A fractional-order analysis of malaria transmission using a ten-compartmental model with Caputo derivatives

This study presents a fractional-order malaria transmission model based on a ten-compartment structure that incorporates Caputo derivatives to capture memory effects in disease dynamics. The model distinguishes non-immune and semi-immune human populations alongside mosquito compartments. We establish mathematical properties including existence, uniqueness, positivity, and boundedness of solutions within a biologically feasible region. An explicit expression for the basic reproduction number R0 is derived using the next-generation matrix approach, and stability conditions for disease-free and endemic equilibria are analyzed via the Matignon criterion. Numerical simulations under realistic parameter settings demonstrate that decreasing the fractional order α delays epidemic peaks, reduces infection intensity, and prolongs disease persistence, highlighting the significant influence of memory effects on malaria dynamics. These results confirm that fractional-order models provide a more accurate representation of transmission patterns compared to classical integer-order frameworks.