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

Authors

  • Ichwal Afrizan Shiddiqie Departement of Mathematics, Universitas Islam Negeri Sunan Gunung Djati Bandung, Indonesia
  • Mia Siti Khumaeroh Departement of Mathematics, Universitas Islam Negeri Sunan Gunung Djati Bandung, Indonesia
  • Diny Zulkarnaen Departement of Mathematics, Universitas Islam Negeri Sunan Gunung Djati Bandung, Indonesia
  • Arista Fitri Diana Institut Teknologi Statistika dan Bisnis Muhammadiyah Semarang, Indonesia

DOI:

https://doi.org/10.15575/kubik.v9i2.30948

Keywords:

Basic reproduction number, vector control, Lyapunov, sensitivity analysis, Zika virus

Abstract

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 SEIHRâ€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 Routhâ€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 diseaseâ€free conditions is globally asymptotic stable when R0 < 1, meanwhile the equilibrium point for endemic conditions is 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 (Ï„ ), and mosquito control rate (ω), reveals that c and ω exert a more significant effect on changes in R0 compared to Ï„ . Therefore, minimizing contact with infected individuals or implementing vector control is more effective than isolating or hospitalizing infected patients.

Author Biography

Mia Siti Khumaeroh, Departement of Mathematics, Universitas Islam Negeri Sunan Gunung Djati Bandung

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Published

2024-09-21

How to Cite

Shiddiqie, I. A., Khumaeroh, M. S., Zulkarnaen, D., & Diana, A. F. (2024). SEIHR-SEI Mathematical Model of Zika Virus Transmission with Vector Control. KUBIK: Jurnal Publikasi Ilmiah Matematika, 9(2), 145–160. https://doi.org/10.15575/kubik.v9i2.30948

Issue

Vol. 9 No. 2 (2024): KUBIK: Jurnal Publikasi Ilmiah Matematika

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