<p>HIV is a severe infection that has been spreading throughout the human population as an epidemic for last few decades. Scrub typhus, on the other hand, is a major zoonotic disease in the northern regions of India. The health of individuals has been significantly affected by both HIV and scrub typhus infections. In this work, a mathematical model is developed to illustrate the dynamics of co-infection of HIV and scrub typhus. Here, we demonstrate that the solutions of the co-infection model maintain non-negativity and boundedness. The next-generation matrix approach is utilized to compute the basic reproduction number. The local and global stability analysis of the co-infection model at the DFE (disease-free equilibrium) state is thoroughly investigated. A bifurcation analysis is performed to identify the potential shifts in disease behavior due to parameter changes. Sensitivity analysis is performed to reveal the relative importance of parameters influencing the infection spread and outcomes. The numerical simulations are conducted to validate the analytical findings. The findings suggest that primary control measures, including the use of insect repellents and the administration of antibiotics, could play a crucial role in preventing scrub typhus and its co-infection. The critical range of parameters for the spread of HIV-scrub typhus co-infection with respect to mite biting rate and HIV contact rate has been respectively identified as 0.00084 <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40808_2024_2198_Article_IEq1.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">$\le$</EquationSource> <EquationSource Format="MATHML"><math> <mo>≤</mo> </math></EquationSource> </InlineEquation> <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40808_2024_2198_Article_IEq2.gif" Format="GIF" Height="18" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">$\beta _{l_{c}}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>β</mi> <msub> <mi>l</mi> <mi>c</mi> </msub> </msub> </math></EquationSource> </InlineEquation> <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40808_2024_2198_Article_IEq3.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">$\le$</EquationSource> <EquationSource Format="MATHML"><math> <mo>≤</mo> </math></EquationSource> </InlineEquation> 0.001 and 0.000076 <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40808_2024_2198_Article_IEq4.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">$\le$</EquationSource> <EquationSource Format="MATHML"><math> <mo>≤</mo> </math></EquationSource> </InlineEquation> <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40808_2024_2198_Article_IEq5.gif" Format="GIF" Height="18" Rendition="HTML" Resolution="72" Type="Linedraw" Width="24" /> </InlineMediaObject> <EquationSource Format="TEX">$\beta _{h_{c}}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>β</mi> <msub> <mi>h</mi> <mi>c</mi> </msub> </msub> </math></EquationSource> </InlineEquation> <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40808_2024_2198_Article_IEq6.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">$\le$</EquationSource> <EquationSource Format="MATHML"><math> <mo>≤</mo> </math></EquationSource> </InlineEquation> 0.0001. Similarly, the critical range of parameters for the spread of HIV-scrub typhus co-infection with respect to scrub typhus progression rate in humans and HIV contact rate has been respectively identified as 0.67 <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40808_2024_2198_Article_IEq7.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">$\le$</EquationSource> <EquationSource Format="MATHML"><math> <mo>≤</mo> </math></EquationSource> </InlineEquation> <InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40808_2024_2198_Article_IEq8.gif" Format="GIF" Height="13" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">$a_{l_{c}}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>a</mi> <msub> <mi>l</mi> <mi>c</mi> </msub> </msub> </math></EquationSource> </InlineEquation> <InlineEquation ID="IEq9"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40808_2024_2198_Article_IEq9.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">$\le$</EquationSource> <EquationSource Format="MATHML"><math> <mo>≤</mo> </math></EquationSource> </InlineEquation> 0.8 and 0.000125 <InlineEquation ID="IEq10"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40808_2024_2198_Article_IEq10.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">$\le$</EquationSource> <EquationSource Format="MATHML"><math> <mo>≤</mo> </math></EquationSource> </InlineEquation> <InlineEquation ID="IEq11"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40808_2024_2198_Article_IEq11.gif" Format="GIF" Height="18" Rendition="HTML" Resolution="72" Type="Linedraw" Width="24" /> </InlineMediaObject> <EquationSource Format="TEX">$\beta _{h_{c}}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>β</mi> <msub> <mi>h</mi> <mi>c</mi> </msub> </msub> </math></EquationSource> </InlineEquation> <InlineEquation ID="IEq12"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40808_2024_2198_Article_IEq12.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">$\le$</EquationSource> <EquationSource Format="MATHML"><math> <mo>≤</mo> </math></EquationSource> </InlineEquation> 0.00015. The outcomes can assist policymakers in developing targeted strategies to diminish the risks of HIV and scrub typhus co-infection.</p>

Mathematical model for the transmission dynamics of HIV-scrub typhus co-infection

期刊论文
发表日期：

2025年1月23日

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Ravi Pathak,
Tarun Kashyap,
Rakesh Kumar

摘要

HIV is a severe infection that has been spreading throughout the human population as an epidemic for last few decades. Scrub typhus, on the other hand, is a major zoonotic disease in the northern regions of India. The health of individuals has been significantly affected by both HIV and scrub typhus infections. In this work, a mathematical model is developed to illustrate the dynamics of co-infection of HIV and scrub typhus. Here, we demonstrate that the solutions of the co-infection model maintain non-negativity and boundedness. The next-generation matrix approach is utilized to compute the basic reproduction number. The local and global stability analysis of the co-infection model at the DFE (disease-free equilibrium) state is thoroughly investigated. A bifurcation analysis is performed to identify the potential shifts in disease behavior due to parameter changes. Sensitivity analysis is performed to reveal the relative importance of parameters influencing the infection spread and outcomes. The numerical simulations are conducted to validate the analytical findings. The findings suggest that primary control measures, including the use of insect repellents and the administration of antibiotics, could play a crucial role in preventing scrub typhus and its co-infection. The critical range of parameters for the spread of HIV-scrub typhus co-infection with respect to mite biting rate and HIV contact rate has been respectively identified as 0.00084 $\le$ $\leq$ $\beta _{l_{c}}$ $β_{l_{c}}$ $\le$ $\leq$ 0.001 and 0.000076 $\le$ $\leq$ $\beta _{h_{c}}$ $β_{h_{c}}$ $\le$ $\leq$ 0.0001. Similarly, the critical range of parameters for the spread of HIV-scrub typhus co-infection with respect to scrub typhus progression rate in humans and HIV contact rate has been respectively identified as 0.67 $\le$ $\leq$ $a_{l_{c}}$ $a_{l_{c}}$ $\le$ $\leq$ 0.8 and 0.000125 $\le$ $\leq$ $\beta _{h_{c}}$ $β_{h_{c}}$ $\le$ $\leq$ 0.00015. The outcomes can assist policymakers in developing targeted strategies to diminish the risks of HIV and scrub typhus co-infection.