Using Atanackovic and Stankovic Numerical Method to Investigate Fractional Order Cholera Model
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Date
October, 2015
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Abstract
In this work, we investigate the dynamical behavior of a fractional order cholera model.
Here, we developed interest in the use of the deterministic model proposed by Codeco in
2001. The fractional order cholera model is converted to a system of ordinary differential
equations of integer order by using Atanackovic and Stankovic numerical method and is
then solved numerically by using the fourth order well-known Runge-Kutta method. All
the feasible equilibria for the system are obtained and the conditions for the existence
of interior equilibrium are determined. Local stability analysis of the cholera model is
studied by using the fractional Routh-Hurwitz stability conditions. The findings reveal
that, the disease dies out at the disease free equilibrium state but will persist at the
endemic state and that the concentration of toxigenic vibrio cholerae in water largely
depends on (i) the rate of exposure to contaminated water (parameter a) and (ii) the
contribution of each effected person to the aquatic environment (parameter ).
Description
A thesis submitted to the Department of Mathematics, Kwame Nkrumah University of Science and Technology in partial fufillment of the requirement for the degree of Master of Philosophy in Applied Mathematics (Mphil.).