TY - JOUR
T1 - Global stability of an age-structure model for TB and its applications to optimal vaccination strategies
AU - Castillo-Chavez, Carlos
AU - Feng, Zhilan
N1 - Funding Information:
We thank Karl Hadeler and Johannes Müller for useful discussions. We thank Horst Thieme and Jorge Velasco-Hernandez for helpful suggestions, and two anonymous referees for comments which improved the manuscript. This research was partially supported by NSF grant DEB-925370 (Presidential Faculty Fellowship Award) to Carlos Castillo-Chavez and by the US Army Research Office through the Mathematical Science Institute of Cornell University (contract DAAL03-91-0027).
PY - 1998/8/1
Y1 - 1998/8/1
N2 - This article focuses on the study of an age-structure model for the disease transmission dynamics of tuberculosis in populations that are subjected to a vaccination program. We first show that the infection-free steady state is globally stable if the basic reproductive number R0 is below one, and that an endemic steady state exists when the reproductive number in the presence of vaccine is above one. We then apply the theoretical results to vaccination policies to determine the optimal age or ages at which an individual should be vaccinated. It is shown that the optimal strategies can be either one- or two-age strategies.
AB - This article focuses on the study of an age-structure model for the disease transmission dynamics of tuberculosis in populations that are subjected to a vaccination program. We first show that the infection-free steady state is globally stable if the basic reproductive number R0 is below one, and that an endemic steady state exists when the reproductive number in the presence of vaccine is above one. We then apply the theoretical results to vaccination policies to determine the optimal age or ages at which an individual should be vaccinated. It is shown that the optimal strategies can be either one- or two-age strategies.
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U2 - 10.1016/S0025-5564(98)10016-0
DO - 10.1016/S0025-5564(98)10016-0
M3 - Article
C2 - 9711046
AN - SCOPUS:0032146737
VL - 151
SP - 135
EP - 154
JO - Mathematical Biosciences
JF - Mathematical Biosciences
SN - 0025-5564
IS - 2
ER -