Stability Analysis of a Caputo Type Fractional Waterborne Infectious Disease Model

Abstract

We introduce a Caputo type fractional waterborne infectious dis-ease model. Disease transmissions of this model has saturation effect of infec-tious individuals on both human-to-human and environment-to-human con-tacts. For this model we find sufficient conditions for local stability of disease free and endemic epidemic equilibriums by linearization and global stability of disease free equilibrium by Liapunov method. Appropriate numerical simula-tions are also given to verify the results.