How Effective is the Vaccine in Reducing Outbreak of Diphtheria? Fadilah Ilahi, Nenden Siti Nurkholipah
UIN Sunan Gunung Djati Bandung
Abstract
Indonesia suffered a diphtheria outbreak in the late of 2017 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. The Indonesian government requires all infants aged 2-4 months old to get DPT vaccine in order to get the immunity against diphtheria-causing bacteria with a single dose of vaccine on each month. The problem is when some infants do not have the complete vaccine so the effectiveness of DPT vaccine is need to be questioned. In this paper, the authors try to construct the model to see how effective the DPT vaccine for those cases. The population assumed to be closed population and consisted of SIR (Susceptible, Infected, and Recovery) population and the vaccine notated as a function of a dose that has taken by the infant. Furthermore, this model will be analyzed the stability 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 complete dose of DPT vaccine plays an effective role in reducing the spread of diphtheria.
Keywords: Diphtheria, vaccine, outbreak, epidemic, basic reproduction number, mathematical model
