Mathematical modeling of malaria epidemic dynamics with enlightenment and therapy intervention using the Laplace-Adomian decomposition method and Caputo fractional order

Abstract

This paper examines malaria, a prevalent mosquito-borne disease in Africa that causes fever, chills, and headaches. Diagnosis involves blood tests, and treatment primarily relies on antimalarial drugs. Mathematical modeling is crucial for disease prevention and eradication strategies. The study uses deterministic models to analyze global malaria transmission patterns, focusing on enlightened therapy's effectiveness as a control measure.

Four compartmental models depict susceptible, latent, infected, and recovered populations, exploring various disease spread scenarios while ensuring model stability and reliability. Epidemiological principles identify disease-free and endemic equilibria, calculating the basic reproduction number. Stability analysis utilizes Lyapunov functions, supported by Laplace transformation and MAPLE18 simulations for solution derivation.

Furthermore, the study investigates the impact of fractional-order derivatives on transmission dynamics and control strategies, analyzing the effects of increasing fractional derivative orders using graphical representations. This research provides insights valuable for public health initiatives and malaria eradication efforts, emphasizing the role of Caputo fractional derivatives in refining malaria control strategies and elucidating the findings for a broader readership appeal.