Modeling fractional order dynamics of Syphilis via Mittag-Leffler law

Syphilis is one the most dangerous sexually transmitted disease which is common in the world. In this work, a mathematical model is formulated with an emphasis on treatment. The reproduction number which presents information on the spread of the disease is determined. The model’s steady states are established, and the disease free state’s local and global stability are studied. The existence and uniqueness of solutions for both Caputo-Fabrizio and Atangana-Baleanu derivative in the Caputo sense are established. Numerical simulations were carried out to support the analytical solution, which indicates that the fractional order derivatives influence the dynamics of the spread of the Syphilis in the community. 2010 MSC 00-01, 99-00