<p>This research focuses on pneumococcal pneumonia respiratory infection caused by <i>Streptococcus pneumoniae</i> bacteria by considering various epidemiological aspects. Researchers have discovered that elevating vaccination and hospitalization rates results in a decline in pneumococcal pneumonia disease cases. This study examines an epidemic model incorporating vaccination and treatment factors to conceptualize pneumococcal pneumonia transmission. A deterministic model with six compartments of pneumococcal pneumonia is built based on vaccinations and treatment to comprehend pneumococcal pneumonia infection spreads and preventative measures. In addition to the positivity, boundedness, existence, and uniqueness of the solution, the biologically viable region is established. The disease-free equilibrium point of global stability is illustrated by employing the Castillo-Chavez stability criterion, and its local stability analysis is demonstrated via the linearization approach, which leads to a result <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40819_2025_1928_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="51" /> </InlineMediaObject> <EquationSource Format="TEX">\(R_{0}<1\)</EquationSource> </InlineEquation>. The next-generation matrix is utilised to calculate the basic reproduction number (<InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40819_2025_1928_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\(R_{0}\)</EquationSource> </InlineEquation>). Stability analysis via the Lyapunov function (LF) proves that the model of an endemic equilibrium is globally stable. Contour plots and 3D meshes are utilized to examine the impact of various parameters on (<InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40819_2025_1928_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\(R_{0}\)</EquationSource> </InlineEquation>). The trajectories of the state variables in the pneumococcal pneumonia model converge toward the equilibrium point. The Partial Rank Correlation Coefficient (PRCC) global technique examines parameter sensitivity. The pneumococcal pneumonia model is numerically solved using the Nonstandard Finite Difference (NSFD) to calculate the numerical results. In the NSFD numerical framework, a pneumococcal pneumonia dynamics model is simulated.</p>

A Mathematical Model of Pneumococcal Pneumonia Infection Dynamics Using Treatment and Vaccination Interventions

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发表日期：

2025年5月26日

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Zakirullah

摘要

This research focuses on pneumococcal pneumonia respiratory infection caused by Streptococcus pneumoniae bacteria by considering various epidemiological aspects. Researchers have discovered that elevating vaccination and hospitalization rates results in a decline in pneumococcal pneumonia disease cases. This study examines an epidemic model incorporating vaccination and treatment factors to conceptualize pneumococcal pneumonia transmission. A deterministic model with six compartments of pneumococcal pneumonia is built based on vaccinations and treatment to comprehend pneumococcal pneumonia infection spreads and preventative measures. In addition to the positivity, boundedness, existence, and uniqueness of the solution, the biologically viable region is established. The disease-free equilibrium point of global stability is illustrated by employing the Castillo-Chavez stability criterion, and its local stability analysis is demonstrated via the linearization approach, which leads to a result \(R_{0}<1\) . The next-generation matrix is utilised to calculate the basic reproduction number ( \(R_{0}\) ). Stability analysis via the Lyapunov function (LF) proves that the model of an endemic equilibrium is globally stable. Contour plots and 3D meshes are utilized to examine the impact of various parameters on ( \(R_{0}\) ). The trajectories of the state variables in the pneumococcal pneumonia model converge toward the equilibrium point. The Partial Rank Correlation Coefficient (PRCC) global technique examines parameter sensitivity. The pneumococcal pneumonia model is numerically solved using the Nonstandard Finite Difference (NSFD) to calculate the numerical results. In the NSFD numerical framework, a pneumococcal pneumonia dynamics model is simulated.