Open AccessKendali Optimal Pada Model Penyebaran Penyakit Difteri dengan Tingkat Imunitas Alami Pada Individu Terpapar
Author(s) -
Nailul Izzati,
Anak Agung Sagung P Putri Risa Andriani
Publication year - 2021
Publication title -
jurnal ilmiah matematika dan terapan/jurnal ilmiah matematika dan terapan
Language(s) - English
Resource type - Journals
eISSN - 2540-766X
pISSN - 1829-8133
DOI - 10.22487/2540766x.2021.v18.i1.15339
Subject(s) - outbreak , population , diphtheria , statistics , biology , mathematics , virology , medicine , environmental health , vaccination
Indonesia is one of the countries where has not been free from diphtheria outbreak. During 2017-2019, there were 2870 diphtheria cases with 96 deaths. With the mortality rate 5-20%, makes studies regarding diphtheria prevention and management strategies become important to do. In this study, a SEIQR mathematical model was constructed by considering the factor of natural immunity rate in exposed individuals. Then, by considering the complete basic immunization coverage and the proportion of the number of individuals with natural immunity rate as control variables, the optimal control problem is formulated to minimize the number of infected poopulation. Optimal control using DOTcvpSB toolbox obtained that the number of exposed population in the model decreased from 4.9% to 0.75%, and the number of infected population decreased from 3.1% to 0.32%.