Causes of Backward Bifurcation in a Tuberculosis-Schistosomiasis Co-infection Dynamics

Abstract

To obtain a thorough understanding of the influence of schistosomiasis infections on the transmission dynamics of tuberculosis, a deterministic mathematical model for the transmission dynamics of tuberculosis (TB) co-infection with schistosomiasis is created and examined. The aim of the research is to examine the reasons behind the backward bifurcation in the co-infection dynamics of tuberculosis and schistosomiasis. The backward bifurcation phenomena can be caused by the following parameters, according to the model's analysis (when the associated reproduction number is less than one), other than the well established route of exogeneous re-infection of latently infected TB individuals, the relative rates at which humans with latent schistosomiasis ($\eta_1$) and active schistosomiasis ($\eta_2$) are infected with TB, respectively, the lowered rate of reinfection with schistosomiasis ($\psi$), the fraction of individuals who experience fast progression to active TB ($p$), the adjustment parameter which accounts for the increased probability of infectiousness of humans with active TB and latent schistosomiasis ($\Pi_1$), the treatment rate of people infected with active TB exposed to schistosomiasis ($\zeta_{T1}$) and the rate of progression to active TB and exposed to schistosomiasis to active TB and active schistosomiasis ($\sigma$).