A SIAR Model Approach to the Impact of Mudik Tradition on Covid-19 Transmission in Indonesia

In Indonesia, on March 2, 2020, the government announced the first case of Covid-19. Preventing the COVID-19 spread in Indonesia is challenging because the people are very diverse, and not everyone has the same understanding of the transmission of COVID-19. In addition, the Indonesians has mudik tradition, going home yearly on Eid al-Fitr. This study developed an epidemic model of Covid-19 spread SIAR by adding migration factors to represent the mudik tradition. The disease-free equilibrium point, the endemic equilibrium point, and its stability were determined. Numerical simulations were done using Covid-19 transmission data to analyze the trend of symptomatic and asymptomatic infected subpopulations. The results show that the dynamic characteristics of Covid-19 cases were semi-stable in compartments S, I, and A. This condition means that S, I, and A will rise at a certain time. In a disease-free situation, the susceptible subpopulation S is stable at a certain value. At the same time, other subpopulations are stable at almost zero and at zero. The susceptible subpopulation S in a disease-free situation is larger than during an epidemic. The number of people in disease-free conditions is smaller than those in epidemic conditions. In addition, migration at a certain level can increase the spread of Covid-19.