Abstract
Diphtheria is an acute disease caused by bacteria (Corynebacterium Diphtheriae). This disease is transmitted through the air and droplets (very small drops of fluid) from infected individuals. Vaccination can be carried out as a preventive measure so as not to be infected with bacteria (Corynebacterium Diphtheriae) and quarantine is carried out as a healing process because this disease is one type of disease included in the hospital-based STP (Integrated Disease Surveillance) data source. This study aims to compile and analyze a model of the spread of diphtheria using the SVIQR model. This model contains five subpopulations, namely susceptible (S), infected (I), cured (R), quarantined (Q) and vaccinated (V). Then determine the numerical simulation by estimating the parameters. From the results of numerical simulations of the mathematical model of diphtheria transmission under the influence of vaccination and quarantine, it shows that by selecting the vaccination fade rate parameter, =0.3795491181<1, which means that the disease-free equilibrium point is stable. The asymptotically stable endemic equilibrium point obtained is =1.207495030>1. The smaller the value of the vaccination fading rate parameter ε, the more asymptotically stable the disease-free point means that the spread of disease or endemic disease can be prevented if the vaccine given does not fade easily.
 Keywords: Stability Analysis, Mathematical Models, Diphtheria, Quarantine, Vaccination.
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