Neural network analysis of the transmission dynamics of leptospirosis infection subject to vaccination and treatment interventions.

The rapid spread of infectious diseases can lead to substantial casualties worldwide, with the greatest impact on economically disadvantaged and resource-deficient nations. The widespread transmission of infection disrupts social life and economic activities, amplifying their impact beyond the public health system. In this paper, we analyze the dynamics of leptospirosis disease considering treatment for humans and vaccination for the animal population along with environmental bacteria control. We analyzed the qualitative behavior of the model, focusing on the positivity and boundedness of the system. The existence and stability conditions of the equilibrium points are analyzed in relation to the basic reproduction number. Real-world leptospirosis case records from Kerala (June 2018 to December 2024) are used to calibrate and evaluate the model's performance. The global sensitivity analysis of R0 is employed to evaluate and illustrate the model parameters. The primary methodological contribution lies in the development of a hybrid deep neural network (DNN) framework that integrates Tanh and ReLU activation functions to accurately capture the complex dynamics of the model. A two-layer DNN is trained using the Levenberg-Marquardt algorithm with a 70%-15%-15% data split. The proposed DNN demonstrates remarkable predictive accuracy, achieving a mean squared error of 10-6 and an absolute error of 10-9. This work introduced a novel framework combining dynamical system theory and deep learning for accurate and computationally efficient analysis of epidemic dynamics.