Model Kontrol Optimal SIR Pada Penyakit Campak
Abstract
The SIR model is one of the epidemic models to describe the spread of infectious diseases with healing and without immunity to these infections. Environmental changes can affect changes in disease patterns that can cause endemic. One of the diseases that cause endemic is Measles (Measles). Therefore, it is necessary to take preventive measures to reduce the rate of spread of the disease, the most effective measure to prevent the spread of the disease is vaccination. Measles transmission prevention events that occur in a population can be modeled in a mathematical form, one of which is the SIR model. The SIR model is divided into four subpopulations, namely the susceptible population or a subpopulation of susceptible individuals to the disease, the infected subpopulation or a subpopulation of infected individuals and can transmit the disease and the recovary subpopulation or individual subpopulation recovering from the disease. Vaccination in this case is the addition of controls to the SIR model, where before being controlled, Measles was only treated normally without vaccines, so that the disease is still common in the community. Giving the right vaccine will reduce the number of infected subpopulations, so that the recovery subpopulation will increase. In this study, the SIR model was developed with the addition of controls. The control in this model is a vaccination given to infected subpopulations, so that the recovery subpopulation has increased, because the number of infected subpopulations has decreased.
Abstrak
Model SIR merupakan salah satu model epidemik untuk menggambarkan penyebaran penyakit infeksi dengan adanya penyembuhan dan tanpa adanya kekebalan terhadap infeksi tersebut. Perubahan lingkungan hidup dapat mempengaruhi perubahan pola penyakit yang dapat menimbulkan endemik. Salah satu penyakit yang menyebabkan endemi yaitu penyakit Campak (Measles). Oleh karena itu perlu adanya tindakan pencegahan untuk mengurangi laju penyebaran penyakit tersebut, tindakan yang dinilai paling efektif untuk mencegah penyebaran penyakit adalah dengan cara vaksinasi. Kejadian pencegahan penularan penyakit Campak yang terjadi pada suatu populasi dapat dimodelkan ke dalam bentuk matematis, salah satunya adalah model SIR. Model SIR dibagi menjadi empat subpopulasi yaitu populasi susceptible atau subpopulasi individu rentan terhadap penyakit, subpopulasi infected atau subpopulasi individu terinfeksi serta dapat menularkan penyakit dan subpopulasi recovary atau subpopulasi individu sembuh dari penyakit. Vaksinasi dalam hal ini adalah penambahan kontrol pada model SIR, dimana sebelum dikontrol, penyakit Campak hanya diobati biasa tanpa pemberian vaksin, sehingga penyakit tersebut masih banyak dijumpai di masyarakat. Pemberian vaksin yang tepat, akan menurunkan jumlah subpopulasi terinfeksi, sehingga subpopulasi recovery akan mengalami kenaikan. Pada penelitian ini mengembangkan model SIR dengan penambahan kontrol. Kontrol pada model tersebut merupakan vaksinasi yang diberikan kepada subpopulasi infected, sehingga subpopulasi recovery mengalami kenaikan, kerena jumlah subpopulasi infected menurun.
References
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