Mathematical Model on Avian Influenza with Quarantine and Vaccination

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.