<p>Rabies poses a significant threat to human health. To address the effects of heterogeneous behaviors on rabies transmission, we propose a nonlocal diffusive model in heterogeneous environment. By means of semigroup theory and uniform persistence theory, we analyze the well-posedness of solution and derive the basic reproduction number <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13662_2025_3926_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>, identified as the spectral radius of the next generation operator <i>P</i>. Our findings indicate the disease-free equilibrium is globally asymptotically stable when <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13662_2025_3926_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><</mo> <mn>1</mn> </math></EquationSource> <EquationSource Format="TEX">$R_{0}<1$</EquationSource> </InlineEquation>, whereas rabies is uniformly persistent when <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13662_2025_3926_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>></mo> <mn>1</mn> </math></EquationSource> <EquationSource Format="TEX">$R_{0}>1$</EquationSource> </InlineEquation>. Numerically, the theoretical results are verified. Moreover, we integrate data to explore the influence of various parameters on rabies transmission in the Philippines. The results suggest that euthanasia of stray dogs and vaccination of owned dogs reduce the risk of rabies outbreaks and highlight that ignoring spatial heterogeneity and nonlocal dispersal may lead to an underestimation of rabies risk. The study provides a foundation for control strategies, emphasizing regional variations and dog activity patterns.</p>

Spatial and temporal dynamics of rabies with nonlocal dispersal in a heterogeneous environment: insights for control strategies in the Philippines

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2025年3月19日

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SongYao Ren,
HongTao Zhang,
Ye Feng,
Li Li,
Jeffrey Lopez Cruz,
Sheng Sun

摘要

Rabies poses a significant threat to human health. To address the effects of heterogeneous behaviors on rabies transmission, we propose a nonlocal diffusive model in heterogeneous environment. By means of semigroup theory and uniform persistence theory, we analyze the well-posedness of solution and derive the basic reproduction number $R_{0}$ $R_{0}$ , identified as the spectral radius of the next generation operator P. Our findings indicate the disease-free equilibrium is globally asymptotically stable when $R_{0} < 1$ $R_{0}<1$ , whereas rabies is uniformly persistent when $R_{0} > 1$ $R_{0}>1$ . Numerically, the theoretical results are verified. Moreover, we integrate data to explore the influence of various parameters on rabies transmission in the Philippines. The results suggest that euthanasia of stray dogs and vaccination of owned dogs reduce the risk of rabies outbreaks and highlight that ignoring spatial heterogeneity and nonlocal dispersal may lead to an underestimation of rabies risk. The study provides a foundation for control strategies, emphasizing regional variations and dog activity patterns.