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

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 \(R_0 = max (R₀ₘ, R₀ₛ) < 1\) 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 \(ω> 0\) ), 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.