TY - JOUR
T1 - A model for tuberculosis with exogenous reinfection
AU - Feng, Zhilan
AU - Castillo-Chavez, Carlos
AU - Capurro, Angel F.
N1 - Funding Information:
This research was partially supported by NSF Grant DEB-925370 (Presidential Faculty Fellowship Award) to Carlos Castillo-Chavez, by NSF Grant DMS-9720558 to Zhilan Feng, and by INCO Grant 950809 of the Commission of European Community Directorate General XII to Angel Capurro. This work was carried out while CCC was visitingthe Institutefor Mathematicsand itsApplications(University of Minnesota, 1999) with NSF support, the Instituto de Investigaciones en Matematicas Aplicadas y Sistemas (UNAM, Mexico, 1998), and Howard University (Washington, D.C., 1999). This paper has greatly benefitted from the comments and suggestions of Sally Blower.
PY - 2000/5
Y1 - 2000/5
N2 - Following primary tuberculosis (TB) infection, only approximately 10% of individuals develop active T.B. 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 reinfaction, i.e., acquiring a new infection from another infectious individual. Our results in this paper suggest that exogenous reinfaction has a drastic effect on the qualitative dynamics of TB. The incorporation of exogenous reinfaction into our TB model allows the possibility of a subcritical bifurcation at the critical value of the basic reproductive number R0 = 1, and hence the existence of multiple endemic equilibria for R0 < 1 and the exogenous reinfaction rate larger than a threshold. Our results suggest that reducing R0 to be smaller than one may not be sufficient to eradicate the disease. An additional reduction in reinfaction rate may be required. These results may also partially explain the recently observed resurgence of TB. (C) 2000 Academic Press.
AB - Following primary tuberculosis (TB) infection, only approximately 10% of individuals develop active T.B. 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 reinfaction, i.e., acquiring a new infection from another infectious individual. Our results in this paper suggest that exogenous reinfaction has a drastic effect on the qualitative dynamics of TB. The incorporation of exogenous reinfaction into our TB model allows the possibility of a subcritical bifurcation at the critical value of the basic reproductive number R0 = 1, and hence the existence of multiple endemic equilibria for R0 < 1 and the exogenous reinfaction rate larger than a threshold. Our results suggest that reducing R0 to be smaller than one may not be sufficient to eradicate the disease. An additional reduction in reinfaction rate may be required. These results may also partially explain the recently observed resurgence of TB. (C) 2000 Academic Press.
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U2 - 10.1006/tpbi.2000.1451
DO - 10.1006/tpbi.2000.1451
M3 - Article
C2 - 10828216
AN - SCOPUS:0034040084
SN - 0040-5809
VL - 57
SP - 235
EP - 247
JO - Theoretical Population Biology
JF - Theoretical Population Biology
IS - 3
ER -