The effectiveness of vaccine in the outbreak of diphtheria: Mathematical model and simulation

Abstract

In December 2017, Indonesia suffered a diphtheria outbreak that struck in 28 provinces. This incident made the public and researchers concerned about the cause of the return of epidemic after the last case in the 1980s. Over the years, DPT (Diphtheria Pertussis Tetanus) vaccine is believed to be the only ways of preventing diphtheria outbreaks. In this paper, the authors will attempt to construct a mathematical model for the case of diphtheria outbreak by involving vaccine parameter in the susceptible compartment. The population assumed to be closed population and consisted of SEIR (Susceptible, Exposed, Infected, and Recovered) population. Furthermore, this model will be analyzed the stability and sensitivity using Eigen values and basic reproduction number (R 0 ). The simulation is done to provide an overview of the effectiveness of the vaccine dynamically. Analysis and simulation results show that vaccine plays an effective role in reducing the spread of diphtheria, but this vaccine is only a preventive, not as a cure.