Mathematical Modelling and Deep Learning Techniques for Predicting Cardiovascular Disease

Putting together mathematical models and deep learning has become a strong way to identify cardiovascular disease (CVD) in recent years. This paper looks at how dynamical systems, control theory, and machine learning methods can work together to make CVD forecast more accurate and reliable. To improve the ability of diagnostic tools to predict the future by using mathematical models like differential equations to describe how the heart works and deep learning architectures like Convolutional Neural Networks (CNNs) and Recurrent Neural Networks (RNNs) for feature extraction. This method considers both the time patterns of how the heart works and the non-linear complexity of risk factors like high blood pressure, high cholesterol, and family tendencies. The most important part of our method is creating a multi-stage prediction model. This model starts with differential equations that show how heart rate and blood pressure change over time. Next, it uses deep learning models that have been trained on large CVD datasets. Normalization and feature engineering 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 findings indicate that combining mathematical models with deep learning makes predictions a lot more accurate than using only standard machine learning models. In particular, adding time dynamics to the model lets it find hidden trends in physiological data that simple models often miss. Deep learning also lets the system learn on its own how different risk factors are related to each other, making it a strong tool for finding CVD early and predicting how bad it will be. The research shows that a mix of approaches could make personalized medicine better by giving doctors accurate and easy to understand prediction tools. In the future, researchers will focus on making these models work better so it can be used in real time in hospital settings. This could help lower the number of people who get cardiovascular disease around the world.