Intrinsic transmission global dynamics of tuberculosis with age structure (Q2888848)

The paper generalizes the SEI system proposed in [\textit{S. M. Blower} et al., ``The intrinsic transmission dynamics of tuberculosis epidemics'', Nature Med. 1, No. 8, 815--821 (1995)] for modeling tuberculosis dynamics in the case of age-structured population. Thus, the resulting system consists of a set of partial differential equations, with time and age as independent variables. Using integration along characteristics, the authors show that the population density is bounded from above by the function of the constant input flow susceptible population multiplied by the exponential of integral of age-dependent mortality rate. It is used for the definition of the globally asymptotically disease-free steady state; the corresponding basic reproductive number governing this stability is derived analytically in an explicit integral form. Another more interesting result is the proof of the existence of an endemic steady state for a basic reproductive number larger than \(1\) and a death rate due to tuberculosis equal to \(0\).