Modeling and Analysis of a Single Species Population with Viral Infection in Polluted Environment

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References

[1] R. M. Anderson and R. M May, “Regulation and Stability of Host-Parasite Population Interactions I: Regultory Processes,” Journal of Animal Ecology, Vol. 47, 1978, pp. 219-247. doi:10.2307/3933

[2] R. M. Anderson and R. M. May, “The Invasion, Persistence, and Spread of Infectious Disease within Animal and Plant Communities,” Transactions of the Royal Society of London, Vol. B 314, No. 1167, 1986, pp. 533-570.

[3] R. M. May and R. M. Anderson, “Regulations and Stability of Host-Parasite Population Interactions II, Destabilizing Processes,” Journal of Animal Ecology, Vol. 47, 1978, pp. 249-267. doi:10.2307/3934

[4] H. W. Hethcote and S. A. Levin, “Periodicity in Epidemiological Models,” In: L. Gross, T. G. Hallam and S. A. Levin, Eds., Applied Mathematical Ecology, SpringerVerlag, Berlin, 1989, pp. 193-211.
doi:10.1007/978-3-642-61317-3_8

[5] M. Begon and R. G. Bowers, “Beyond Host-Parasite Dynamics,” In: B. T. Grenfell and A. P. Dobson, Eds., Ecology of Disease in Natural Populations, Cambridge University Press, Cambridge, 1995, pp. 479-509.

[6] B. T. Grenfell and A. P. Dobson, Eds., “Ecology of Disease in Natural Populations,” Cambridge University press, Cambridge, 1995.

[7] H. W. Hethcote, W. Wang and L. Yi, “Species Coexistence and Periodicity in Host-Host Pathogen Model,” Journal of Mathematical Biology, Vol. 51, No. 6, 2005, pp. 629-660.

[8] T.-W. Hwang and Y. Kuang, “Deterministic Extinction Effect of Parasite on Host Populations,” Journal of Mathematical Biology, Vol. 46, 2003, pp. 17-30.
doi:10.1007/s00285-002-0165-7

[9] H. Mccallum and A. P. Dobson, “Detecting Diseases and Parasite Threats to Endangered Species Ecosystems,” Trends in Ecology and Evolution, Vol. 19, 1995, pp. 190-194. doi:10.1016/S0169-5347(00)89050-3

[10] M. Zhien, B. J. Song and T. G. Hallam, “The Threshold of Survival for the System in Fluctuating Environment,” Bulletin of Mathematical Biology, Vol. 57, No. 3, 1989, pp. 311-323.

[11] H. P. Liu and M. Zhien, “The Threshold of Survival for the System of Two Species in a Polluted Environment,” Journal of Mathematical Biology, Vol. 30, No. 1, 1991, pp. 49-61.

[12] L. Zhan, Z. S. Shun and W. Ke, “Persistence and Extinction of Single Population in a Polluted Environment, Electronic,” Journal of Differential Equations, Vol. 108, 2004, pp. 1-5.

[13] N. Nuraini, E. Soewono and K. A. Sidarto, “A Mathematical Model of Dengue Internal Transmission Process,” Journal of Indonesia Mathematical Society, Vol. 13, No. 1, 2007, pp. 123-132.

[14] N. M. May, “Los Alamos Mathematical Model Gauges Epidemic Potential of Emerging Diseases,” LOS ALAMOS, New Mexico, 27 May 2008.

[15] W. M. Liu, “Criterion of Hopf-Bifurcation without Using Eigenvalues,” Journal of Mathematical Analysis and Application, Vol. 250, 1994.

[16] D. Greenhalgh and M. Haque, “A Predator-Prey Model with Disease in Prey Species Only,” Mathematical Methods of Applied Sciences, Vol. 30, 2007, pp. 911-929.
doi:10.1002/mma.815

[17] K. P. Hadeler and H. I. Freedman, “Predator-Prey Populations with Parasitic Infection,” Journal of Mathematical Biology, Vol. 27, No. 6, 1989, pp. 609-631.

[18] M. Haque and E. Venturino, “The Role of Transmissible Disease in Holling-Tanner Predator-Prey Model,” Theoritical Population Biology, Vol. 70, No. 3, 2006, pp. 273-863.

[19] E. Beltrami and T. O. Carroll, “Modelling the Role of Viral Disease in Recurrent Phytoplankton Blooms,” Journal of Mathematical Biology, Vol. 32, 1994, pp. 857-863. doi:10.1007/BF00168802

[20] S. Sinha, O. P. Misra and J. Dhar, “Study of a Prey-Predator Dynamics under the Simultaneous Effect of Toxicant and Disease,” The Journal of Nonlinear Analysis and its Applications, Vol. 1, No. 2, 2008, pp. 102-117.

[21] S. Sinha, O. P. Misra and J. Dhar, “A Two Species Competition Model under the Simultaneous Effect of Toxicant and Disease,” Non-Linear Analysis-Real World Application, Elsevier Publication, Vol. 11, 2010, pp. 1131-1142.

[22] S. Sinha, O. P. Misra and J. Dhar, “Modeling a Predator Prey System with Infected Prey in Polluted Environment,” Applied Mathematical Modeling, Elsevier Publication, Vol. 34, 2010, pp. 1861-1872.

[23] J. K. Hale, “Ordinary Differential Equations,” 2nd Edition, Kriegor, Basel, 1980.