An investigation of the transmission dynamics of M. tuberculosis
We develop an age-structured deterministic model (TBDYN3) of the transmission dynamics of M. tuberculosis in England and Wales since 1900. The model estimates the age-specific risks of developing' primary', 'endogenous' and 'exogenous' disease and analyzes the incubation period, serial interval, lifetime risks and basic and net reproduction numbers for tuberculosis. Best-fitting disease risk estimates predict peaks in both morbidity and mortality rates among young adults for successive birth cohorts during the pre-chemotherapy era, which fit observed patterns. Model predictions attribute much of the adult morbidity until the 1940s to exogenous reinfection. Chemotherapy, introduced after 1950, accelerated the decline in the risk of infection and the overall morbidity for all age groups. Age and calendar year at infection are shown to determine the lifetime risks of developing tuberculosis, the incubation period and the serial interval. Twenty year olds faced higher lifetime risks of respiratory tuberculosis following infection (e. g. 26% and 17% in 1900 and 1950 respectively) than did any other age group. Estimates suggest that about 3% and over 25% of diseased 20 year olds in 1900 experienced initial infections in 1900 and during infancy respectively. Analogous estimates are provided for other age groups and calendar years. Although tuberculous incidence and mortality declined since the 19th century, the estimated net reproduction number slightly exceeded one from 1900 until 1930 and declined thereafter. We discuss the implications of this paradox for diseases for which epidemiological parameters can change appreciably during a serial interval. Inferences about the basic reproduction number for tuberculosis are drawn by simulating the introduction of a sputum-positive case into an uninfected population identical in demography to that in England and Wales since 1900. A 'founder' case would have led to about 3 secondary cases in 1900, to about 2 by 1950 and to less than 1 after 1960.