A Nonlinear Mathematical Framework for Cardiac Tissue Disease Progression With ECG Signal Dynamics, Bifurcation Theory, Sensitivity Analysis, and Optimal Control

In this work, a nonlinear deterministic mathematical model is proposed to explore the evolution of cardiac tissue behavior from healthy to at-risk, to damaged, to treated, and to recovered and the consequences of these changes on the dynamics of electrocardiogram (ECG) signals. The model seeks to set up a single solution to understand how diseases develop, how the nonlinear tissue laws mimic this behavior, and how treatments affect the outcome. Analytical investigations determine the positivity and boundedness of solutions, and disease-free and endemic equilibrium states are detected. The basic reproduction number is obtained as a threshold parameter that regulates cardiac stress persistence. Using bifurcation and stability analysis, the authors find transcritical, backward, and Hopf bifurcations; by changing the stress transmission and treatment effectiveness, cardiac tissue and ECG dynamics change. The partial rank correlation coefficients (PRCC) approach is used to conduct the global sensitivity analysis that determines the most influential parameters affecting the disease progression and long-term system behavior, which is illustrated by numerical simulations showing the nonlinear transition of the system. Moreover, an optimal control scheme is studied to assess therapeutic strategies that decrease damage and improve healing in the tissues. Their findings offer a theory in favor of myocardial progression of cardiac disease and the value of effective treatment interventions for stabilizing the heart and improving recovery outcomes.