Stability analysis of SIVS epidemic model with vaccine ineffectiveness

Vaccination is the act of getting a vaccine to help the immune system develop protection from a disease. Vaccination is a good and efficient step to protect population from epidemic. However, vaccines do not necessarily provide perfect immunity to body because not all type of vaccines have 100% effectiveness. The ineffectiveness of a vaccine affects the dynamics of the spread of an infectious disease. The dynamics of the spread of infectious diseases with vaccine ineffectiveness can be approached by mathematical models. Tins paper aims to analyze the stability of SIVS epidemic model with vaccine ineffectiveness. Based on model analysis result, the model obtained two equilibrium points namely, the disease free-equilibrium point (0) and endemic equilibrium point In addition, the basic reproduction number (R0) also obtained, which determines the existence and stability of equilibrium point. Disease free-equilibrium point (£0) local asymptotically stable if R0 < 1, then through phase plane simulation it conclude that endemic equilibrium point (Ex) local asymptotically stable if Rq > 1. Based on numerical simulation results, it shows that vaccine ineffectiveness affects the high spread of disease.