Fractional-Order Mathematical Modeling and Analysis of Malaria Incorporating Control Measures via the Adams–Bashforth–Moulton Method

Abstract

The epidemiological features of malaria infection are taken into consideration in this paper as a fractional-order mathematical model in Caputo derivative. The activities that the model uses to manage the disease are treatment and vaccination to study the effects of the controls on the disease dynamics. The theory of Lyapunov functions determines and verifies the existence and uniqueness of solutions within the frame of the fractional order and the stability of the endemic equilibrium point. The model is numerically obtained with the help of the fractional Adams-Bashforth-Moulton algorithm that will indicate the alteration of the model parameters, and the fractional orders of the model parameters to the impact of each of the mentioned parameters on the course of the disease. It has been established through the application of simulation that the more the disease is treated and vaccinated the less the prevalence of malaria and that the fractional-order models have high level of flexibility and realism than the classical integer order equations. The paper identifies the importance of fractional modeling in the description of the interactions between the effects of memory and nonlocal interaction between the biological systems and this enhances the understanding and control of infectious diseases. The model does however assume that the population is homogeneous mixed and hypothetical values of the parameters thus preventing the empirical validation. To make the model more predictive and practical to use in the formulation of effective control schemes against malaria, then the future research must be capable of addressing the spatial heterogeneity, stochasticity.