Global Stability of Mathematical Models for Heart Disease Transmission and Prevention Dynamics

Heart disease remains a leading cause of global mortality, underscoring the urgent need for effective prevention and control strategies. This study analyses a compartmental mathematical model that capture the transmission and prevention dynamics of heart disease, incorporating both lifestyle-related and genetic risk factors. The model consists of six compartments—susceptible, two exposed classes (lifestyle and genetic), infected, treated, and recovered populations. Analytical methods are employed to establish the positivity and boundedness of solutions, determine the disease-free equilibrium (DFE), and compute the basic reproduction number ????0 using the next-generation matrix approach. Global stability of the DFE is proven via LaSalle’s Invariance Principle and an appropriately constructed Lyapunov function. Numerical simulations implemented in R programming validate the theoretical results, demonstrating that when ????0<1, the disease can be eradicated. Findings highlight the pivotal role of primary prevention, lifestyle modification, early detection, and treatment in reducing disease prevalence. This framework offers valuable insights for designing public health interventions and provides a basis for future model extensions incorporating demographic and spatial complexities.