Abstract
In this investigation, a mathematical compartmental model of the malaria disease transmission dynamical process with an associated learning mechanism between vector-to-host and vice-versa with memory, relapse, and reinfection conditions is proposed and analysed. Stability analysis of the disease-free equilibrium (DFE) concerning the fractional-order derivative α and the reproductive number R0 is evaluated. We find the α that depends on R0, for which we have two cases: i if R0<1, then DFE is always locally asymptotically stable (LAS), ii if R0>1, then DFE is always unstable. The model is solved numerically by using the Corrector-Predictor numerical method. The numerical simulation is performed to verify the analytic results.
•A mathematical compartmental model of the malaria disease transmission dynamical process is analysed.•Stability analysis of the disease-free equilibrium concerning the fractional-order α derivative and the reproductive number R0 is computed.•The model is solved numerically by using the Corrector-Predictor numerical method.•The numerical simulation is performed to verify the analytic results.