<p>Malaria continues to be a critical global health issue due to its profound impact on human development. This study explores the dynamics of malaria transmission within a population exhibiting multiple human susceptibilities, which arise from behavioral, locational, and occupational factors. We have formulated a nonlinear, time-dependent differential equation model to capture these dynamics. The model distinguishes between low- and high-risk susceptible human populations, offering a detailed analysis of malaria transmission patterns. We calculated the basic reproduction number <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40435_2024_1522_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>, along with the disease-free equilibrium (DFE) and endemic equilibrium (EE) points. The DFE is locally asymptotically stable when <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40435_2024_1522_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="51" /> </InlineMediaObject> <EquationSource Format="TEX">$R_{0}<1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>R</mi> <mn>0</mn> </msub> <mo><</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>, while the EE is globally asymptotically stable when <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40435_2024_1522_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="51" /> </InlineMediaObject> <EquationSource Format="TEX">$R_{0}>1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>R</mi> <mn>0</mn> </msub> <mo>></mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>. Additionally, the model exhibits a backward bifurcation. Moreover, we have graphically illustrated the impact of multiple human susceptibilities. These effects become more evident over time: as the proportion of highly susceptible individuals within the population increases, the overall transmission rate rises accordingly. Furthermore, the mosquito-human contact rate and the mosquito death rate have exhibited effects consistent with our expectations.</p>

Mathematical analysis of the transmission dynamics for malaria in individuals with varying levels of risk

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2025年1月25日

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Gekonga Wanchoke Chacha,
Sarinah Banu Mohamed Siddik,
Fatmawati

摘要

Malaria continues to be a critical global health issue due to its profound impact on human development. This study explores the dynamics of malaria transmission within a population exhibiting multiple human susceptibilities, which arise from behavioral, locational, and occupational factors. We have formulated a nonlinear, time-dependent differential equation model to capture these dynamics. The model distinguishes between low- and high-risk susceptible human populations, offering a detailed analysis of malaria transmission patterns. We calculated the basic reproduction number $R_{0}$ $R_{0}$ , along with the disease-free equilibrium (DFE) and endemic equilibrium (EE) points. The DFE is locally asymptotically stable when $R_{0}<1$ $R_{0} < 1$ , while the EE is globally asymptotically stable when $R_{0}>1$ $R_{0} > 1$ . Additionally, the model exhibits a backward bifurcation. Moreover, we have graphically illustrated the impact of multiple human susceptibilities. These effects become more evident over time: as the proportion of highly susceptible individuals within the population increases, the overall transmission rate rises accordingly. Furthermore, the mosquito-human contact rate and the mosquito death rate have exhibited effects consistent with our expectations.