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

Abstract

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 [Formula: see text] and global asymptotic stability at the endemic equilibrium when [Formula: see text] via Lyapunov functions. The model exhibits backward bifurcation as temporary immunity decays (when [Formula: see text]), suggesting that [Formula: see text], though necessary, is not sufficient for eradication of Mycoplasma pneumoniae. Optimal control with time-varying vaccination [Formula: see text], intensified treatment [Formula: see text], and prevention compliance [Formula: see text] reduces infectious and hospitalised compartments by 90-[Formula: see text], 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.