Fetal heart rate variability (FHRV) is a critical indicator of fetal well-being and autonomic nervous system development during labor. Traditional monitoring methods often provide limited insights, potentially leading to delayed interventions and suboptimal outcomes. This study proposes an advanced predictive analytics approach by integrating approximate entropy analysis with a hidden Markov model (HMM) within a digital twin framework to enhance real-time fetal monitoring. We utilized a dataset of 469 fetal electrocardiogram (ECG) recordings, each exceeding one hour in duration, to ensure sufficient temporal information for reliable modeling. The FHRV data were preprocessed and partitioned into parasympathetic and sympathetic components based on downward and non-downward beat detection. Approximate entropy was calculated to quantify the complexity of FHRV patterns, revealing significant correlations with umbilical cord blood gas parameters, particularly pH levels. The HMM was developed with four hidden states representing discrete pH levels and eight observed states derived from FHRV data. By employing the Baum–Welch and Viterbi algorithms for training and decoding, respectively, the model effectively captured temporal dependencies and provided early predictions of the fetal acid–base status. Experimental results demonstrated that the model achieved 85% training and 79% testing accuracy on the balanced dataset distribution, improving from 78% and 71% on the imbalanced dataset. The integration of this predictive model into a digital twin framework offers significant benefits for timely clinical interventions, potentially improving prenatal outcomes.

The modeling of lactation curves is an essential aspect of formulating farm managerial practices in dairy cows. In this study, we propose and examine a Markov-Dependent stochastic approach to modeling lactation curves in dairy cows, with the aim of developing a model that accurately fits lactation curves for a maximum number of lactations. Specifically, we develop a special type of Gamma Type Markov Chain Model that considers the first-order linear regressive property, which makes the model more realistic and reliable. We compared the proposed model with three other models - quadratic model, mixed log function, and wood model - using various goodness of fit measures such as adjusted R², root mean square error (RMSE), and Bayesian Information Criteria (BIC). Our results showed that lactation curve modeling using the proposed model could help set management strategies at the farm level. However, it is important to optimize the modeling process regularly before implementing these strategies to enhance productivity in dairy cows. Our study contributes to the existing literature by proposing a novel approach that accounts for Markov dependence and linear regression in modeling lactation curves, which can lead to more accurate and reliable predictions. This modeling approach has practical implications for dairy farmers who seek to maximize productivity and efficiency while minimizing costs.