Modeling rotavirus transmission with booster vaccination using Hilfer–Katugampola fractional derivatives: a public health perspective

This study develops a fractional-order mathematical model using the Hilfer–Katugampola derivative to assess rotavirus transmission dynamics under booster vaccination strategies, addressing limitations of classical integer-order models in capturing memory effects and waning immunity. We formulated a compartmental model with five states (Susceptible, Vaccinated, Boosted, Infected, Recovered) using Hilfer–Katugampola fractional derivatives. The basic reproduction number $${R}_{0}$$ was derived analytically, and stability conditions were established. Numerical simulations employed predictor–corrector methods with parameters estimated from epidemiological data. The fractional-order model demonstrated superior flexibility in capturing real-world transmission patterns, with memory effects reducing peak infections by 15–25% compared to integer-order models (based on baseline parameter set with $$\alpha =0.85$$ ). Optimal booster administration at 3 months post-primary vaccination reduced disease prevalence by 42.3% compared to no booster strategy. Sensitivity analysis identified fractional order $$\alpha $$ and booster timing $$\psi $$ as critical parameters influencing $${R}_{0}$$ . Hilfer–Katugampola fractional modeling provides a flexible framework for rotavirus dynamics prediction. Optimized booster strategies informed by fractional calculus can reduce disease burden by approximately 40% (under baseline scenarios), offering valuable insights for public health planning in high-burden regions.