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<p>This research develops a human-vector interaction model for malaria transmission, categorized by susceptible, infectious, and recovered (SIR) states, and innovatively augmented to incorporate spatial dynamics through the addition of a diffusion term for each class. This modification allows the model to account for the disease’s spread due to individual mobility. The study conducted a thorough qualitative and quantitative analysis of the model, revealing a disease-free equilibrium that is stable in the absence of infected immigrant influx, provided the basic reproductive number (<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40808_2025_2315_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>) falls below unity. Introduction of infected immigrants shifts the model to only exhibit endemic equilibrium states. Vaccination coverage scenarios illustrated that a malaria-free community could be realized without the influx of infected immigrants, especially with expanded vaccination among children. Additionally, the research identified that an integrated strategy combining vaccination, the use of personal protective equipment, and treatment represents the optimal approach to control malaria incidence. This strategy is most effective with the complete halt of infected human migration, underlining the model’s novel consideration of spatial diffusion in understanding and combating malaria transmission.</p>

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Analyzing spatial diffusion and vaccination strategies in malaria epidemics: a numerical approach

  • 期刊论文

  • 发表日期：

    2025年3月6日

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  • Rahat Zarin,
  • Usa Wannasingha Humphries

摘要

This research develops a human-vector interaction model for malaria transmission, categorized by susceptible, infectious, and recovered (SIR) states, and innovatively augmented to incorporate spatial dynamics through the addition of a diffusion term for each class. This modification allows the model to account for the disease’s spread due to individual mobility. The study conducted a thorough qualitative and quantitative analysis of the model, revealing a disease-free equilibrium that is stable in the absence of infected immigrant influx, provided the basic reproductive number ( \(R_0\) R 0 ) falls below unity. Introduction of infected immigrants shifts the model to only exhibit endemic equilibrium states. Vaccination coverage scenarios illustrated that a malaria-free community could be realized without the influx of infected immigrants, especially with expanded vaccination among children. Additionally, the research identified that an integrated strategy combining vaccination, the use of personal protective equipment, and treatment represents the optimal approach to control malaria incidence. This strategy is most effective with the complete halt of infected human migration, underlining the model’s novel consideration of spatial diffusion in understanding and combating malaria transmission.