Impact of Antiviral Treatment of Avian Influenza in Poultry Farm

Subject Areas : International Journal of Mathematical Modelling & Computations

Abdul Malek ¹ , Ashabul Hoque ²

1 - Department of Mathematics, University of Rajshahi, Rajshahi-62025, Bangladesh
2 - Department of Mathematics, University of Rajshahi, Rajshahi-62025, Bangladesh

Received: 2020-10-01 Accepted : 2021-05-28 Published : 2021-09-01

Keywords: Stability, Treatment, Jacobi matrix, Drug resistance, Lyapunov, Avian influenza,

Abstract :

In the present paper, we have focused on the antiviral treatment of avian influenza to predict the situation of the disease and analyzed the stability of the model at the equilibrium points (disease-free and endemic). In this concern, we have applied the SITR model based on the well-known SIR model to calculate the basic reproduction number and final size relation. Important parameters, such as susceptible, infective, treatment, and removal (SITR) rate under the compartmental method have been studied theoretically. The analytical results highlight that the model results are locally and globally stable at disease-free equilibrium if the basic reproduction number is less than one and it is locally and globally stable at endemic equilibrium if the basic reproduction number is greater than one. The numerical simulations of the developed model (SITR) are performed graphically with the help of the Range-Kutta method and we have also observed that each compartment has much affected by the infection and death rate, whereas re-susceptive has no significant effect on compartments.