Approximate solutions to malaria transmission models with seasonality and awareness: A comparative analysis of ADM and HPM

Abimbola Abolarinwa; Isaac O Olusola

doi:10.48185/jmam.v7i2.1981

Authors

Abimbola Abolarinwa
aabolarinwa@unilag.edu.ng
Department of Mathematics, University of Ibadan, Ibadan, Nigeria
Isaac O Olusola Department of Mathematics, University of Ibadan, Ibadan, Nigeria

Keywords:

Mathematical Modeling, Semi-Analytic Method, Non-linear Differential Equations, Epidemiology, Intervention Strategies, Seasonality. 2010 MSC: 34A34, 65L70, 93A30, 93C15.

Abstract

Mathematical modelling provides critical insights into malaria transmission dynamics and interven tion efficacy. While standard numerical solvers provide quantitative solutions, semi-analytical methods yield closed-form series approximations that enhance qualitative and parametric understanding. This study com paratively investigates two prominent semi-analytical techniques, the Adomian Decomposition Method (ADM) and the Homotopy Perturbation Method (HPM), applied to a seasonally-forced malaria transmission model. The underlying formulation encompasses human behavioral awareness, a structured mosquito life cycle, and seasonal forcing, resulting in a twelve-dimensional coupled non-autonomous nonlinear system. Explicit recur sive algorithms for ADM and HPM are derived and validated against fourth-fifth order Runge–Kutta numeri cal benchmarks using biologically realistic parameters. The comparative evaluation indicates compartment dependent performance: HPM exhibits high precision for human epidemiological classes over short intervals, while ADM demonstrates superior stability across mosquito developmental stages and awareness dynam ics over extended time periods. Numerical experiments further show that intensified awareness campaigns significantly curtail infection prevalence across both host and vector populations. The methods remain com putationally tractable for 12D systems. Our findings therefore provide practical guidance for selecting semi analytical schemes according to compartment and time-scale in high-dimensional epidemiological systems.

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