Latent Infectivity and Refined Equilibrium Conditions in Mycoplasma Pneumoniae Transmission Dynamics

This research focuses on the transmission dynamics of Mycoplasma pneumoniae [Formula: see text]. A mathematical model has been developed that explicitly incorporates infectivity during the latent period and differentiates between the spontaneous recovery rate of latent individuals and the treatment rate of symptomatic patients. The key innovation involves decomposing the basic reproduction number [Formula: see text] into two components: [Formula: see text], representing transmission from latent individuals, and [Formula: see text] from infected patients. Notably, the spontaneous recovery rate of latent individuals influences both [Formula: see text] and [Formula: see text]. Additionally, a secondary threshold [Formula: see text], related to waning immunity, plays a significant role in disease persistence. It is noted that [Formula: see text] does not ensure a stable endemic equilibrium unless [Formula: see text]; conversely, [Formula: see text] may still allow an unstable endemic equilibrium if [Formula: see text]. Sensitivity analysis reveals that the transmission of [Formula: see text] is influenced by key parameters, with spontaneous recovery rate and transmission rates being critical drivers, it is worth noting that the transmission rate of latently infected persons has a more substantial impact on disease transmission than the transmission rate of infected persons. Optimal control strategies, including preventive measures, targeted treatment, and interventions for latent infections, are developed to minimize the disease burden. This work improves the understanding of [Formula: see text] spread and designs effective control strategies.