Stability Analysis of Equilibrium Points of Newcastle Disease Model of Village Chicken in the Presence of Wild Birds Reservoir

Abstract

Newcastle is a viral disease of chicken and other avian species. In this paper, the stability analysis of the disease free and endemic equilibrium points of the Newcastle disease model of the village chicken in the absence of any control are studied. The Hurwitz matrix criterion is applied to study the stability of the Newcastle disease free equilibrium point, . 0 Q The result shows that the disease free equilibrium point is locally asymptotically stable iff the principle leading minors of the Hurwitz Matrix, n G (for nR  ) are all positive. Using the Castillo Chavez Theorem we showed that, the disease free equilibrium point is globally asymptotically when . 1 0  R Furthermore, using the logarithmic function and the LaSalle’s Theorem, the endemic equilibrium point is found globally asymptotically stable for . 1 0  R Finally the numerical simulations confirm the existence and stability of the equilibrium points of the model. This reveals that, proper interventions are needed so as to decrease the frequently occurrence of the Newcastle disease in the village chicken population.