An investigation of Susceptible–Exposed–Infectious–Recovered (SEIR) tuberculosis model dynamics with pseudo-recovery and psychological effect

Tuberculosis is one of the most pressing issues of the modern era, posing a severe health risk to humans in recent decades. This study proposes a Susceptible–Exposed–Infectious–Recovered (SEIR) tuberculosis epidemic transmission model with psychological effects and pseudo-recovery. We consider a compartmental mathematical model in which the entire population is divided into four compartments based on their natural features. The model is validated, and parameter values are estimated using Indonesian data from 2002 to 2022. To investigate their epidemiological significance, we proved the positivity and boundedness of solutions, as well as the local and global stability of equilibria. Sensitivity analysis is used to find the most influential parameters with the most significant influence on the basic reproduction number, $R_0$. The bifurcation procedure tools of the center manifold theory are used to conduct a bifurcation study. Mathematical conditions ensure the inferred event of forward bifurcation. We performed numerical simulations that support our theoretical findings.