Mathematical Modeling of Chlamydia Trachomatis–Hepatitis B Virus Coinfection: Invasion, Synergistic Interaction, Vaccination, and Treatment

A deterministic compartmental model is developed to investigate the transmission dynamics of chlamydia trachomatis and Hepatitis B virus (HBV) coinfection in the presence of vaccination, treatment, and synergistic interaction. The 14-compartment model incorporates HBV vaccination with waning protection, chlamydia treatment, acute-to-chronic progression of HBV infection, temporary natural immunity, secondary acquisition, and synergistic modification of acquisition and infectiousness during coinfection. The model is shown to be well posed, with solutions remaining positive and bounded in the biologically feasible region. The disease-free equilibrium and pathogen-specific reproduction components are derived using the next-generation matrix approach, yielding the overall invasion threshold R0=maxRC,RH. Mutual invasion reproduction numbers characterize the ability of each pathogen to invade an endemic environment generated by the other, whereas endemic equilibria and their local stability properties are established, and forward transcritical bifurcations are identified at the pathogen-specific epidemic thresholds. Sensitivity analysis shows that transmission intensity and infectious period reduction are important determinants of pathogen invasion, whereas chronic HBV infectiousness and vaccination characteristics substantially influence the HBV reproduction component. Although the synergistic interaction parameters do not directly affect the disease-free invasion threshold, they become influential after infection is established. Numerical simulations show that stronger synergistic interaction increases the 20-year coinfection prevalence by approximately 93.1% relative to the corresponding no-synergy scenario, whereas simultaneous intensification of chlamydia treatment and HBV vaccination reduces the simulated coinfection prevalence by approximately 22.8% relative to the baseline intervention setting. These findings highlight the distinction between pathogen-specific invasion and postinvasion synergistic dynamics and demonstrate the importance of considering both processes when evaluating integrated control strategies for chlamydia–HBV coinfection.