Fractional Order SIR Model with Constant Population
Eric Okyere *
Department of Basic Sceinces, University of Health and Allied Sciences, Ho, Ghana.
Francis Tabi Oduro
Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana.
Samuel Kwame Amponsah
Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana.
Isaac Kwame Dontwi
Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana.
Nana Kena Frempong
Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana.
*Author to whom correspondence should be addressed.
Abstract
The main objective of this paper is to formulate an epidemiological model using fractional order derivatives which has an advantage over the classical integer order models due to its memory effect property. Our mathematical formulation of the non-integer order initial value problem will be based on the famous fractional order Caputo derivative. We discuss and show the existence of non-negative solutions of the mathematical model. We further investigate local asymptotic stability analysis of model equilibria. Finally, numerical solutions are presented using Adams-type predictor-corrector method to illustrate fractional model trajectories.
Keywords: Initial value problem, caputo derivatives, predictor-corrector method, asymptotic stability, model equilibria