MATHEMATICAL MODEL OF REPELLENT EFFECT IN DENGUE TRANSMISSION

Handayani, Dewi; Gunadi, Audri Utami; Rachmawati, Ria Nurlita

doi:10.30598/barekengvol18iss2pp1037-1052

Akses terbuka Jurnal SINTA 3

MATHEMATICAL MODEL OF REPELLENT EFFECT IN DENGUE TRANSMISSION

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

DOI: 10.30598/barekengvol18iss2pp1037-1052
ISSN: 2615-3017, 1978-7227
Terbit: 2024-05-25
Penerbit: PATTIMURA UNIVERSITY
Bahasa: eng
Lisensi: creativecommons.org/licenses/by-sa/4.0

Abstrak

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%.

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Bandung Institute of Technology
Riau University
Institut Teknologi Del
Institut Teknologi Telkom Purwokerto
University of Indonesia
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Rekan penulis	Organisasi	Artikel bersama
Roberd Saragih	Bandung Institute of Technology	7
Dewi Suhika	Bandung Institute of Technology	2
Mochamad Apri	Bandung Institute of Technology	2
Khozin Mu’tamar	Riau University	2
Janson Naiborhu	Bandung Institute of Technology	2
Tegar Arifin Prasetyo	Institut Teknologi Del	1
Aminatus Sa’adah	Institut Teknologi Telkom Purwokerto	1
Susilo Susilo	Afiliasi tidak diketahui	1
Gufron Amirullah	Afiliasi tidak diketahui	1
Rizkia Suciati	Afiliasi tidak diketahui	1
Sutarno	Afiliasi tidak diketahui	1
Rena Lestari	Afiliasi tidak diketahui	1
Annisa Puji Astuti	Afiliasi tidak diketahui	1
Deni Parlindungan	Afiliasi tidak diketahui	1
Nurhamidah Nurhamidah	Afiliasi tidak diketahui	1
Wardah Izzati Agustiningtias	Afiliasi tidak diketahui	1
Yosie Andriani	Afiliasi tidak diketahui	1
Hanna Hilyati Aulia	Afiliasi tidak diketahui	1
Nurliana Nurliana	Afiliasi tidak diketahui	1
Roma Wijaya	Afiliasi tidak diketahui	1
Dian Permata Sari	Afiliasi tidak diketahui	1
Arifuddin M. Arif	Afiliasi tidak diketahui	1
Yati Afiyanti	University of Indonesia	1

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Sumber metadata: OAI-PMH (metadata jurnal) https://ojs3.unpatti.ac.id/index.php/barekeng/oai, pertama di-harvest 5 Nov 2026, terakhir terlihat 8 Nov 2026.

Metadata asli (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>
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	<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>
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