Model Matematika SVEIAR Penularan Covid-19 di Indonesia dengan Intervensi Vaksinasi dan Tradisi Mudik

In early 2020, the Covid-19 epidemic started in China, rapidly spreading across the globe, including Indonesia. Indonesian society is known for its diversity and complexity, making it difficult to predict trends in the number of infected, deceased, and recovered individuals. This study develops a Covid-19 transmission epidemic model, called SV EIAR, which accounts for interventions such as vaccination and the mudik tradition (the practice of returning to hometowns during Eid). In this model, the susceptible (S) compartment refers to the subpopulation of individuals who are susceptible to the virus, while vaccinated (V) represents those who have been vaccinated twice. The exposed (E) compartment includes individuals who are infected but still in the incubation period and unable to spread the virus. Infection (I) refers to individuals who are symptomatic, and asymptomatic (A) includes those who are infected but show no symptoms. Lastly, the recover (R) compartment represents individuals who have recovered from the infection. The analysis of the model involves identifying the reproduction number, estimating the disease-free and endemic equilibrium points, and analyzing their stability. Numerical simulations were carried out using Covid-19 transmission data from Indonesia to predict the trends of the infected and asymptomatic populations. The results suggest that the dynamics of Covid-19 cases are semi-stable in the susceptible (S), exposed (E), infected (I), and asymptomatic (A) compartments, meaning that these populations will increase over time. In a disease-free situation, the susceptible population (S) remains stable at a certain value, while other populations are stable at nearly zero. The susceptible population in the disease-free state is larger than during an epidemic, while other populations are smaller in the disease-free state compared to the epidemic. Additionally, the study found that vaccination can help reduce the transmission of Covid-19, while the practice of mudik can increase the spread of the virus.