Background Malaria remains a major global public health problem, particularly affecting children under 5 years of age and pregnant women in regions where temperatures are favorable for transmission. Despite continuous control efforts, malaria continues to pose a significant health and economic burden, underscoring the need for rigorous quantitative assessment of intervention strategies. Methods A mathematical model was developed to analyse and evaluate the impact of three control measures: treatment of infected individuals, the use of LLINs, and indoor residual spraying (IRS). Due to the nature of the available data, the analysis was initiated with the model incorporating treatment. The effective reproduction number (<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12936_2025_5622_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="23" /> </InlineMediaObject> <EquationSource Format="TEX">$\mathcal {R}_e$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="script">R</mi> <mi>e</mi> </msub> </math></EquationSource> </InlineEquation>) was derived using the next-generation matrix approach to better understand the transmission dynamics. Furthermore, optimal control theory was applied to determine the most effective combination of control strategies. Results Numerical simulations of the model with treatment indicate that treating infected individuals is an effective approach to reducing malaria transmission. When the three control strategies were tested individually, treatment of infectious humans was found to be more effective than either spraying insecticides or using LLINs alone. In combined strategies, the use of LLINs together with treatment emerged as the most effective control approach. Notably, applying all three controls simultaneously did not yield a significant improvement compared to the combination of LLINs and treatment. Conclusions This study demonstrates that combining LLINs with the treatment of infected individuals provides the most cost-effective and efficient strategy for managing malaria transmission. These findings highlight the importance of integrating personal protection and prompt treatment in malaria control programs, particularly in high-transmission settings.

Optimal control analysis of malaria infection in children under 5 years and pregnant women under the influence of temperature

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2025年11月17日

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Paul Kuya Robert,
Jacob Ismail Irunde,
Adeline P. Mtunya

摘要

Background

Malaria remains a major global public health problem, particularly affecting children under 5 years of age and pregnant women in regions where temperatures are favorable for transmission. Despite continuous control efforts, malaria continues to pose a significant health and economic burden, underscoring the need for rigorous quantitative assessment of intervention strategies.

Methods

A mathematical model was developed to analyse and evaluate the impact of three control measures: treatment of infected individuals, the use of LLINs, and indoor residual spraying (IRS). Due to the nature of the available data, the analysis was initiated with the model incorporating treatment. The effective reproduction number ( $\mathcal {R}_e$ $R_{e}$ ) was derived using the next-generation matrix approach to better understand the transmission dynamics. Furthermore, optimal control theory was applied to determine the most effective combination of control strategies.

Results

Numerical simulations of the model with treatment indicate that treating infected individuals is an effective approach to reducing malaria transmission. When the three control strategies were tested individually, treatment of infectious humans was found to be more effective than either spraying insecticides or using LLINs alone. In combined strategies, the use of LLINs together with treatment emerged as the most effective control approach. Notably, applying all three controls simultaneously did not yield a significant improvement compared to the combination of LLINs and treatment.

Conclusions

This study demonstrates that combining LLINs with the treatment of infected individuals provides the most cost-effective and efficient strategy for managing malaria transmission. These findings highlight the importance of integrating personal protection and prompt treatment in malaria control programs, particularly in high-transmission settings.