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A model for tuberculosis with exogenous reinfection. (English) Zbl 0972.92016

Summary: Following primary tuberculosis (TB) infection, only approximately \(10\%\) of individuals develop active TB. Most people are assumed to mount an effective immune response to the initial infection that limits proliferation of the bacilli and leads to long-lasting partial immunity both to further infection and to reactivation of latent bacilli remaining from the original infection. Infected individuals may develop active TB as a consequence of exogenous reinfection, i.e., acquiring a new infection from another infectious individual.
Our results in this paper suggest that exogenous reinfection has a drastic effect on the qualitative dynamics of TB. The incorporation of exogenous reinfection into our TB model allows the possibility of a subcritical bifurcation at the critical value of the basic reproductive number \({\mathcal R}_0=1\), and hence the existence of multiple endemic equilibria for \({\mathcal R}_0<1\) and the exogenous reinfection rate larger than a threshold. Our results suggest that reducing \({\mathcal R}_0\) to be smaller than one may not be sufficient to eradicate the disease. An additional reduction in reinfection rate may be required. These results may also partially explain the recently observed resurgence of TB.

MSC:

92C50 Medical applications (general)
92C60 Medical epidemiology
92D30 Epidemiology
34D99 Stability theory for ordinary differential equations
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