@article{MAKHILLJMMS20115528178,
    title = {Mathematical Model of the Impact of Vaccination on the Transmission Dynamics of Fowl pox in Poultry},
    journal = {Journal of Modern Mathematics and Statistics},
    volume = {5},
    number = {5},
    pages = {102-105},
    year = {2011},
    issn = {1994-5388},
    doi = {jmmstat.2011.102.105},
    url = {https://makhillpublications.co/view-article.php?issn=1994-5388&doi=jmmstat.2011.102.105},
    author = {Udofia Ekere and},
    keywords = {Fowl pox,vaccination,herd immunity,critical proportion,reproductive ratio,Nigeria},
    abstract = {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.}
    }