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Dynamics of a Heroin Epidemic Model with Very Population

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DOI: 10.4236/am.2011.26097    5,045 Downloads   9,502 Views   Citations

ABSTRACT

Based on the model provided by the Mulone and Straughan [1], we relax the population which are constant and obtain the drug-free equilibrium which is global asymptotically stable under some conditions. The system has only uniqueness positive endemic equilibrium which is globally asymptotically stable by using the second compound matrix.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

X. Wang, J. Yang and X. Li, "Dynamics of a Heroin Epidemic Model with Very Population," Applied Mathematics, Vol. 2 No. 6, 2011, pp. 732-738. doi: 10.4236/am.2011.26097.

References

[1] G. Mulone and B. Straughan, “A Note on Heroin Epidemics,” Mathematical Biosciences, Vol. 218, No. 2, 2009, pp. 138-141. doi:10.1016/j.mbs.2009.01.006
[2] NIDA InfoFacts: Heroin. http://www.nida.nih.gov/infofacts/heroin.html
[3] E. White and C. Comiskey, “Heroin Epidemics, Treatment and ODE Modelling,” Mathematical Biosciences, Vol. 208, No. 1, 2007, pp. 312-324. doi:10.1016/j.mbs.2006.10.008
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[5] O. Diekmann, J. A. P. Heesterbeek and J. A. J. Metz, “On the Definition and the Computation of the Basic Reproduction Ratio R0 in Models for Infectious Diseases in Heterogenous Populations,” Journal of Mathematical Biology, Vol. 28, No. 4, 1990, pp. 365-382. doi:10.1007/BF00178324
[6] M. Y. Li and J. S. Muldowney, “Global Stability for the SEIR Model in Epidemiology,” Mathematical Biosciences, Vol. 125, No. 2, 1995, pp. 155-164. doi:10.1016/0025-5564(95)92756-5
[7] J. K. Hale, “Ordinary Differential Equations,” John Wiley and Sons, New York, 1969.

  
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