Open AccessOptimal control of diphtheria epidemic model with prevention and treatment
Author(s) -
Nur Izzati,
Alessandro Andriani,
R. Robi’aqolbi
Publication year - 2020
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1663/1/012042
Subject(s) - diphtheria , optimal control , pontryagin's minimum principle , outbreak , immunization , maximum principle , routine immunization , epidemic model , epidemic disease , computer science , transmission (telecommunications) , mathematical optimization , mathematics , medicine , vaccination , virology , immunology , environmental health , telecommunications , antibody , population
Diphtheria is an infectious and deadly disease that spread through droplet transmission. Nevertheless, diphtheria can be prevented by immunization. One of many ways to gain immunity against the disease is by getting a vaccine. Diphtheria vaccine should be given at least three times in one’s lifetime and will be effective if given every ten years. However, the immunization program in developing countries, such as Indonesia, is not optimal yet, and that is one of the causes of the outbreak. Therefore, it is necessary to optimize the immunization program. In this study, we propose a mathematical model to describe the spreading of diphtheria disease. We formulate an optimal control problem on the SEIQR model to minimize the spreading through quarantine and optimize the proportion of vaccinated people through the immunization campaign. Here, we apply Pontryagin Minimum Principle to find the characteristics of the solution of optimal control problems analytically, and DOTcvpSB is used to solve the problem numerically. Based on the analytical and numerical solutions, the optimal control problem constructed could minimize the spread of the outbreak and its cost function.