Sensitivity analysis and applications of Laplace Adomian Decomposition Method in solving fractional order malaria model

Abstract

This study explores the sensitivity analysis and implementation of the Laplace-Adomian Decomposition Method (LADM) in solving a fractional-order malaria transmission model utilizing the Caputo fractional derivative. A deterministic compartmental model comprising eight ordinary differential equations is formulated to capture the dynamics of malaria spread. Key mathematical properties of the model, including the positivity of solutions and the existence of an invariant region, are rigorously examined. Stability analysis reveals that the disease-free equilibrium remains locally stable when the basic reproduction number is less than one, based on the next-generation matrix approach. To approximate solutions of the fractional-order system, LADM is employed, generating a rapidly converging infinite series under appropriate conditions. Parameter values are estimated using MATLAB’s fmincon optimization algorithm, calibrated with empirical malaria data extracted from published sources. LADM integrates the Laplace transform with the Adomian Decomposition Method by first applying the Laplace transform, breaking down nonlinear terms via Adomian polynomials, and finally applying the inverse Laplace transform to derive the solution. The study successfully applies LADM to obtain approximate solutions for the malaria model and reaffirms that the disease-free equilibrium is stable when the reproduction number falls below one. Findings also show that enhancing treatment efficacy within the human population leads to a marked decline in malaria prevalence. Sensitivity analysis identifies key parameters that influence disease transmission, highlighting that reducing contact between susceptible individuals and infectious mosquitoes, alongside prompt treatment of infected individuals, is vital for disease control. Unlike previous models based solely on classical ADM, this work integrates the Laplace transform to improve both convergence speed and solution accuracy. Moreover, real malaria data from Nigeria is incorporated to ensure practical relevance and accuracy of the model.