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<p><i>Mycoplasma pneumoniae</i> is one of the causative agents of community-acquired infections, with epidemic cycles recorded over 37 years and a current international revival after the COVID-19 pandemic. This study elaborates and critically examines a deterministic thirteen-compartmental mathematical model to understand the dynamics of <i>Mycoplasma pneumoniae</i>, including vulnerability stratification, dual-strain progression, and intervention pathways in healthcare. The positivity and boundedness of solutions are proved to establish the well-posedness of the model biologically. Local asymptotic stability of the disease-free equilibrium (DFE) is established when <InlineEquation ID="IEq1"><EquationSource Format="TEX">\(R_0 = \max (R_{0m}, R_{0s}) &lt; 1\)</EquationSource></InlineEquation> and global asymptotic stability at the endemic equilibrium when <InlineEquation ID="IEq2"><EquationSource Format="TEX">\(R_0&gt; 1\)</EquationSource></InlineEquation> via Lyapunov functions. The model exhibits backward bifurcation as temporary immunity decays (when <InlineEquation ID="IEq3"><EquationSource Format="TEX">\(\omega&gt; 0\)</EquationSource></InlineEquation>), suggesting that <InlineEquation ID="IEq4"><EquationSource Format="TEX">\(R_0 &lt; 1\)</EquationSource></InlineEquation>, though necessary, is not sufficient for eradication of <i>Mycoplasma pneumoniae</i>. Optimal control with time-varying vaccination <InlineEquation ID="IEq5"><EquationSource Format="TEX">\(u_1(t)\)</EquationSource></InlineEquation>, intensified treatment <InlineEquation ID="IEq6"><EquationSource Format="TEX">\(u_2(t)\)</EquationSource></InlineEquation>, and prevention compliance <InlineEquation ID="IEq7"><EquationSource Format="TEX">\(u_3(t)\)</EquationSource></InlineEquation> reduces infectious and hospitalised compartments by 90–<InlineEquation ID="IEq8"><EquationSource Format="TEX">\(99\%\)</EquationSource></InlineEquation>, while the absence of controls allows endemic persistence. The results provide an evidence-based framework for designing targeted, cost-efficient interventions to control <i>Mycoplasma pneumoniae</i> epidemics and safeguard vulnerable populations.</p>

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A dual-strain compartmental model for Mycoplasma pneumoniae transmission dynamics with vulnerability stratification and optimal control strategies

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月4日

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  • Remigius Okeke Aja,
  • Sussan Ijeoma Ezeh,
  • William Atokolo,
  • Godwin Onuche Acheneje,
  • Ali Raza,
  • Edrisa Jawo

摘要

Mycoplasma pneumoniae is one of the causative agents of community-acquired infections, with epidemic cycles recorded over 37 years and a current international revival after the COVID-19 pandemic. This study elaborates and critically examines a deterministic thirteen-compartmental mathematical model to understand the dynamics of Mycoplasma pneumoniae, including vulnerability stratification, dual-strain progression, and intervention pathways in healthcare. The positivity and boundedness of solutions are proved to establish the well-posedness of the model biologically. Local asymptotic stability of the disease-free equilibrium (DFE) is established when \(R_0 = \max (R_{0m}, R_{0s}) < 1\) and global asymptotic stability at the endemic equilibrium when \(R_0> 1\) via Lyapunov functions. The model exhibits backward bifurcation as temporary immunity decays (when \(\omega> 0\)), suggesting that \(R_0 < 1\), though necessary, is not sufficient for eradication of Mycoplasma pneumoniae. Optimal control with time-varying vaccination \(u_1(t)\), intensified treatment \(u_2(t)\), and prevention compliance \(u_3(t)\) reduces infectious and hospitalised compartments by 90–\(99\%\), while the absence of controls allows endemic persistence. The results provide an evidence-based framework for designing targeted, cost-efficient interventions to control Mycoplasma pneumoniae epidemics and safeguard vulnerable populations.