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SEIHR-SEI Mathematical Model of Zika Virus Transmission with Vector Control

KUBIK: Jurnal Publikasi Ilmiah Matematika · Vol. 9 No. 2 (2024) · hlm. 145–160

DOI
10.15575/kubik.v9i2.30948
ISSN
2686-0341, 2338-0896
Terbit
2024-09-21
Penerbit
Department of Mathematics, Faculty of Science and Technology, UIN Sunan Gunung Djati Bandung
Bahasa
eng

Abstrak

Zika virus (ZIKV) is transmitted by Aedes Aegypti mosquito, which is recognized as a vector for viruses causing dengue fever and chikungunya. This study uses SEIHR‐SEI mathematical model to analyze the dynamics of Zika virus transmission. In this model, human population (host) is classified into five compartments: Susceptible Humans (Sh), Exposed Humans (Eh), Infected Humans (Ih), Hospitalized Humans (Hh) and Recovered Humans (Rh). Meanwhile, the mosquito population (vector) is divide into three compartments: Susceptible Vectors (Sv), Exposed Vectors (Ev), and Infected Vectors (Iv). Stability analysis is conducted using Routh‐Hurwitz criteria for assessing local stability and Lyapunov function for evaluating global stability. Moreover, Basic Reproduction Number (R0), which represents the average number of new infections produced by one infected individual in a susceptible population, is derived by using the Next Generation Matrix (NGM) method. The result shows that the equilibrium point for disease‐free conditions is globally asymptotic stable when R0 1. The simulation result using endemic data and sensitivity analysis of three parameters, including contact rate between susceptible humans and infected humans (c), hospitalization rate of infected individuals (τ ), and mosquito control rate (ω), reveals that c and ω exert a more significant effect on changes in R0 compared to τ. Therefore, minimizing contact with infected individuals or implementing vector control is more effective than isolating or hospitalizing infected patients.

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  • Sunan Gunung Djati State Islamic University Bandung
  • Padjadjaran University
  • Bandung Institute of Technology
  • Institut Teknologi Statistika dan Bisnis Muhammadiyah Semarang
  • Universitas Kalbis
  • Sumatera Institute of Technology
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Rekan penulisOrganisasiArtikel bersama
Esih SukaesihSunan Gunung Djati State Islamic University Bandung2
Siti JulaehaSunan Gunung Djati State Islamic University Bandung1
Ipah JunaediSunan Gunung Djati State Islamic University Bandung1
Feni Siti FathonahSunan Gunung Djati State Islamic University Bandung1
Riad Taufik LazwardiUniversitas Kalbis1
Fadilah IlahiSunan Gunung Djati State Islamic University Bandung1
Della Isna AmatillahSunan Gunung Djati State Islamic University Bandung1
Arief Fatchul HudaSunan Gunung Djati State Islamic University Bandung1
Fahrudin MuhtarullohSunan Gunung Djati State Islamic University Bandung1
Evi Wardah MardiahSunan Gunung Djati State Islamic University Bandung1
Asep Solih AwalluddinSunan Gunung Djati State Islamic University Bandung1
Hathifah Fidya AmaliaSunan Gunung Djati State Islamic University Bandung1
Inge WahyuniAfiliasi tidak diketahui1
Edy SoewonoBandung Institute of Technology1
Nuning NurainiBandung Institute of Technology1
Nursanti AnggrianiPadjadjaran University1
Asep Kuswandi SupriatnaPadjadjaran University1
Laura LauraPadjadjaran University1
Nela RizkaSumatera Institute of Technology1
Elvi Syukrina EriantoSunan Gunung Djati State Islamic University Bandung1
Najmudin NuwariSunan Gunung Djati State Islamic University Bandung1

