Stability Analysis and Numerical Simulation of a Zika Virus Disease Model with Controls

Authors

  • Emmanuel C. Duru Department of Mathematics, Michael Okpara University of Agriculture, Umudike, Nigeria Author
  • Michael C. Anyanwu Department of Mathematics, Michael Okpara University of Agriculture, Umudike, Nigeria Author
  • Godwin C. E. Mbah Department of Mathematics, University of Nigeria, Nsukka, Nigeria Author

DOI:

https://doi.org/10.64229/9qn9ef62

Keywords:

Bifurcation, Center-manifold theorem, Endemic equilibrium, Zika virus

Abstract

Zika virus disease is a flavivirus disease transmitted among humans through the bites of infectious Aedes aegypti mosquitoes, through blood transfusions, during sexual intercourse, and during pregnancy. A novel model that incorporates treatment and utilization of Sterile-insect technique as control measures is proposed. This model incorporates the occurrence of asymptomatic cases in the midst of the controls unlike in previous studied considered. Stability analyses show that the zika-free equilibrium point is locally and globally asymptotically stable when the zika control number, , is less than one, and unstable otherwise. A bifurcation analysis was conducted, leveraging the center manifold theorem to ascertain the conditions for stability of the endemic equilibrium point. The effects of the controls considered are demonstrated through the presentation of plots. The findings indicated that the combination of both measures yielded superior outcomes in comparison to the utilization of the controls individually. MATLAB was used for the simulation and plots.

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Published

2026-02-09

Issue

Vol. 2 No. 1 (2026)

Section

Articles

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Copyright (c) 2026 Emmanuel C. Duru, Michael C. Anyanwu, Godwin C. E. Mbah (Author)

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This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Duru, E. C. ., Anyanwu, M. C. ., & Mbah, G. C. E. . (2026). Stability Analysis and Numerical Simulation of a Zika Virus Disease Model with Controls. Global Integrated Mathematics, 2(1), 41-57. https://doi.org/10.64229/9qn9ef62