A Mathematical Model for Cholera Transmission Dynamics considering Primary and Booster Vaccinations as Controls
O. Abu & E. Jalija
Department of Mathematics and Statistics
Federal Polytechnic, Idah, Nigeria
Email: abuonoja2008@yahoo.com
Corresponding Author: O. Abu
ABSTRACT
Cholera is an acute diarrheal illness caused by infection with the bacteria vibrio cholerae. In this paper, a mathematical model for cholera transmission dynamics with an arbitrary contact rate function, considering primary and booster vaccinations as controls is formulated and analyzed. First, a constant contact rate function was assumed and the equilibrium analysis and numerical simulation were carried out. Secondly, a seasonally forced contact rate function was assumed and the numerical simulation was performed. In the first case, the analytical results showed that the disease-free (respectively endemic) equilibrium state is locally and asymptotically stable for (respectively ). These analytical results were also buttressed by the results of the numerical simulation. In the second case, the numerical results showed the seasonal variations in the number of infected people when there is no control. However, with effective primary and booster vaccinations, the spread of cholera can be controlled. The findings in this study suggest that effective primary and booster vaccination programs are crucial for the control of cholera.
Keywords: mathematical model, booster vaccination, disease-free equilibrium, endemic equilibrium
