A Comparative Numerical Study of a Classical Model and Fractional Model for Leishmaniasis

Leishmaniasis, a complex disease, necessitates comprehensive research for a better understanding. Mathematical modeling can significantly enhance the precision of epidemiological studies and offer valuable insights. In this study, we employ classical derivatives and empirical data from Sudan to explore a conventional leishmaniasis model. However, our primary objective is to propose an innovative mathematical model for Leishmaniasis, utilizing the Caputo fractional-order derivative operator instead of the standard operator. To compare the two models, we conduct numerical analyses that emphasize the dynamics of the Leishmaniasis model, using the fractional Adams–Bashforth method. Additionally, we analyze the stability of the suggested dynamical model at disease-free and endemic equilibrium points, representing significant extremes in the model. These findings illuminate the potential of fractional calculus in effectively addressing epidemic threats.