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Researchers have made significant strides in understanding car-following behaviour and traffic flow, especially with the advent of intelligent and networked technologies. Diverse mathematical models analyse traffic flow, each with pros and cons. This study focuses on a sensitivity-based mathematical model for uphill and downhill highways, examining position, velocity, and acceleration profiles to predict traffic jam occurrence. The model employs an ordinary differential equation and a machine learning-based approach (machine learning procedure neural network) for numerical solutions, exhibiting high accuracy (1 0− 8− 1 0− 10) compared to the reference Runge–Kutta method For accuracy, reliability and stability of the results are evaluated by various performance indicators and statistical terms. For multiple independent executions, mean absolute deviation, root mean square error and error in Nash–Sutcliffe …