Abstract

This talk focuses on a mathematical model of dengue fever transmission, incorporating delay terms to reflect realistic time delays in the disease dynamics. Using the next-generation matrix approach, the basic reproduction number ($R_0$) is derived, providing critical insight into the conditions for disease persistence or eradication. The model is further analyzed through nondimensionalization to simplify the system and identify key parameters. Equilibrium points are determined, and their stability is examined in the presence of delays. Numerical simulations are presented for specific parameter sets to illustrate the dynamics, highlighting the impact of delays on disease progression and stability. These findings provide valuable insights into the role of temporal factors in infectious disease modeling and contribute to a deeper understanding of disease dynamics.