A Caputo fractional-order malaria transmission model with heterogeneous immunity and control of asymptomatic carriers

Abstract

Malaria remains a persistent public health challenge in sub-Saharan Africa, driven by complex transmission dynamics involving heterogeneous host immunity and asymptomatic reservoirs. This study develops a fractional-order compartmental model using Caputo derivatives to capture memory effects in malaria transmission. The model stratifies the human population based on immune status non-immune and semi-immune and explicitly incorporates screening and treatment of asymptomatic carriers. The basic reproduction number is derived via the next-generation matrix method, and the local stability of the disease-free equilibrium is analyzed using fractional stability theory. Positivity, boundedness, and Hyers–Ulam stability of the model are established. Numerical simulations reveal that memory effects (via the fractional order ) significantly influence the speed of disease progression and convergence to equilibrium. Furthermore, interventions targeting asymptomatic carriers and personal protection measures substantially reduce transmission. The findings underscore the importance of incorporating memory-dependent dynamics and heterogeneous immunity in malaria modeling to guide more effective, long-term control strategies.