MEMORY-DRIVEN EPIDEMIC SIMULATION USING CAPUOTO DERIVATIVES AND VIM

Abstract

This work introduces a non-integer order SIR framework formulated with Caputo operators and addressed through the VIM scheme to capture memory-driven dynamics in infectious disease transmission. In contrast to traditional solvers like RK4 that rely on abrupt compartment shifts, the Caputo–VIM formulation incorporates historical dependence and complex feedback. Applied to malaria, the second iteration demonstrates a postponed epidemic apex with an elongated recovery trajectory, yielding a faithful reflection of relapse cycles and immunological persistence. The approach ensures analytical clarity and enhanced biological realism in long-term epidemic simulations. Moreover, the fractional framework highlights the sensitivity of epidemic outcomes to memory kernels, offering a flexible tool for tailoring intervention strategies. It bridges mathematical rigor with epidemiological insight, enabling deeper exploration of relapse phenomena and immunity waning. Such integration paves the way for predictive models that better align with real-world disease persistence and control challenges.