<p>The desert locust (<i>Schistocerca gregaria</i>), a globally destructive pest, exhibits population dynamics shaped by environmental and climatic factors. This study introduces a non-autonomous compartmental model that integrates control strategies to explore the dynamics of biphasic locusts, focusing on interactions between seasonal rainfall and stage-specific interventions. The model incorporates a rainfall-driven carrying capacity, density-dependent phase transitions, and targeted controls across egg, hopper, band, and adult stages. Theoretical analyzes confirm the robustness of the model, showing that a locust-free equilibrium is locally and globally asymptotically stable when the control offspring number <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40808_2025_2430_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="52" /> </InlineMediaObject> <EquationSource Format="TEX">$\mathcal {N}_c < 1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi mathvariant="script">N</mi> <mi>c</mi> </msub> <mo><</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>, while non-trivial equilibria (swarm-free, solitarious-free or co-existence states) arise when <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40808_2025_2430_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="52" /> </InlineMediaObject> <EquationSource Format="TEX">$\mathcal {N}_c > 1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi mathvariant="script">N</mi> <mi>c</mi> </msub> <mo>></mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>. The global sensitivity analysis of the autonomous model, combined with numerical simulations, reveals how control strategies and initial conditions influence long-term dynamics. Simulations indicate that <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40808_2025_2430_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="81" /> </InlineMediaObject> <EquationSource Format="TEX">$20\%-40\%$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>20</mn> <mo>%</mo> <mo>-</mo> <mn>40</mn> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation> control efficacy can reduce outbreaks to recession levels, preventing plague-scale infestations. Unlike previous models, this holistic framework captures the entire life cycle, offering a powerful tool for integrated locust management. These insights equip policymakers with actionable strategies to mitigate locust impacts.</p>

Modeling desert locust dynamics with rainfall-driven phase transitions and stage-specific control

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发表日期：

2025年5月14日

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Dejen Ketema Mamo,
Mathew N. Kinyanjui,
Nourridine Siewe

摘要

The desert locust (Schistocerca gregaria), a globally destructive pest, exhibits population dynamics shaped by environmental and climatic factors. This study introduces a non-autonomous compartmental model that integrates control strategies to explore the dynamics of biphasic locusts, focusing on interactions between seasonal rainfall and stage-specific interventions. The model incorporates a rainfall-driven carrying capacity, density-dependent phase transitions, and targeted controls across egg, hopper, band, and adult stages. Theoretical analyzes confirm the robustness of the model, showing that a locust-free equilibrium is locally and globally asymptotically stable when the control offspring number $\mathcal {N}_c < 1$ $N_{c} < 1$ , while non-trivial equilibria (swarm-free, solitarious-free or co-existence states) arise when $\mathcal {N}_c > 1$ $N_{c} > 1$ . The global sensitivity analysis of the autonomous model, combined with numerical simulations, reveals how control strategies and initial conditions influence long-term dynamics. Simulations indicate that $20\%-40\%$ $20 % - 40 %$ control efficacy can reduce outbreaks to recession levels, preventing plague-scale infestations. Unlike previous models, this holistic framework captures the entire life cycle, offering a powerful tool for integrated locust management. These insights equip policymakers with actionable strategies to mitigate locust impacts.