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MATHEMATICAL MODEL OF REPELLENT EFFECT IN DENGUE TRANSMISSION

BAREKENG: Jurnal Ilmu Matematika dan Terapan · Vol. 18 No. 2 (2024) · pp. 1037–1052

DOI
10.30598/barekengvol18iss2pp1037-1052
ISSN
2615-3017, 1978-7227
Published
2024-05-25
Publisher
PATTIMURA UNIVERSITY
Language
eng
License
creativecommons.org/licenses/by-sa/4.0

Abstract

Dengue is a disease caused by the dengue virus, transmitted through the bite of an infected female Aedes aegypti. Dengue virus is a member of the genus Flavivirus, family Flaviviridae. Indonesia is one of the countries with the most dengue cases in Southeast Asia. Therefore, dengue transmission must be controlled to reduce the increase in dengue cases. One of the controls is by using repellents. Repellent is one of the human protection strategies to avoid mosquito bites used by spraying or smearing. This study models dengue transmission by reviewing the effect and control of repellent. A mathematical model of repellent effect and control in dengue transmission uses a SIR compartment model. The SIR model is modified by involving mosquitoes and the human population. Repellent is used in both susceptible humans, infected humans, and recovered humans. Numerical and analytical simulations are conducted to analyze the behavior of each compartment of the mosquito and human populations in dengue transmission. Analytical results show that the factors affecting the spread of infection are the transmission rate of the dengue virus and the loss of human-repellent protection. The transmission rate of dengue virus in the interval increases the infected human by 2.73%, while the rate of loss of human repellent protection in the interval increases the infected human by 0.03%. Optimal control is used to minimize the number of infected humans who do not use repellent. The results of numerical simulations on the optimal control problem show that an increase in the proportion of healthy humans who have campaign effect and use repellent regularly in the range of 14.67% can reduce infected individuals by 0.647%.

Collaboration network of the authors

26 authors · 53 co-authorship links · 8 across different organisations

Hover or tap a name to highlight its co-authors. Double-click to open the author's page.

  • Bandung Institute of Technology
  • Riau University
  • Institut Teknologi Del
  • Institut Teknologi Telkom Purwokerto
  • University of Indonesia
  • Affiliation unknown
  • Different organisations
  • Same organisation
  • Affiliation unknown
  • Thicker line = more joint articles · bigger circle = more articles
Show as table
Co-authorOrganisationJoint articles
Roberd SaragihBandung Institute of Technology7
Dewi SuhikaBandung Institute of Technology2
Mochamad ApriBandung Institute of Technology2
Khozin Mu’tamarRiau University2
Janson NaiborhuBandung Institute of Technology2
Tegar Arifin PrasetyoInstitut Teknologi Del1
Aminatus Sa’adahInstitut Teknologi Telkom Purwokerto1
Susilo SusiloAffiliation unknown1
Gufron AmirullahAffiliation unknown1
Rizkia SuciatiAffiliation unknown1
SutarnoAffiliation unknown1
Rena LestariAffiliation unknown1
Annisa Puji AstutiAffiliation unknown1
Deni ParlindunganAffiliation unknown1
Nurhamidah NurhamidahAffiliation unknown1
Wardah Izzati AgustiningtiasAffiliation unknown1
Yosie AndrianiAffiliation unknown1
Hanna Hilyati AuliaAffiliation unknown1
Nurliana NurlianaAffiliation unknown1
Roma WijayaAffiliation unknown1
Dian Permata SariAffiliation unknown1
Arifuddin M. ArifAffiliation unknown1
Yati AfiyantiUniversity of Indonesia1

Affiliations come from OpenAlex; journal OAI-PMH metadata carries none. Authors without an OpenAlex ID are matched by name, which can merge or split people.

Metadata source: OAI-PMH (metadata jurnal) https://ojs3.unpatti.ac.id/index.php/barekeng/oai, first harvested 5 Nov 2026, last seen 8 Nov 2026.
Original metadata (oai_dc) 
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	<dc:title xml:lang="en-US">MATHEMATICAL MODEL OF REPELLENT EFFECT  IN DENGUE TRANSMISSION</dc:title>
	<dc:creator>Handayani, Dewi</dc:creator>
	<dc:creator>Gunadi, Audri Utami</dc:creator>
	<dc:creator>Rachmawati, Ria Nurlita</dc:creator>
	<dc:description xml:lang="en-US">Dengue is a disease caused by the dengue virus, transmitted through the bite of an infected female Aedes aegypti. Dengue virus is a member of the genus Flavivirus, family Flaviviridae. Indonesia is one of the countries with the most dengue cases in Southeast Asia. Therefore, dengue transmission must be controlled to reduce the increase in dengue cases. One of the controls is by using repellents. Repellent is one of the human protection strategies to avoid mosquito bites used by spraying or smearing. This study models dengue transmission by reviewing the effect and control of repellent. A mathematical model of repellent effect and control in dengue transmission uses a SIR compartment model. The SIR model is modified by involving mosquitoes and the human population. Repellent is used in both susceptible humans, infected humans, and recovered humans. Numerical and analytical simulations are conducted to analyze the behavior of each compartment of the mosquito and human populations in dengue transmission. Analytical results show that the factors affecting the spread of infection are the transmission rate of the dengue virus and the loss of human-repellent protection. The transmission rate of dengue virus in the interval &amp;nbsp;increases the infected human by 2.73%, while the rate of loss of human repellent protection in the interval &amp;nbsp;increases the infected human by 0.03%. Optimal control is used to minimize the number of infected humans who do not use repellent. The results of numerical simulations on the optimal control problem show that an increase in the proportion of healthy humans who have campaign effect and use repellent regularly in the range of 14.67% can reduce infected individuals by 0.647%.</dc:description>
	<dc:publisher xml:lang="en-US">PATTIMURA UNIVERSITY</dc:publisher>
	<dc:date>2024-05-25</dc:date>
	<dc:type>info:eu-repo/semantics/article</dc:type>
	<dc:type>info:eu-repo/semantics/publishedVersion</dc:type>
	<dc:format>application/pdf</dc:format>
	<dc:identifier>https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/11530</dc:identifier>
	<dc:identifier>10.30598/barekengvol18iss2pp1037-1052</dc:identifier>
	<dc:source xml:lang="en-US">BAREKENG: Jurnal Ilmu Matematika dan Terapan; Vol 18 No 2 (2024): BAREKENG: Journal of Mathematics and Its Application; 1037-1052</dc:source>
	<dc:source>2615-3017</dc:source>
	<dc:source>1978-7227</dc:source>
	<dc:source>10.30598/barekengvol18iss2year2024</dc:source>
	<dc:language>eng</dc:language>
	<dc:relation>https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/11530/7913</dc:relation>
	<dc:rights xml:lang="en-US">Copyright (c) 2024 Dewi Handayani, Audri Utami Gunadi, Ria Nurlita Rachmawati</dc:rights>
	<dc:rights xml:lang="en-US">http://creativecommons.org/licenses/by-sa/4.0</dc:rights>
</oai_dc:dc>