This paper investigates the dynamical properties of mathematical models for COVID-19 transmission, with a focus on understanding the behavior and stability of various model configurations. We analyze a suite of compartmental models, including the Susceptible-ExposedInfectious-Recovered-Susceptible (SEIRS) models, incorporating factors like latency periods, varying transmission rates, and the impact of interventions. Using techniques from dynamical systems theory, we perform stability analysis to determine the conditions under which equilibrium exist and whether they are stable or unstable. Our analysis reveals critical thresholds for reproduction numbers and provides insights into how changes in parameters, such as infection rates and recovery times, affect the long-term dynamics of the epidemic. Numerical simulations further illustrate the transient and asymptotic behavior of the system. The results underscore the importance of timely interventions and adaptive strategies in managing the spread of COVID-19, offering valuable guidance for predicting and controlling future outbreaks.