Mathematical Modelling and Deep Learning Techniques for Predicting Cardiovascular Disease

Putting together mathematical models and deep learning has become a strong way toidentify cardiovascular disease (CVD) in recent years. This paper looks at howdynamical systems, control theory, and machine learning methods can work togetherto make CVD forecast more accurate and reliable. To improve the ability ofdiagnostic tools to predict the future by using mathematical models like differentialequations to describe how the heart works and deep learning architectures likeConvolutional Neural Networks (CNNs) and Recurrent Neural Networks (RNNs) forfeature extraction. This method considers both the time patterns of how the heartworks and the non-linear complexity of risk factors like high blood pressure, highcholesterol, and family tendencies. The most important part of our method is creatinga multi-stage prediction model. This model starts with differential equations thatshow how heart rate and blood pressure change over time. Next, it uses deep learningmodels that have been trained on large CVD datasets. Normalization and featureengineering methods are used to prepare the information. Key measures like age,BMI, and cholesterol levels are used as inputs. Metrics like precision, sensitivity,specificity, and F1-score are used to judge how well the model works. Early findingsindicate that combining mathematical models with deep learning makes predictions alot more accurate than using only standard machine learning models. In particular,adding time dynamics to the model lets it find hidden trends in physiological datathat simple models often miss. Deep learning also lets the system learn on its ownhow different risk factors are related to each other, making it a strong tool for findingCVD early and predicting how bad it will be. The research shows that a mix ofapproaches could make personalized medicine better by giving doctors accurate andeasy to understand prediction tools. In the future, researchers will focus on makingthese models work better so it can be used in real time in hospital settings. This couldhelp lower the number of people who get cardiovascular disease around the world.