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Savanna fire has many types: Savanna woody, Savanna vegetation, and grassland. In this paper, Savanna vegetation is studied, characterized by low trees and high grass. It grows in hot and seasonally dry conditions. The Savanna vegetation is described by relating to the environment and climate. Savanna vegetation is considered a metastable mixture of trees and grass and is advanced to explain stability. The Savanna vegetation is modeled with first-order linear differential equations having grass, trees, and sapling (young trees) as components. Furthermore, the model is evaluated numerically by integrating the global search technique Sine-Cosine algorithm and local search technique Interior point algorithm. Comprehensive numerical experiments are conducted to analyze numerical results. To validate solution of proposed technique, Runge-Kutta order four method isolution is taken as a reference solution …