Hopf Bifurcation Analysis of a Zika Virus Transmission Model with Two Time Delays

Year 2025, , 13 - 21, 28.03.2025

Müge Meyvacı

https://doi.org/10.33187/jmsm.1607113

Abstract

This study focuses on a mathematical model of Zika virus transmission that incorporates multiple time delays. The inclusion of time delays in the model takes into account the incubation period in humans and the latency of disease transmission from mosquitoes. The qualitative behavior of the model was examined in four different conditions by analyzing the characteristic equation corresponding to the endemic equilibrium point. Furthermore, the two distinct time lags were selected as the bifurcation parameter, while the existence of a Hopf bifurcation at the endemic equilibrium point for threshold parameters was confirmed. Subsequently, numerical simulations were used to validate the theoretical analysis for each case using MATLAB.

Keywords

Bifurcation, Hopf bifurcation, Stability

Ethical Statement

It is declared that during the preparation process of this study, scientific and ethical principles were followed and all the studies benefited from are stated in the bibliography.

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