Transmission dynamics of tuberculosis with multiple re-infections

Abstract

We propose and analyze an epidemic model describing the transmission dynamics of tuberculosis (TB) with the possibilities of re-infections and fast progression of the disease. The qualitative behavior of the system is studied, covering several distinct aspects of disease transmission. The epidemiological threshold, known as the basic reproduction number, R0, is determined using the next-generation matrix approach. It is observed that the present epidemic system may exhibit a backward bifurcation for R0 < 1. Therefore, we may conclude that reducing R0 to less than unity is not sufficient for eradication of tuberculosis. However, reducing R0 to less than the sub-threshold obtained in the absence of recurrent TB, it is possible to eradicate the disease. We notice that a sufficient proportion of newly infected individuals developing a direct progression to the active stage can overcome the possibility of backward bifurcation. We also insight the qualitative nature of backward bifurcation with variation in re-infection level. It is found that increasing the level of re-infections makes the disease eradication more challenging. The theoretical investigations are being supplemented by numerical simulations whenever necessary.