Fractional-Order Modeling of Malaria Dynamics: A Mixed Fractional-Integer Model Approach for Epidemiological Analysis
Keywords:
Fractional differential equations, Malaria transmission; Stochastic, Caputo derivative;, Malaria Transmission, Stochastic Models, Mixed Integer-Fractional Models, Epidemiological Modeling, Numerical Simulation, Control StrategiesAbstract
Standard malaria models overlook how human immunity and healthcare decisions depend on past experiences (memory effect) and how random environmental fluctuations shape transmission. To address this, we developed a hybrid model: human infection dynamics use fractional-order calculus to capture memory, whereas mosquito dynamics remain integer-order but include environmental stochasticity. The analysis confirmed the existence, positivity, boundedness, and stability of the solution, with the basic reproduction number derived using next-generation methods. We solved the system using a fractional Adams–Bashforth–Moulton algorithm for humans and Euler–Maruyama for the stochastic mosquito component, calibrating the parameters with Nigeria’s 2023 WHO malaria data and national surveys. Nigeria accounts for approximately 26–27% of global cases and 31% of deaths, making locally grounded models essential. Simulations show that stronger memory effects delay and lower epidemic peaks while prolonging the outbreaks. Critically, environmental randomness can drive disease extinction even when the deterministic reproduction number exceeds one. Incorporating both memory and stochasticity yields more realistic malaria dynamics and offers a refined framework for evaluating control strategies in high-burden settings.
DOI: https://doi.org/10.5281/zenodo.21990512
