We formulated a discrete time delay mathematical model to investigate the yellow fever disease’s transmission pattern. We established the stability of the delay system by identifying the equilibrium point that is both endemic and free of yellow fever through analytical investigations. Stability was also determined by computing the basic reproduction number using the next generation matrix method. We then conducted numerical simulation and results show that time delay plays a significant role in the case of stability of the endemic equilibrium point as equilibrium is quickly achieved for smaller time delays and vice versa. The basic reproduction number obtained using the model parameter is 0.68876; which shows that the yellow fever free equilibrium point is locally asymptotically stable. The implication of the boundedness is that the disease is controllable.
Keywords: Epidemiology, Yellow fever, discrete time delay
