<p>This study presents a mathematical model incorporating the effects of memory on the spread of Q fever, considering humans, animals, and environmental contamination of <i>Coxiella burnetii</i>. The model is formulated using a system of fractional-order differential equations with the Caputo fractional derivative to capture the long-term impact of past infections and environmental contamination. A mathematical analysis is performed, including positivity and boundedness of solutions, ensuring biological feasibility. The existence and uniqueness of solutions are established to confirm the model’s well-posedness. Stability analysis is conducted using Hyers–Ulam stability analysis, which guarantees that small perturbations in initial conditions do not lead to significant deviations in the system’s behavior. Sensitivity analysis is carried out to determine the most influential parameters affecting disease transmission, and a sensitivity heat map analysis is used to visualize their impact. From the sensitivity heat map analysis, it is noticed that the model parameters are more sensitive to the susceptible humans, <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40808_2025_2354_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">\(S_{h}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>S</mi> <mi>h</mi> </msub> </math></EquationSource> </InlineEquation>; recovered humans, <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40808_2025_2354_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="23" /> </InlineMediaObject> <EquationSource Format="TEX">\(R_{h}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>R</mi> <mi>h</mi> </msub> </math></EquationSource> </InlineEquation>; susceptible cattle, <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40808_2025_2354_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\(S_c\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>S</mi> <mi>c</mi> </msub> </math></EquationSource> </InlineEquation>; recovered cattle, <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40808_2025_2354_Article_IEq4.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">\(R_c\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>R</mi> <mi>c</mi> </msub> </math></EquationSource> </InlineEquation>; and the bacteria in the environment. Numerical simulations further demonstrate the role of memory in prolonging disease persistence, highlighting that ignoring historical effects may underestimate the long-term risks of Q fever outbreaks with consideration of human, animal, and environmental contamination.</p>

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Modeling the effect of memory on the spread of Query fever considering humans, animals and the environment

  • Joshua Kiddy Kwasi Asamoah,
  • Isaac K. Adu,
  • Fredrick A. Wireko,
  • Stephen B. Lassong,
  • Fatmawati Fatmawati

摘要

This study presents a mathematical model incorporating the effects of memory on the spread of Q fever, considering humans, animals, and environmental contamination of Coxiella burnetii. The model is formulated using a system of fractional-order differential equations with the Caputo fractional derivative to capture the long-term impact of past infections and environmental contamination. A mathematical analysis is performed, including positivity and boundedness of solutions, ensuring biological feasibility. The existence and uniqueness of solutions are established to confirm the model’s well-posedness. Stability analysis is conducted using Hyers–Ulam stability analysis, which guarantees that small perturbations in initial conditions do not lead to significant deviations in the system’s behavior. Sensitivity analysis is carried out to determine the most influential parameters affecting disease transmission, and a sensitivity heat map analysis is used to visualize their impact. From the sensitivity heat map analysis, it is noticed that the model parameters are more sensitive to the susceptible humans, \(S_{h}\) S h ; recovered humans, \(R_{h}\) R h ; susceptible cattle, \(S_c\) S c ; recovered cattle, \(R_c\) R c ; and the bacteria in the environment. Numerical simulations further demonstrate the role of memory in prolonging disease persistence, highlighting that ignoring historical effects may underestimate the long-term risks of Q fever outbreaks with consideration of human, animal, and environmental contamination.