Fluctuating Role of Parameters in the Analysis of the Continues and Discrete Version of a Susceptible-Incubated-Infected Model


The article concentrates on the role of fluctuating parameters for removable population from the incubated class in a susceptible-incubated-infected model. The discrete analogous of this model is also investigated. Conditions for local asymptotic stability are derived for both the disease free and endemic cases. Numerical simulations are performed to validate the theoretical results.

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P. Das, D. Mukherjee, K. Das and A. Sabarmathi, "Fluctuating Role of Parameters in the Analysis of the Continues and Discrete Version of a Susceptible-Incubated-Infected Model," International Journal of Modern Nonlinear Theory and Application, Vol. 1 No. 2, 2012, pp. 47-50. doi: 10.4236/ijmnta.2012.12006.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] M. J. Stutzer, “Chaotic Dynamics and bifurcation in a Micro Model,” Journal of Economic Dynamics and Control, Vol. 2, 1980, pp. 353-376. doi:10.1016/0165-1889(80)90070-6
[2] R. L. Deveney, “An Introduction to Chaotic Dynamical Systems,” Addison-Wisely Publishing Company Inc., Boston, 1986.
[3] H. Inaba, “Threshold and Stability Results for an AgeStructured Epidemic Model,” Journal of Mathematical Biology, Vol. 28, No. 4, 1990, pp. 411-34. doi:10.1007/BF00178326
[4] M. Y. Li and J. S. Muldowney, “Global Stability for the SEIR Model in Epidemiology,” Mathematical Bioscience, Vol. 125, No. 2, 1995, pp. 155-164. doi:10.1016/0025-5564(95)92756-5
[5] R. C. Hilborn, “Chaos and Non-Linear Dynamics: An Introduction for Scientist and Engineers,” 2nd Edition, Oxford University Press, Oxford, 2000.
[6] S. Elaydi, “An Introduction to Difference Equation,” Springer-Verlag, Berlin, 2005.
[7] A. D’Onofrio, P. Manfredi and E. Salinelli, “Vaccinating Behaviour, Information, and the Dynamics of SIR Vaccine Preventable Diseases,” Theoretical Population Biology, Vol. 71, No. 3, 2007, pp. 301-317. doi:10.1016/j.tpb.2007.01.001
[8] W. M. Schaffer and T. V. Bronnikova, “Parametric Dependence in Model Epidemics,” Journal of Bioogical Dynamics, Vol. 1, No. 2, 2007, pp. 183-195. doi:10.1080/17513750601174216
[9] F. M. Hilker, H. Malchow, M. Langlais and S. V. Petrovskii, “Oscillations and Waves in a Virally Infected Plankton System, Transition from Lysogeny to Lysis,” Journal of Ecological Complexity, Vol. 3, No. 3, 2006, pp. 200-208.
[10] G. Q. Sun, G. Zhang, Z. Jin and L. Li, “Predator Cannibalism can Give Rise to Regular Spatial Pattern in a Predator-Prey System,” Nonlinear Dynamics, Vol. 58, No. 1, 2009, pp. 75-84. doi:10.1007/s11071-008-9462-z
[11] J. Dhar, A. K. Sharma, “The Role of the Incubation Period in a Disease Model,” Applied Mathematics E-Notes, Vol. 9, 2009, pp. 146-153.

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