<p>This study delves into the dynamics of the Zika virus using a reaction–advection–diffusion model that incorporates the periodic release of Wolbachia-harboring male mosquitoes, vector-bias, and seasonal influences. We define the basic reproduction number <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13662_2025_3969_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <msub> <mi>R</mi> <mn>0</mn> </msub> </math></EquationSource> <EquationSource Format="TEX">$R_{0}$</EquationSource> </InlineEquation>. The threshold dynamics are analyzed to identify critical points that determine disease persistence or elimination. When <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13662_2025_3969_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="51" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <msub> <mi>R</mi> <mn>0</mn> </msub> <mo>&lt;</mo> <mn>1</mn> </math></EquationSource> <EquationSource Format="TEX">$R_{0}&lt;1$</EquationSource> </InlineEquation>, there exists a globally attractive disease-free <i>T</i>-periodic solution. If <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13662_2025_3969_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="51" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <msub> <mi>R</mi> <mn>0</mn> </msub> <mo>&gt;</mo> <mn>1</mn> </math></EquationSource> <EquationSource Format="TEX">$R_{0}&gt;1$</EquationSource> </InlineEquation>, then the disease persists uniformly across the population. Numerical simulations are employed to validate these theoretical insights and to demonstrate the effectiveness of the Wolbachia release strategy, vector-bias, and advection in controlling Zika transmission. These results indicate that the implementation of Wolbachia incompatible insect technique can effectively control the spread of Zika, failing to account for seasonality or vector-bias may lead to an underestimation of the risk of Zika spread, and increasing the advection rate can help reduce the risk of disease transmission.</p>

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Dynamical analysis of a reaction–advection–diffusion Zika model with Wolbachia incompatible insect technique and vector-bias

  • Liping Wang,
  • Xinyu Wang,
  • Peng Wu

摘要

This study delves into the dynamics of the Zika virus using a reaction–advection–diffusion model that incorporates the periodic release of Wolbachia-harboring male mosquitoes, vector-bias, and seasonal influences. We define the basic reproduction number R 0 $R_{0}$ . The threshold dynamics are analyzed to identify critical points that determine disease persistence or elimination. When R 0 < 1 $R_{0}<1$ , there exists a globally attractive disease-free T-periodic solution. If R 0 > 1 $R_{0}>1$ , then the disease persists uniformly across the population. Numerical simulations are employed to validate these theoretical insights and to demonstrate the effectiveness of the Wolbachia release strategy, vector-bias, and advection in controlling Zika transmission. These results indicate that the implementation of Wolbachia incompatible insect technique can effectively control the spread of Zika, failing to account for seasonality or vector-bias may lead to an underestimation of the risk of Zika spread, and increasing the advection rate can help reduce the risk of disease transmission.