Impact of punitive sanctions on the spread of academic fraud.

Abstract

School fraud has become a serious issue that has increasingly affected the education system in
recent years. In this study, school fraud is treated as an infectious phenomenon that spreads within a school
community through interactions between individuals who commit fraud and the broader student population.
To identify the key factors influencing this undesirable behavior, we propose a mathematical model composed
of three strongly coupled ordinary differential equations (ODEs) that describe the interactions among
the three components of a school group. We establish the existence and uniqueness of the solution to the
model, demonstrate the existence of a unique equilibrium point, and prove that this equilibrium is globally
asymptotically stable. Finally, we present numerical simulations that support our theoretical findings.