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

Affiliation(s)

IMS Engineering College, Adyatmik Nagar, Ghaziabad, India.

School of Mathematics and Allied Sciences, Jiwaji University, Gwalior, India.

IMS Engineering College, Adyatmik Nagar, Ghaziabad, India.

School of Mathematics and Allied Sciences, Jiwaji University, Gwalior, India.

Abstract

In this paper, a mathematical model is proposed to study the effect of pollutant and virus induced disease on single species animal population and its essential mathematical features are analyzed. It is observed that the susceptible population does not vanish when it is only under the effect of infection but in the polluted environment, it can go to extinction. Also, it has been observed that the replication threshold obtained, increases on account of pollutant concentration consequently decreasing the susceptible population. Further persistence results for the proposed model are obtained and the condition for the existence of the Hopf-bifurcation is derived. Finally, numerical simulation in support of analytical results is carried out.

In this paper, a mathematical model is proposed to study the effect of pollutant and virus induced disease on single species animal population and its essential mathematical features are analyzed. It is observed that the susceptible population does not vanish when it is only under the effect of infection but in the polluted environment, it can go to extinction. Also, it has been observed that the replication threshold obtained, increases on account of pollutant concentration consequently decreasing the susceptible population. Further persistence results for the proposed model are obtained and the condition for the existence of the Hopf-bifurcation is derived. Finally, numerical simulation in support of analytical results is carried out.

Cite this paper

S. Chauhan and O. Misra, "Modeling and Analysis of a Single Species Population with Viral Infection in Polluted Environment,"*Applied Mathematics*, Vol. 3 No. 6, 2012, pp. 662-672. doi: 10.4236/am.2012.36100.

S. Chauhan and O. Misra, "Modeling and Analysis of a Single Species Population with Viral Infection in Polluted Environment,"

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