### Sensitivity Analysis for Avian Influenza (Bird Flu) Epidemic Model with Exposed class

#### Abstract

This paper established that the mathematical modeling of Avian Influenza disease proposed has solution and unique when compare with other models in literature. Three equilibrium points were obtained, which stability of the system is investigated around. From analysis, the model stability depend on; first, $\beta_4\,X$ must be less than $(k+n)$, secondly, the characteristic equation has all it coefficients of the $\lambda$ positive provided

$e\,r+e\,d+r\,d>\beta_2\,S\,\gamma\,\theta\,$ and $ S\gamma\,\theta (\beta_2\,e+\beta_3\,\alpha)$

Also, the model is stable at Avian Influenza Persistent equilibrium as the system satisfies $J=F(0)G'(0)-F'(0)G(0)>0$ (Bellman and Cooke's $[2]$) condition.

Hence, the model is locally asymptotically stable at both Disease Free and Persistent Equilibrium.

Finally, the sensitivity analysis also, revealed that the factor responsible for the outbreak of Avian Influenza are majorly, four parameters and they are $\gamma, ~\beta_2,~\beta_{3},~\theta$. These parameters are capable of preventing spread of Avian Influenza while restricting the movement of infected individuals during treatment session will go a long way manage the spread of Avian Influenza.

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