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<p>The global malaria pandemic poses a significant threat to public health and is causing concern for those living in tropical and subtropical regions. The scientific communities are searching for more effective strategies to control the condition as a result of its concerning implications. This study introduced and applied a nonlinear mathematical model to analyse the changing conditions of malaria disease transmission within a community. Our research represents a significant advancement in the field of disease prevention by incorporating two additional control factors into the mathematical model that is recommended. These factors are indicative of mosquito pesticide and treatment. Both equilibrium points and the reproduction number <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(R_{0}\)</EquationSource> </InlineEquation> are computed. When <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(R_{0} &lt; 1\)</EquationSource> </InlineEquation>, the disease-free equilibrium state is stable both locally and globally. If <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(R_{0} &gt; 1\)</EquationSource> </InlineEquation> and the Routh–Hurwitz requirements are met, the endemic equilibrium point arises and is stable. We illustrate the utility of the model by applying it to the real-world scenario of a disease outbreak in India. We use annual data gathered from 2001 to 2022 from India to optimize the proposed model. This allows for an evaluation of how well the proposed model reflects real-life conditions. The variance in the significance level <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(R_{0}\)</EquationSource> </InlineEquation> was measured using a sensitivity analysis of the LHS-PRCC. The optimum control problem was formulated using Pontryagin’s maximal approach. Using an iterative forward–backward Runge–Kutta fourth order approach, the optimality system was stimulated. The primary findings demonstrate that every control parameter effectively stops the spread of malaria.</p>

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Stability and an Optimal Study of the Malaria Epidemic in the Region of India: A Mathematical Analysis

  • 期刊论文

  • 发表日期：

    2025年9月18日

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  • P. Sireesha Devi,
  • G. Ranjith Kumar

摘要

The global malaria pandemic poses a significant threat to public health and is causing concern for those living in tropical and subtropical regions. The scientific communities are searching for more effective strategies to control the condition as a result of its concerning implications. This study introduced and applied a nonlinear mathematical model to analyse the changing conditions of malaria disease transmission within a community. Our research represents a significant advancement in the field of disease prevention by incorporating two additional control factors into the mathematical model that is recommended. These factors are indicative of mosquito pesticide and treatment. Both equilibrium points and the reproduction number \(R_{0}\) are computed. When \(R_{0} < 1\) , the disease-free equilibrium state is stable both locally and globally. If \(R_{0} > 1\) and the Routh–Hurwitz requirements are met, the endemic equilibrium point arises and is stable. We illustrate the utility of the model by applying it to the real-world scenario of a disease outbreak in India. We use annual data gathered from 2001 to 2022 from India to optimize the proposed model. This allows for an evaluation of how well the proposed model reflects real-life conditions. The variance in the significance level \(R_{0}\) was measured using a sensitivity analysis of the LHS-PRCC. The optimum control problem was formulated using Pontryagin’s maximal approach. Using an iterative forward–backward Runge–Kutta fourth order approach, the optimality system was stimulated. The primary findings demonstrate that every control parameter effectively stops the spread of malaria.