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, we formulate and analyze a mathematical model of Syphilis with an emphasis on treatment in the sense of Caputo-Fabrizio (CF) and Atangana-Baleanu (Mittag-Leffler law) derivatives. The basic reproduction number of the CF model which presents information on the spread of the disease is determined. The model’s steady states were found, and the disease-free state’s local and global stability are established based on the basic reproduction number. 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 Syphilis in any community induced with the disease.