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<p>Malaria remains one of deadly diseases affecting many parts of the world. It is transmitted through the bites of the female Anopheles mosquito amongst humans. Many researches have suggested using treatment of humans and vector control by insecticide spray or treated bed-nets as control measures. These methods are good but studies have shown that there is an increase in resistance to treatment by malaria parasites as well as resistance to insecticides by mosquitoes. This underscores the need for continuous study of the disease for better measures to control it. A system of nonlinear ordinary differential equations is used to study and analyze the disease in this work. Three control measures; vaccination, treatment and use of sterile-insect technology are considered in this work. The model is shown to be well-posed mathematically and epidemiologically. The disease-free equilibrium point is shown to be locally and globally asymptotically stable when the basic reproduction number, <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\:{R}_{0}\)</EquationSource> </InlineEquation> is less than one, and unstable otherwise. The global stability of the disease-free equilibrium point is a confirmation that there exists a unique endemic equilibrium point in the system and the absence of backward bifurcation in the model. The model was fitted with real data from Nigeria. Sensitivity analysis is also performed on the basic reproduction number to show how key parameters of the system affect the endemicity of the disease. The work showed how treatment, vaccination and vector control by use of sterile insect technology effectively helped to control the spread of the disease. Plots are presented to show the dynamics of the disease. MATLAB and Maple were used in the simulation and mathematical analysis.</p>

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A Mathematical Model for Malaria with Human and Vector Controls in Nigeria

  • 期刊论文

  • 发表日期：

    2025年9月19日

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  • Emmanuel C. Duru,
  • G. C. E. Mbah,
  • M. C. Anyanwu

摘要

Malaria remains one of deadly diseases affecting many parts of the world. It is transmitted through the bites of the female Anopheles mosquito amongst humans. Many researches have suggested using treatment of humans and vector control by insecticide spray or treated bed-nets as control measures. These methods are good but studies have shown that there is an increase in resistance to treatment by malaria parasites as well as resistance to insecticides by mosquitoes. This underscores the need for continuous study of the disease for better measures to control it. A system of nonlinear ordinary differential equations is used to study and analyze the disease in this work. Three control measures; vaccination, treatment and use of sterile-insect technology are considered in this work. The model is shown to be well-posed mathematically and epidemiologically. The disease-free equilibrium point is shown to be locally and globally asymptotically stable when the basic reproduction number, \(\:{R}_{0}\) is less than one, and unstable otherwise. The global stability of the disease-free equilibrium point is a confirmation that there exists a unique endemic equilibrium point in the system and the absence of backward bifurcation in the model. The model was fitted with real data from Nigeria. Sensitivity analysis is also performed on the basic reproduction number to show how key parameters of the system affect the endemicity of the disease. The work showed how treatment, vaccination and vector control by use of sterile insect technology effectively helped to control the spread of the disease. Plots are presented to show the dynamics of the disease. MATLAB and Maple were used in the simulation and mathematical analysis.