Dynamics of an Infectious Disease Model with Transmission Delay from Recovery to Susceptibility

In this study, an extended SIR model with vaccination and treatment is considered by introducing a delay in the transition from the recovered class back to the susceptible class. This delay reflects the time it takes for individuals to lose immunity after recovery or vaccination. To understand the dynamics of the disease, both local and global stability of the equilibrium points are analyzed. Local stability conditions are derived using the basic reproduction number and characteristic equations, while global stability is established through Lyapunov’s method. A numerical example is included to demonstrate how different values of the delay affect the system.