Analysis of a new social hierarchy-based fractional-order model for malaria transmission dynamics with control measures

Malaria remains a major global health challenge, particularly in regions where socioeconomic inequalities shape exposure risk and access to prevention. In this study, we propose a novel fractional-order malaria transmission model incorporating social hierarchy, mathematically integrating Caputo, Caputo–Fabrizio, and Atangana–Baleanu operators to account for memory effects, immunity waning, and delayed intervention impacts, and epidemiologically distinguishing low- and high-class populations to quantify the influence of socioeconomic disparities on transmission and control. The basic reproduction number ( $$R_{0}$$ ) was derived using the next-generation approach, and sensitivity analysis identified mosquito-to-human and human-to-mosquito transmission probabilities, mosquito recruitment, and mortality as the most influential drivers. Numerical simulations over a 200-day horizon showed that lower fractional orders slowed epidemic growth and prolonged infectious periods, while non-singular kernels produced smoother, more realistic post-peak declines. Socioeconomic differences had a significant impact on outcomes. with low-class populations experiencing up to threefold higher peaks in exposure and infectiousness due to reduced access to care and preventive measures. Model projections revealed daily new cases peaking near 2500 under high transmission, and $$R_{0}$$ oscillating before settling between 3 and 7. Three-dimensional parameter surfaces further identified combinations of vector control and treatment coverage sufficient to reduce $$R_{0}$$ below one. These findings demonstrate the value of fractional-order modeling for capturing complex malaria dynamics and highlight the need for equity-focused interventions, including strengthened vector control, expanded rapid diagnostics, and improved treatment access in disadvantaged communities, to achieve sustainable reductions in malaria transmission.