<p>Malaria remains a significant global health challenge. In this study, we focus on the strategy of releasing Wolbachia-carrying male mosquitoes to control the spread of malaria. Considering the impact of vector-bias and temperature on malaria transmission, we establish a reaction–diffusion periodic-delay malaria model incorporating Wolbachia release strategy and vector-bias. Then, the basic reproduction number <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="33_2025_2600_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\(R_0\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>R</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation> is defined. The dynamic behavior of the model is analyzed in depth. A globally attractive disease-free <i>T</i>-periodic solution exists when <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="33_2025_2600_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="51" /> </InlineMediaObject> <EquationSource Format="TEX">\(R_ 0&lt;1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>R</mi> <mn>0</mn> </msub> <mo>&lt;</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>. Conversely, if <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="33_2025_2600_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="51" /> </InlineMediaObject> <EquationSource Format="TEX">\(R_ 0&gt;1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>R</mi> <mn>0</mn> </msub> <mo>&gt;</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>, then the disease exhibits uniform persistence. Furthermore, when all coefficients are constant and the vector-bias is disregarded, we demonstrate that the positive constant steady state is globally attractive, provided that <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="33_2025_2600_Article_IEq4.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="51" /> </InlineMediaObject> <EquationSource Format="TEX">\(R_0&gt;1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>R</mi> <mn>0</mn> </msub> <mo>&gt;</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>. Finally, numerical simulations are conducted to validate the theoretical results and further illustrate the effectiveness of the Wolbachia release strategy and vector-bias. These results suggest that the release of Wolbachia-carrying male mosquitoes can effectively reduce the transmission potential of malaria, and disregarding vector-bias can lead to an underestimation of the risk of malaria spread.</p>

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Threshold dynamics of a periodic-delay reaction–diffusion malaria model with Wolbachia incompatible insect technique and vector-bias

  • Liping Wang,
  • Wei Zhou,
  • Peng Wu

摘要

Malaria remains a significant global health challenge. In this study, we focus on the strategy of releasing Wolbachia-carrying male mosquitoes to control the spread of malaria. Considering the impact of vector-bias and temperature on malaria transmission, we establish a reaction–diffusion periodic-delay malaria model incorporating Wolbachia release strategy and vector-bias. Then, the basic reproduction number \(R_0\) R 0 is defined. The dynamic behavior of the model is analyzed in depth. A globally attractive disease-free T-periodic solution exists when \(R_ 0<1\) R 0 < 1 . Conversely, if \(R_ 0>1\) R 0 > 1 , then the disease exhibits uniform persistence. Furthermore, when all coefficients are constant and the vector-bias is disregarded, we demonstrate that the positive constant steady state is globally attractive, provided that \(R_0>1\) R 0 > 1 . Finally, numerical simulations are conducted to validate the theoretical results and further illustrate the effectiveness of the Wolbachia release strategy and vector-bias. These results suggest that the release of Wolbachia-carrying male mosquitoes can effectively reduce the transmission potential of malaria, and disregarding vector-bias can lead to an underestimation of the risk of malaria spread.