Dynamics of an SIRD model with Crowley-Martin incidence rate by using the machine learning approach

In this paper, we propose an SIRD model that incorporates the Crowley-Martin-type incidence rate and Holling type-II treatment rate, providing a more realistic representation of how contact limitations and healthcare capacity affect disease transmission compared to traditional bilinear models. We establish the existence, positivity, and boundedness of the model solutions to ensure well-posedness. The basic reproduction number R0 is computed using the next-generation matrix. We also examine the local and global stability of the proposed model. To estimate unknown parameters, we employ the epi-DNN method, which combines epidemiological knowledge with deep learning. Subsequently, we train machine learning models on the output of the compartmental model and compare their forecasts with real data. This two-step approach improves interpretability and combines a biology-driven model with advanced learning techniques, resulting in a robust and adaptable framework for modelling and forecasting real-world epidemic dynamics.