TY - GEN AU - Madhab Bharman AU - Madhab Barman TI - Analysis and Simulations of Network-Based Nonlinear Epidemic Models U1 - 517.988 MAD PY - 2024/// PB - Mathematic KW - Hopf bifurcation; Epidemic; Compartmental Model; Spatial- disease spread; Population mobility; Graph Laplacian; Local Sta- bilith N1 - The study of epidemic dynamics is crucial for understanding and controlling the spread; Finally, our work contributes to the evolving field of epidemic modeling by integrating graph Laplacian diffusion into the framework N2 - The study of epidemic dynamics is crucial for understanding and controlling the spread of infectious diseases. In recent years, there has been a growing interest in employ- ing graph theory and network science to model the complex interactions among in- dividuals and understand spatial disease spread in a population. This thesis explores the application of graph Laplacian diffusion in epidemic modeling of well-established epidemic models such as Susceptible-Infectious-Removed (SIR), Susceptible-Exposed- Infectious-Removed (SEIR), Susceptible-Asymptomatic-Infectious-Removed (SAIR), and more ER -