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 \ (R₀ = (R₀₌, R₀ₒ) 1\) via Lyapunov functions. The model exhibits backward bifurcation as temporary immunity decays (when \ (> 0\) ), suggesting that \ (R₀ < 1\), though necessary, is not sufficient for eradication of Mycoplasma pneumoniae. Optimal control with time-varying vaccination \ (u₁ (t) \), intensified treatment \ (u₂ (t) \), and prevention compliance \ (u₃ (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.
Aja et al. (Sat,) studied this question.