Optimum Control in the model of blood fever disease with vaccines and treatment

Volume 6, Issue 6, December 2021     |     PP. 87-100      |     PDF (377 K)    |     Pub. Date: December 13, 2021
DOI: 10.54647/mathematics11303    91 Downloads     5847 Views  

Author(s)

PARDI AFFANDI, Faculty of Mathematics and Natural Science, Lambung Mangkurat University
M.Mahfudz S, Faculty of Mathematics and Natural Science, Lambung Mangkurat University
Oscar A.B, Faculty of Mathematics and Natural Science, Lambung Mangkurat University
A. Rahim, Kopertis Wilayah XI Kalimantan

Abstract
Dengue Hemorrhagic Fever (DHF) is a disease caused by an arbovirus that enters the human body through the Aedes aegypti or Aedes albopictus mosquito. Dengue Hemorrhagic Fever (DHF) is characterized by symptoms of dengue fever; headache; reddish skin that looks like measles; and muscle and joint pain. In some patients, dengue fever can turn into one of two life-threatening forms that lead to decreased immunity. Various ways have been done to prevent the cause of DHF, but the results have not been optimal. The problem of the spread of the dengue virus can also be modeled mathematically and through the stability of the equilibrium point, the dynamics or behavior of the model can be determined. DHF spread can be suppressed by giving control in the form of treatment. This type of treatment is given to infected individuals. This treatment can be controlled optimally by applying the Pontryagin maximum principle. Pontryagin's maximum principle is the optimal control solution in accordance with the objective of maximizing the performance index. The purpose of this study is to discuss a mathematical model for the transmission of the dengue virus in the human body. As an effort to inhibit dengue virus replication, treatment control is used in the model, starting from the formation of a model from determining assumptions, parameters so that the SIV-T model is obtained, determining stability analysis, and then involving optimal control with Pontryagin's minimum principle to carry out optimal control strategies for the fever disease model. Dengue Hemorrhagic Fever (DHF) was also simulated using the software. The results of this study are to explain how the model of the spread of the dengue virus in the human body is formed, obtained 2 equilibrium points, namely a disease-free equilibrium point, local asymptotically stable, and a local asymptotically stable endemic point. The optimal control strategy in the spread model of the dengue virus aims to maximize the number of healthy cells by administering a control in the form of treatment.

Keywords
DHF disease model, optimal control, Pontryagin's maximum principle.

Cite this paper
PARDI AFFANDI, M.Mahfudz S, Oscar A.B, A. Rahim, Optimum Control in the model of blood fever disease with vaccines and treatment , SCIREA Journal of Mathematics. Volume 6, Issue 6, December 2021 | PP. 87-100. 10.54647/mathematics11303

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