Co-dynamics of COVID-19, HIV and TB with information-dependent vaccination behavior and waning immunity

Despite advances in understanding and mitigating the impacts of COVID-19, TB, and HIV, these diseases remain significant public health concerns. This study aimed to provide a novel model that considers reinfection and waning immunity and investigates the role of vaccination behavior in halting co-infection and triple infection of these diseases. The basic properties of the model were examined to ensure mathematical and epidemiological well-posedness. Reproduction numbers were calculated using the next-generation matrix method. These numbers were used as threshold values to examine the stability analyses of equilibria and investigate how one disease affects another. Reproduction number analyses showed that an increase in HIV and TB cases can elevate the transmission of COVID-19, highlighting the importance of monitoring multiple diseases. Stability analyses were conducted to investigate the equilibrium behavior of the system. The central manifold theory is used to demonstrate the occurrence of backward bifurcation in the COVID-19 sub-model. This analysis suggests that even when the basic reproduction number is below one, multiple endemic equilibria can still persist, leading to ongoing levels of infection. This finding underscores the need for robust control strategies. Parametric estimation and curve fitting were conducted using Ethiopian data. Numerical simulations were employed to explore the interplay between key behavioral parameters. The simulation results emphasize the significance of information-dependent vaccination in eliminating COVID-19 and its associated co-infections with HIV and TB, particularly in the face of challenges such as vaccine ineffectiveness, low vaccination coverage, and waning immunity.