Penerapan Model Discrete Time Markov Chain Susceptible Vaccinated Infected Recovered (DTMC SVIR) pada Pola Penyebaran Penyakit Difteri di Indonesia

Abstract

Epidemic is the spread of disease that appears in a population in an area within a certain time. Susceptible infected recovered (SIR) epidemic model describes the spread of disease with each recovered individual having a permanent immune system to a disease. One way of disease control can be done with vaccination. Epidemic model that considers vaccination is susceptible vaccinated infected recovered (SVIR) model. Population in SVIR model is divided into the susceptible group (S), vaccinated group (V), infected group (I), and recovered group (R). SVIR model that follows Markov process with discrete time intervals is discrete time Markov chain susceptible vaccinated infected recovered (DTMC SVIR) model. This study discusses the application of DTMC SVIR model to the pattern of diphtheria disease spread in Indonesia. The results present the DTMC SVIR model on diphtheria disease patterns in Indonesia with contact rate β = 0,0000021026, vaccination rate α = 0,0154360815, vaccine failure rate θ = 0,029375, and cure rate γ = 0,0238095238. Simulated model with initial values N = 100 and I(0) = 2 showed that epidemic ended at t = 21 and with N = 500, V(0) = 15,  and  I(0) = 10 showed that epidemic ended at t = 62.