Furaha Michael Chuma

Work place: The Nelson Mandela African Institution of Science and Technology, P.O Box 447, Arusha-Tanzania

E-mail: furahac@nm-aist.ac.tz


Research Interests: Computational Mathematics


Furaha Michael Chuma is the Assistant Lecturer of Mathematics at Dar es University College of Education, Tanzania. He received his Masters degree in Mathematical Modeling from the University of Dar es salaam and currently pursuing his Ph.D in Applied Mathematics and Computations at Nelson Mandela African Institution of Science and Technology, Arusha-Tanzania. His areas of interest include Ecological Modelling and Mathematical Epidemiology.

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

By Furaha Michael Chuma Gasper Godson Mwanga

DOI: https://doi.org/10.5815/ijmsc.2019.02.01, Pub. Date: 8 Apr. 2019

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,Q0. The result shows that the disease free equilibrium point is locally asymptotically stable iff the principle leading minors of the Hurwitz Matrix,   (for n∈ℝ+) are all positive. Using the Castillo Chavez Theorem we showed that, the disease free equilibrium point is globally asymptotically when R0<1. Furthermore, using the logarithmic function and the LaSalle’s Theorem, the endemic equilibrium point is found globally asymptotically stable for R0>1. 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.

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