Exploring the dynamics of leprosy transmission with treatment through a fractal–fractional differential model

Leprosy continues to be a significant public health challenge in many parts of the world, necessitating novel approaches to understanding and controlling its transmission. The dynamics of leprosy are examined in this study by means of a caputo fabrizio fractal–fractional differential system model. Leprosy transmission and treatment are complex and non-linear processes that can be captured by fractal–fractional derivatives. The temporal progression of the disease is the primary focus of our mathematical analysis, which evaluates a variety of parameter values, including initial population densities and compartmental transitions. Through simulations, we examine the impact of critical parameters on the severity and spread of diseases, as well as the rates of recovery and treatment. Numerical results of the model offer valuable insights into the impact of these parameters on leprosy dynamics, which is beneficial for public health interventions. The stability analysis of the model identifies supplementary conditions that are necessary for the success of disease control. By incorporating these novel mathematical techniques, we hope to improve our understanding of leprosy transmission and ultimately contribute to more effective control strategies. Based on our findings, additional studies investigating the relation between population density, treatment accessibility, and recovery rates are warranted. We hope that by graphically representing the relationships between these factors, we can draw attention to the possibility of targeted interventions that can reduce the transmission of leprosy. This study provides a strong basis for future studies on infectious disease modeling and aids leprosy-affected communities in developing strategies to mitigate the disease’s impact.