Fractional ABC Dynamics and Nonlinear Transmission Analysis of Dengue–Malaria Co-infection with Reinfection

The persistent co-circulation of dengue and malaria in tropical regions poses a significant epidemiological challenge, particularly because classical integer-order models fail to capture the memory-driven reinfection, relapse, and recrudescence mechanisms that sustain long-term disease transmission. To overcome these limitations, this study develops a high-dimensional nonlinear co-infection model formulated using the Atangana–Baleanu–Caputo (ABC) fractional derivative, which incorporates nonsingular and nonlocal kernels to realistically represent hereditary effects in host–vector dynamics. The model integrates primary and secondary dengue infections, recurrent malaria pathways, and interactions across two mosquito species within a unified fractional-order framework. Analytical results establish positivity, boundedness, and existence–uniqueness of solutions, and the basic reproduction number R0 is rigorously derived via the next-generation matrix method. Numerical simulations reveal that decreasing the fractional order substantially prolongs transient dynamics, increases infection peaks, and strengthens disease persistence relative to the classical system; in particular, when, both pathogens exhibit sustained endemicity amplified under fractional dynamics. These findings demonstrate that memory effects encoded by the ABC operator play a critical role in shaping reinfection outcomes, cross-immunity decay, and recurrent malaria episodes. The proposed framework provides a mathematically rigorous and epidemiologically insightful foundation for understanding nonlinear co-infection dynamics and underscores the importance of fractional calculus in improving predictive modeling and informing long-term vector-borne disease control strategies.