Fractional-Order Analysis of Malaria Dynamics in Dire Dawa City: A Laplace an Adomian Decomposition Approach

Malaria remains a significant public health challenge in Dire Dawa City, Ethiopia, exacerbated by seasonal rainfall that drives mosquito populations and transmission. Fractional-order models offer a promising approach to capturing memory effects in epidemiological dynamics, improving predictive accuracy for intervention planning. This study aimed to formulate a fractional-order model capturing malaria transmission dynamics in Dire Dawa, solve it using numerical and analytical methods, analyze the impact of key parameters, evaluate existing interventions, and propose optimized control measures. A fractional-order SIR model ( = 0.95) was developed using the Grünwald-Letnikov method for numerical solutions and the Laplace Adomian Decomposition Method (LADM) for analytical validation, simulating dynamics over 365 days. Parameters like transmission rates (), (), and recovery rate () were varied to assess their impact, and interventions (bed nets, treatment) were evaluated with optimized timing. The model accurately captured malaria dynamics, with peak prevalence reaching 200,000 under baseline conditions, reduced by 20% with bed nets, 15% with treatment, and 40% with an optimized combined strategy starting at day 60. Transmission rates significantly influenced prevalence, with a 53% increase in peak infections for a 40% rise in (). Fractional-order modeling effectively informs malaria control in Dire Dawa, highlighting the importance of early, combined interventions. Deploy bed nets and enhance treatment access by day 60 with 80–90% coverage to minimize prevalence.