Ahmed Adam Younis Ahmed2017-12-202017-12-202017http://hdl.handle.net/123456789/9799Thesis Presented as a Partial Ful llment for MASTER OF SCIENCE IN MATHEMATICS in the Department of Mathematics & Applied Mathematics ALNEELAIN UNIVERSITYAbstract Cholera is an epidemic disease caused by the bacteria Vibrio cholera. In this thesis, nonlinear mathematical models for spread of an infectious epidemic cholera disease with carriers in environment and transmission dynamics are developed and analysed. It is assumed that all susceptible are a ected by carrier population density. These models illustrate how population interact with each other depending on certain rates. By varying some parameters the models can be studied. This thesis analyzes the mathematical models created and shows the implementation of the numerical method Runge-Kutta of order four. The numerical simulations show that for certain parameter valuesMathematics