%0 Journal Article
%T Mathematical Model of the Impact of Vaccination on the Transmission Dynamics of Fowl pox in Poultry
%A Udofia Ekere Sunday
%A Inyama Simeon Chioma
%J Journal of Modern Mathematics and Statistics
%D 2012
%I 
%R 10.3923/jmmstat.2011.102.105
%X In this study, the researchers present the mathematical model of the impact of vaccination on the transmission dynamics of fowl pox in poultry. The model resulted in a system of 1st order ordinary differential equation. Analyzing the system using methods from dynamical system theory together with Routh-Harwitz theorem, it was established that the disease-free equilibrium is locally stable if the effective reproductive ratio R¦Ñ = (1 - ¦Ñ) ¦Á¦Â/d1+r1+¦Ì in the presence of vaccination is <1 and unstable if it is >1. Using the condition for control, the critical proportion that needs to be vaccinated to achieve herd immunity for fowl pox is established as ¦Ñc = ¦Á¦Â - (d1+r1+¦Ì)/¦Á¦Â. From this research, researchers discover that fowl pox can be eradicated from the poultry through vaccination provided the critical proportion ¦Ñc is achieved.
%U http://www.medwellonline.net/abstract/?doi=jmmstat.2011.102.105