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A.A. Adeniji,M.C. Kekana,M.Y. Shatalov 한국전산응용수학회 2023 Journal of applied mathematics & informatics Vol.41 No.5
This paper summarizes some research findings that show how the differential transform method (DTM) is used to resolve the Holling-Tanner model. To confirm the application, effectiveness, and correctness of the approach, a comparison between the differential transform method (DTM) and the Adomian decomposition method (ADM) is carried out, and an accurate solution representation in truncated series is discovered. The approximate solution obtain using both techniques and comparison demonstrates same outcome which remains a preferred numerical method for resolving a system of nonlinear differential equations.
N. Jeeva,K.M. Dharmalingam,S.E. Fadugba,M.C. Kekana,A.A. Adeniji 한국전산응용수학회 2024 Journal of applied mathematics & informatics Vol.42 No.4
This study focuses on SIR model for SARS-CoV-2. The SIR model classifies a population into three compartments: susceptible $S(t)$, infected $I(t)$, and recovered $R(t)$ individuals. The SARS-CoV-2 model considers various factors, such as immigration, birth rate, death rate, contact rate, recovery rate, and interactions between infected and healthy individuals to explore their impact on population dynamics during the pandemic. To analyze this model, we employed two powerful semi-analytical methods: the Laplace Adomian decomposition method (LADM) and the differential transform method (DTM). Both techniques demonstrated their efficacy by providing highly accurate approximate solutions with minimal iterations. Furthermore, to gain a comprehensive understanding of the system behavior, we conducted a comparison with the numerical simulations. This comparative analysis enabled us to validate the results and to gain valuable understanding of the responses of SARS-CoV-2 model across different scenarios.