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This paper proposes a modification to the Hestenes-Stiefel (HS) method by devising a spectral parameter using a modified secant relation to solve nonlinear least-squares problems. Notably, in the implementation, the proposed method differs from existing approaches, in that it does not require a safeguarding strategy and its Hessian matrix is positive and definite throughout the iteration process. Numerical experiments are conducted on a range of test problems, with 120 instances to demonstrate the efficacy of the proposed algorithm by comparing it with existing techniques in the literature. However, the results obtained validate the effectiveness of the proposed method in terms of the standard metrics of comparison. Additionally, the proposed approach is applied to address motion-control problems in a robotic model, resulting in favorable outcomes in terms of the robot’s motion characteristics.

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Schistosomiasis is a parasitic disease from the family of Schistosomatidae and genus Schistosoma, which is caused by blood flukes. The disease is endemic in many countries and still a serious threat to global public health and development. In this paper, a new deterministic model is designed and analyzed qualitatively to explore the dynamics of schistosomiasis transmission in human, cattle and snail populations. Results from our mathematical analysis show that the model has a disease-free equilibrium (DFE) which is locally asymptotically stable (LAS) whenever a particular epidemiological threshold quantity, also known as basic reproduction number ([Formula: see text]) is less than unity. Further analysis shows that the model has a unique endemic equilibrium (EE) which is globally asymptotically stable whenever [Formula: see text] and unstable when [Formula: see text]. Furthermore, We adopt partial rank correlation coefficient for sensitivity analysis to reveal the most important parameters for effective control and mitigation of schistosomiasis disease in a community. Finally, we obtain some numerical results by simulating the entire dynamics of the model, which show that the infections in the compartments of each population decrease with respect to time. This further indicates that avoiding contact with infected human, cattle or infested water is vital to prevent the spread of schistosomiasis disease infection.