Deterministic and fractional-order modeling of measles dynamics with harmonic mean incidence rate and quarantine impact

A novel mathematical model which explores the transmission dynamics of infectious diseases integrating nonlinear incidence and quarantine measures is presented in this study. Five different compartments: susceptible, latent, infectious, quarantined and recovered individuals presents total population. Saturation effects in disease transmission are modeled through a nonlinear infection rate while quarantine and recovery processes are explicitly incorporated. Parameters are estimated using a genetic algorithm based on cumulative monthly case data for measles in Indonesia. The basic reproduction number is derived to assess the potential for outbreak persistence. Stability analysis of the equilibrium states is conducted, and sensitivity analysis identifies key parameters influencing disease spread. Furthermore, the model is extended using Atangana-Baleanu Caputo (ABC) fractional derivative to explore memory-dependent effects in disease dynamics. Numerical simulations illustrate how fractional-order values impact infection trajectories. The findings emphasize the importance of timely isolation and recovery in controlling outbreaks and suggest that fractional-order modeling can enhance understanding of long-term epidemic behavior.