Home > Journals > SCIREA Journal of Mathematics > Archive > Paper Information

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    9 Downloads     509 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. Vol. 6 , No. 6 , 2021 , pp. 87 - 100 . https://doi.org/10.54647/mathematics11303

References

[ 1 ] Affandi, P., Faisal 2018. Optimal control mathemathical SIR model of malaria spread in South Kalimantan, Journal of Physics: Conference Series 1116 (2), 02200.
[ 2 ] Affandi, P., 2020. Optimal control for dysentery epidemic model with treatment, International Journal of Scientific and Technology Research, 2020, 9(3).
[ 3 ] Affandi, P., Salam N 2021. Optimal Control of diarrhea Disease model with Vaccination and Treatment, Journal of Physics: Conference Series, 2021, 1807(1), 012032.
[ 4 ] Affandi P., Faisal. (2017). Optimal Control Model of Malaria Spread in South Kalimantan, Halaman 54-61.
[ 5 ] Affandi, P., 2017. Kendali Optimal pada Penentuan Interval Waktu dan Dosis Optimal pada Penyakit Malaria. https://publikasi ilmiah.ums.ac.id /handle/11617/10150.
[ 6 ] Affandi, P., 2019. Kendali Optimal Pada Model Penyakit Scabies. Konferensi Pendidikan Nasional 1 (1), 187-196.
[ 7 ] Kermack, W. O. and McKendrick, A. G., 1927. A Contribution to the Mathematical Theory of Epidemics, Royal Society.
[ 8 ] Bellomo, N.& L. Preziosi. 1995. Modelling Mathematical Method and Scientific Computation . CRC press. Florida.
[ 9 ] Lotfi Tadj, A.M Sarhan, Awad El-Gohary Optimal control of an inventory system with ameliorating and deteriorating items. Applied Sciences 243-255.
[ 10 ] Affandi, P., 2015, Optimal Inventory Control Stochastic With Production Deteriorating. IOP Conference Series: Materials Science and Enginering, 300 (2018) 012019 doi:10.1088/1757-899X/300/1/012019.
[ 11 ] Esteva, L., dan Vargas, C., 1998, Analysis of a Dengue Disease Transmission Model, Mathematical Biosciences, 150, 131-151.
[ 12 ] Sheng-Qun Deng 1., Xian Yang 1., 2020. A Review on Dengue Vaccine Development, National Library of Medicine.
[ 13 ] Puntani Pongsumpun1., 2019. Optimal control of the dengue dynamical transmission with vertical transmission. Advances in Diffrence Equations. A Springer open Journal.
[ 14 ] Laporan Dinas Kesehatan Kota Banjarmasin. Kasus DBD Di Kota Banjarmasin Tahun 2013-2016. Banjarmasin: Dinas Kesehatan Kota Banjarmasin Provinsi Kalimantan Selatan; 2016.
[ 15 ] Data Profil Kesehatan Propinsi Kalimantan tahun 2019.
[ 16 ] Katrina Pareallo., W. Sanusi, 2018. Kontrol optimal pada model epidemik SIR penyakit demam berdarah Indonesian Journal of Fundamental Sciences Vol.4, No.2, October 2018.
[ 17 ] Rodrigues, H.S., Monteiro, M.T.T., dan Torres, D.F.M., 2010, Insecticide Control in a Dengue Epidemics Model, Numerical Analysis and Applied Mathematics, 1281, 979-982.
[ 18 ] Dumont, Y., dan Chiroleu, F.,, 2010, Vector Control for the Chikungunya
[ 19 ] Disease, Mathematical Biosciences and Engineering, 7, 313-345.
[ 20 ] Farlow, S.J.1994. An Introduction to Differential Equation and Their Applications. Dover Publications, United States of America.
[ 21 ] Braun, M. 1992. Differential Equation and Their Application-Fourth Edition. John Wiley & Sons. New York.
[ 22 ] Perko, L. 1991.Differential Equation an Dynamical systems. Text in Apllied Mathematic vol 7. Springer-Verlag, New York, USA.
[ 23 ] Gantmacher, F.R. 1959. The Theory of Matrices. Chelsea Publishing Company. New York.
[ 24 ] Burghes, D.N. 1980. Introduction to Control Theory Including Optimal Control. Springer-Verlag. New York.
[ 25 ] Muhammad Altaf Khan, Fatmawati, 2021, Dengue infection modeling and its optimal control analysis in East Java, Indonesia Research Article Volume 7, Issue 1.

Submit A Manuscript
Review Manuscripts
Join As An Editorial Member
Most Views
Article
by Sergey M. Afonin
3057 Downloads 59576 Views
Article
by Jian-Qiang Wang, Chen-Xi Wang, Jian-Guo Wang, HRSCNP Research Team
15 Downloads 45052 Views
Article
by Syed Adil Hussain, Taha Hasan Associate Professor
2418 Downloads 24075 Views
Article
by Omprakash Sikhwal, Yashwant Vyas
2486 Downloads 20228 Views
Article
by Munmun Nath, Bijan Nath, Santanu Roy
2364 Downloads 19950 Views
Upcoming Conferences