Analisis Model Epidemi SVEIR Pada Penyebaran Penyakit Campak dengan Tiga Kali Vaksinasi

Silvitasari Silvitasari, Kridha Pusawidjayanti

Abstract


In 2021, there will be 9 million cases of measles worldwide. Twenty-two countries have large numbers of measles infections. The Ministry of Health of the Republic of Indonesia or Ministry of Health recorded that there were more than 3,341 cases of measles spread across 223 districts/cities in 31 provinces. The control of measles cases carried out by the Indonesian government has been through vaccination since 2000. The first vaccine is given to children aged nine months, the second vaccine is given to children aged 18 months, and the third dose is in grades 1-6 of elementary school (SD). This research uses the SVEIR mathematical model for the spread of measles with adjustments to government efforts and recommendations from the Indonesian Pediatrician Association (IDAI) to prevent an increase in the spread of measles through preventative vaccination. In this SVEIR model, there are seven classes, namely Susceptible (S), first dose vaccination (V1), second dose vaccination (V2), third dose vaccination (V3), Exposed (E), Infected (I), and Recovered (R). This research aims to analyze the SVEIR model on the spread of measles with three vaccinations, the stability of the equilibrium point, and determine the effect of vaccination in controlling measles. The analysis results show that the endemic equilibrium point is asymptotically unstable, and the non-endemic equilibrium point is asymptotically stable with R_0=0.0736829 <1. This indicates that measles will disappear on the 260th day or around 8.5 months after implementing the vaccination program.


Keywords


Measles, SVEIR Model, Stability, Basic Reproduction Number, Equilibrium Point

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References


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DOI: http://dx.doi.org/10.12962/limits.v21i2.20710

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