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All Journal International Journal of Computing Science and Applied Mathematics-IJCSAM
Aprilia Saniatul Rahmawati
Universitas Sebelas Maret
Mathematics

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A Simulation of the Discrete Time Markov ChainSusceptible Vaccinated Exposed Infected Recovered (DTMC SVEIR) Model with Relapse Cases in theSpread of Tuberculosis* Respatiwulan Respatiwulan; Hasih Pratiwi; Sri Sulistijowati Handajani; Yuliana Susanti; Kiki Ferawati; Muhammad Bayu Nirwana; Andreas Rony Wijaya; Aprilia Saniatul Rahmawati; Embun Zahra Nirmala
(IJCSAM) International Journal of Computing Science and Applied Mathematics Vol. 12 No. 2 (2026)
Publisher : LPPM Institut Teknologi Sepuluh Nopember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.12962/j24775401.ijcsam.v12i2.10716

Abstract

Tuberculosis (TB) is a contagious disease that pri-marily affects the lungs and spreads through the air whenan infected person coughs, sneezes, or spits. TB remains as asignificant global health issue, with millions of cases and deathsannually. There are mathematical epidemiological models thathave been developed, including SIR, SEIR, and SVEIR forexplaining the spread of disease pattern. The SVEIR modelexplains the impact of vaccination on disease transmission such asTB. In TB cases, the recovered individuals could be relapsed andbe infected again. This study discussed a Discrete Time MarkovChain (DTMC) SVEIR model and applied model simulation toTB disease. The population is divided into five groups such assusceptible, vaccinated, exposed, infected, and recovered. Thechanges of group’s state follow Markov process in discretetime observation. The model is extension from DTMC SEIRwith relapse by adding Vaccinated compartment. The modelis expressed as transition probability that explain the changesof state in each group. The simulation results indicate that thespread of the disease is significantly influenced by parametersvalue such as contact rate, vaccination rate, vaccine effectiveness,relapse rate, and recovery rate. If contact rate higher thanthe recovery rate then the number of infected individuals willincrease. The other hand, if vaccination works effectively thenthe number of susceptible individuals decrease. Lower relapserates lead to higher recovery numbers, whereas higher relapserates accelerate reinfection
Co-Authors Andreas Rony Wijaya Embun Zahra Nirmala Handajani, Sri Sulistijowati Kiki Ferawati Muhammad Bayu Nirwana Pratiwi, Hasih Respatiwulan Respatiwulan Yuliana Susanti