Journal of Immunological Techniques & Infectious Diseases 2329-9541

Research Article, J Immunol Tech Infect Dis Vol: 5 Issue: 4

Mathematical Model on Avian Influenza with Quarantine and Vaccination

Bimal Kumar Mishra1* and Durgesh Nandini Sinha2
1Department of Mathematics, Birla Institute of Technology, Mesra, Ranchi-835215, India
2Department of Mathematics, Temple University, Philadelphia, PA USA
Corresponding author : Bimal Kumar Mishra
Department of Mathematics, Birla Institute of Technology, Mesra, Ranchi-835215, India
E-mail: [email protected]
Received: October 05, 2016 Accepted: November 02, 2016 Published: November 07, 2016
Citation: Mishra BK, Sinha DN (2016) A Mathematical Model on Avian Influenza with Quarantine and Vaccination. J Immunol Tech Infect Dis 5:4. doi: 10.4172/2329-9541.1000152

Abstract

Avian influenza virus poses risks to both bird and human population. In primary strain, mutation increases the infectiousness of avian influenza. A mathematical model of Avian Influenza for both human and bird population is formulated. We have computed the basic reproduction number and for both human and bird population respectively and we prove that the model is locally and globally asymptotically stable for disease-free equilibrium point when and . We also prove that the unique endemic equilibrium point is globally asymptotically stable in bird population when . Extensive numerical simulations and sensitivity analysis for various parameters of the model are carried out. The effect of Vaccination and Quarantined class with Recovered class are critically analyzed.

Keywords: Epidemic model; Avian Influenza; Stability; Human population; Bird population

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