Analytical and data-driven fractional-order malaria transmission model with vector and non-vector pathways

Classical malaria models often focus solely on vector-borne transmission and employ integer-order dynamics that neglect memory effects. Yet malaria spread can also occur through non-vector exposure routes, and its progression is influenced by historical infection and immunity patterns. To capture these effects, a fractional-order modeling approach is required. We develop a Caputo fractional-order malaria model of order $$q \in (0,1]$$ that integrates both vector and non-vector transmission pathways while embedding memory effects in human and mosquito dynamics. Analytical properties—including positivity, boundedness, disease-free equilibrium, and fractional local stability—are derived. The Adams–Bashforth–Moulton (ABM) predictor–corrector scheme is implemented for numerical simulation and validated against the classical case (q = 1) to ensure accuracy and convergence. Numerical experiments reveal that decreasing the fractional order q substantially modifies malaria dynamics: epidemic peaks are delayed, oscillatory persistence is prolonged, and long-term infection memory is amplified. Incorporating non-vector exposure pathways increases infection persistence and improves correspondence with field data. Parameter estimation and data fitting using weekly malaria incidence from the Nigeria Centre for Disease Control (NCDC) confirm the model’s reliability in reproducing outbreak patterns. The proposed fractional-order malaria model provides a unified analytical and computational framework that captures both memory-dependent and multi-route transmission effects. The ABM scheme proves efficient and accurate for fractional epidemic systems, and the accompanying MATLAB implementation supports reproducibility and application to malaria forecasting and control strategies.