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Sumber metadata: OAI-PMH (metadata jurnal) https://journal.uinsgd.ac.id/index.php/kubik/oai, pertama di-harvest 7 Nov 2026, terakhir terlihat 8 Nov 2026.
Metadata asli (oai_dc) 
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	<dc:title xml:lang="en-US">SEIHR-SEI Mathematical Model of Zika Virus Transmission with Vector Control</dc:title>
	<dc:creator>Shiddiqie, Ichwal Afrizan</dc:creator>
	<dc:creator>Khumaeroh, Mia Siti</dc:creator>
	<dc:creator>Zulkarnaen, Diny</dc:creator>
	<dc:creator>Diana, Arista Fitri</dc:creator>
	<dc:subject xml:lang="en-US">Basic reproduction number</dc:subject>
	<dc:subject xml:lang="en-US">vector control</dc:subject>
	<dc:subject xml:lang="en-US">Lyapunov</dc:subject>
	<dc:subject xml:lang="en-US">sensitivity analysis</dc:subject>
	<dc:subject xml:lang="en-US">Zika virus</dc:subject>
	<dc:description xml:lang="en-US">Zika virus (ZIKV) is transmitted by Aedes Aegypti mosquito, which is recognized as a vector for viruses causing dengue fever and chikungunya. This study uses SEIHR‐SEI mathematical model to analyze the dynamics of Zika virus transmission. In this model, human population (host) is classified into five compartments: Susceptible Humans (Sh), Exposed Humans (Eh), Infected Humans (Ih), Hospitalized Humans (Hh) and Recovered Humans (Rh). Meanwhile, the mosquito population (vector) is divide into three compartments: Susceptible Vectors (Sv), Exposed Vectors (Ev), and Infected Vectors (Iv). Stability analysis is conducted using Routh‐Hurwitz criteria for assessing local stability and Lyapunov function for evaluating global stability. Moreover, Basic Reproduction Number (R0), which represents the average number of new infections produced by one infected individual in a susceptible population, is derived by using the Next Generation Matrix (NGM) method. The result shows that the equilibrium point for disease‐free conditions is globally asymptotic stable when R0 &lt; 1, meanwhile the equilibrium point for endemic conditions is stable when R0 &gt; 1. The simulation result using endemic data and sensitivity analysis of three parameters, including contact rate between susceptible humans and infected humans (c), hospitalization rate of infected individuals (τ ), and mosquito control rate (ω), reveals that c and ω exert a more significant effect on changes in R0 compared to τ . Therefore, minimizing contact with infected individuals or implementing vector control is more effective than isolating or hospitalizing infected patients.</dc:description>
	<dc:publisher xml:lang="en-US">Department of Mathematics, Faculty of Science and Technology, UIN Sunan Gunung Djati Bandung</dc:publisher>
	<dc:date>2024-09-21</dc:date>
	<dc:type>info:eu-repo/semantics/article</dc:type>
	<dc:type>info:eu-repo/semantics/publishedVersion</dc:type>
	<dc:type xml:lang="en-US">Peer-reviewed Article</dc:type>
	<dc:format>application/pdf</dc:format>
	<dc:identifier>https://journal.uinsgd.ac.id/index.php/kubik/article/view/30948</dc:identifier>
	<dc:identifier>10.15575/kubik.v9i2.30948</dc:identifier>
	<dc:source xml:lang="en-US">KUBIK: Jurnal Publikasi Ilmiah Matematika; Vol. 9 No. 2 (2024): KUBIK: Jurnal Publikasi Ilmiah Matematika; 145-160</dc:source>
	<dc:source xml:lang="id-ID">KUBIK; Vol 9 No 2 (2024): KUBIK: Jurnal Publikasi Ilmiah Matematika; 145-160</dc:source>
	<dc:source>2686-0341</dc:source>
	<dc:source>2338-0896</dc:source>
	<dc:source>10.15575/kubik.v9i2</dc:source>
	<dc:language>eng</dc:language>
	<dc:relation>https://journal.uinsgd.ac.id/index.php/kubik/article/view/30948/11730</dc:relation>
	<dc:rights xml:lang="en-US">Copyright (c) 2024 Mia Siti Khumaeroh</dc:rights>
</oai_dc:dc>