 (2011), pp. 931–946 doi: 10.1016/j.nonrwa.2010.08.017
   Web of Science ®Google Scholar
• V. Lsksmikantham, D. D. Bainov, P. S. Simeonov, Theory of Impulsive Differential Equations, World Scientific, Singapore, 1989
   Google Scholar
• D. Migliori, H. Malchow, E. Venturino, Containment strategies of epidemic invasions, Int. J. Comput. Math. 89 (2012), pp. 639–678 doi: 10.1080/00207160.2011.648627
   Web of Science ®Google Scholar
• M. G. Roberts, R. R. Kao, The dynamics of an infectious disease in a population with pulses, Math. Biosci. 149 (1998), pp. 23–36 doi: 10.1016/S0025-5564(97)10016-5
   PubMed Web of Science ®Google Scholar
• S. Tang, L. Chen, Multiple attractors in stage-structured population models with birth pulses, Bull. Math. Biol. 65 (2003), pp. 479–495 doi: 10.1016/S0092-8240(03)00005-3
   PubMed Web of Science ®Google Scholar