TY  - JOUR
T1  - Mathematical Model of the Impact of Vaccination on the Transmission Dynamics of Fowl pox in Poultry
AU - Sunday, Udofia Ekere AU - Chioma, Inyama Simeon 
JO  - Journal of Modern Mathematics and Statistics
VL  - 5
IS  - 5
SP  - 102
EP  - 105
PY  - 2011
DA  - 2001/08/19
SN  - 1994-5388
DO  - jmmstat.2011.102.105
UR  - https://makhillpublications.co/view-article.php?doi=jmmstat.2011.102.105
KW  - Fowl pox
KW  -vaccination
KW  -herd immunity
KW  -critical proportion
KW  -reproductive ratio
KW  -Nigeria
AB  - 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<SUB>&#961;</SUB> = (1 - &#961;) &#945;&#946;/d<SUB>1</SUB>+r<SUB>1</SUB>+&#956; in the presence of vaccination is &lt;1 and unstable if it is &gt;1. Using the condition for control, the critical proportion that needs to be vaccinated to achieve herd immunity for fowl pox is established as &#961;<SUB>c</SUB> = &#945;&#946; - (d<SUB>1</SUB>+r<SUB>1</SUB>+&#956;)/&#945;&#946;. From this research, researchers discover that fowl pox can be eradicated from the poultry through vaccination provided the critical proportion &#961;<SUB>c</SUB> is achieved.
ER  -