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Secure QoS routing over disjoint paths is a challenging problem that requires balancing the trade-off between network security and bandwidth guarantees. This paper proposes a mathematical model that can address this problem by formulating it as an optimization problem with a linear objective function and linear or bilinear constraints. The objective function aims to minimize the compromise probability of the paths, while the constraints ensure that the total bandwidth of the paths meets the QoS requirements. The paper also presents a numerical study of the model using different scenarios and parameters. The results show that the model can effectively provide secure QoS routing over disjoint paths with a high bandwidth guarantee level and a low compromise probability. The paper also analyzes the sensitivity of the solutions to the QoS requirements and reveals that there is usually some margin in the bandwidth …