Stability analysis and optimal control of mathematical epidemic model with medical treatment

Abdulloh Jaelani; Novi Dwi Yolanda Fitri

doi:10.1063/5.0042363

Stability analysis and optimal control of mathematical epidemic model with medical treatment

Abdulloh Jaelani
, Fatmawati
, Novi Dwi Yolanda Fitri

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Citation (Scopus)

Abstract

In this work, we analyze a mathematical epidemic model with vaccination. We assumed the vaccination has done on newborns and populations of susceptible individuals who have not vaccinated. We also study the model with medical treatment as a control variable. From the model without control, we show that the model has two equilibria, namely the disease-free equilibrium and endemic equilibrium. The local stability of the equilibrium and the existence of the endemic equilibrium depend on the basic reproduction number. Thus, the optimal control problem is solved by using Pontryagin's Maximum Principle. The simulation results show that the implementation of the cure treatment as a control variable can reduce the number of exposed and infectious by 99.99% in 20th year after the intervention.

Original language	English
Title of host publication	International Conference on Mathematics, Computational Sciences and Statistics 2020
Editors	Cicik Alfiniyah, Fatmawati, Windarto
Publisher	American Institute of Physics Inc.
ISBN (Electronic)	9780735440739
DOIs	https://doi.org/10.1063/5.0042363
Publication status	Published - 26 Feb 2021
Event	International Conference on Mathematics, Computational Sciences and Statistics 2020, ICoMCoS 2020 - Surabaya, Indonesia Duration: 29 Sept 2020 → …

Publication series

Name	AIP Conference Proceedings
Volume	2329
ISSN (Print)	0094-243X
ISSN (Electronic)	1551-7616

Conference

Conference	International Conference on Mathematics, Computational Sciences and Statistics 2020, ICoMCoS 2020
Country/Territory	Indonesia
City	Surabaya
Period	29/09/20 → …

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

SDG 3 Good Health and Well-being

Access to Document

10.1063/5.0042363

Cite this

Jaelani, A., Fatmawati, & Fitri, N. D. Y. (2021). Stability analysis and optimal control of mathematical epidemic model with medical treatment. In C. Alfiniyah, Fatmawati, & Windarto (Eds.), International Conference on Mathematics, Computational Sciences and Statistics 2020 Article 040001 (AIP Conference Proceedings; Vol. 2329). American Institute of Physics Inc.. https://doi.org/10.1063/5.0042363

@inproceedings{8694efdfb71d4f15962f3a2db3ff8d7b,

title = "Stability analysis and optimal control of mathematical epidemic model with medical treatment",

abstract = "In this work, we analyze a mathematical epidemic model with vaccination. We assumed the vaccination has done on newborns and populations of susceptible individuals who have not vaccinated. We also study the model with medical treatment as a control variable. From the model without control, we show that the model has two equilibria, namely the disease-free equilibrium and endemic equilibrium. The local stability of the equilibrium and the existence of the endemic equilibrium depend on the basic reproduction number. Thus, the optimal control problem is solved by using Pontryagin's Maximum Principle. The simulation results show that the implementation of the cure treatment as a control variable can reduce the number of exposed and infectious by 99.99\% in 20th year after the intervention.",

author = "Abdulloh Jaelani and Fatmawati and Fitri, \{Novi Dwi Yolanda\}",

note = "Publisher Copyright: {\textcopyright} 2021 American Institute of Physics Inc.. All rights reserved.; International Conference on Mathematics, Computational Sciences and Statistics 2020, ICoMCoS 2020 ; Conference date: 29-09-2020",

year = "2021",

month = feb,

day = "26",

doi = "10.1063/5.0042363",

language = "English",

series = "AIP Conference Proceedings",

publisher = "American Institute of Physics Inc.",

editor = "Cicik Alfiniyah and Fatmawati and Windarto",

booktitle = "International Conference on Mathematics, Computational Sciences and Statistics 2020",

}

Jaelani, A , Fatmawati & Fitri, NDY 2021, Stability analysis and optimal control of mathematical epidemic model with medical treatment. in C Alfiniyah, Fatmawati & Windarto (eds), International Conference on Mathematics, Computational Sciences and Statistics 2020., 040001, AIP Conference Proceedings, vol. 2329, American Institute of Physics Inc., International Conference on Mathematics, Computational Sciences and Statistics 2020, ICoMCoS 2020, Surabaya, Indonesia, 29/09/20. https://doi.org/10.1063/5.0042363

Stability analysis and optimal control of mathematical epidemic model with medical treatment. / Jaelani, Abdulloh ; Fatmawati; Fitri, Novi Dwi Yolanda.
International Conference on Mathematics, Computational Sciences and Statistics 2020. ed. / Cicik Alfiniyah; Fatmawati; Windarto. American Institute of Physics Inc., 2021. 040001 (AIP Conference Proceedings; Vol. 2329).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Stability analysis and optimal control of mathematical epidemic model with medical treatment

AU - Jaelani, Abdulloh

AU - Fatmawati,

AU - Fitri, Novi Dwi Yolanda

PY - 2021/2/26

Y1 - 2021/2/26

N2 - In this work, we analyze a mathematical epidemic model with vaccination. We assumed the vaccination has done on newborns and populations of susceptible individuals who have not vaccinated. We also study the model with medical treatment as a control variable. From the model without control, we show that the model has two equilibria, namely the disease-free equilibrium and endemic equilibrium. The local stability of the equilibrium and the existence of the endemic equilibrium depend on the basic reproduction number. Thus, the optimal control problem is solved by using Pontryagin's Maximum Principle. The simulation results show that the implementation of the cure treatment as a control variable can reduce the number of exposed and infectious by 99.99% in 20th year after the intervention.

AB - In this work, we analyze a mathematical epidemic model with vaccination. We assumed the vaccination has done on newborns and populations of susceptible individuals who have not vaccinated. We also study the model with medical treatment as a control variable. From the model without control, we show that the model has two equilibria, namely the disease-free equilibrium and endemic equilibrium. The local stability of the equilibrium and the existence of the endemic equilibrium depend on the basic reproduction number. Thus, the optimal control problem is solved by using Pontryagin's Maximum Principle. The simulation results show that the implementation of the cure treatment as a control variable can reduce the number of exposed and infectious by 99.99% in 20th year after the intervention.

UR - https://www.scopus.com/pages/publications/85102526375

U2 - 10.1063/5.0042363

DO - 10.1063/5.0042363

M3 - Conference contribution

AN - SCOPUS:85102526375

T3 - AIP Conference Proceedings

BT - International Conference on Mathematics, Computational Sciences and Statistics 2020

A2 - Alfiniyah, Cicik

A2 - Fatmawati, null

A2 - Windarto, null

PB - American Institute of Physics Inc.

T2 - International Conference on Mathematics, Computational Sciences and Statistics 2020, ICoMCoS 2020

Y2 - 29 September 2020

ER -

Stability analysis and optimal control of mathematical epidemic model with medical treatment

Abstract

Publication series

Conference

UN SDGs

Access to Document

Fingerprint

Cite this