The history of tuberculosis

Abstract

Tuberculosis has claimed its victims throughout much of known human history. It reached epidemic proportions in Europe and North America during the 18th and 19th centuries, earning the sobriquet, "Captain Among these Men of Death." Then it began to decline. Understanding of the pathogenesis of tuberculosis began with the work of Théophile Laennec at the beginning of the 19th century and was further advanced by the demonstration of the transmissibility of Mycobacterium tuberculosis infection by Jean-Antoine Villemin in 1865 and the identification of the tubercle bacillus as the etiologic agent by Robert Koch in 1882. Clemens von Pirquet developed the tuberculin skin test in 1907 and 3 years later used it to demonstrate latent tuberculous infection in asymptomatic children. In the late 19th and early 20th centuries sanatoria developed for the treatment of patients with tuberculosis. The rest provided there was supplemented with pulmonary collapse procedures designed to rest infected parts of lungs and to close cavities. Public Health measures to combat the spread of tuberculosis emerged following the discovery of its bacterial cause. BCG vaccination was widely employed following World War I. The modern era of tuberculosis treatment and control was heralded by the discovery of streptomycin in 1944 and isoniazid in 1952.

A Mathematical Model of Tuberculosis with Drug Resistance Effects

“…Figure 4 shows that when η increases then 1 α the death rate of the resistant increases implying the decrease in R as the result of increasing deaths in I and ES R . Note that for 0.3 η = the ES R class is much greater than I implying much more deaths.…”

“…Figure 2 represents the flow of individuals into the different compartments and it has been constructed with these assumptions: recruitment is by births only, a variable population, a constant mortality rate, no permanent immunity to tuberculosis, no immediate infectivity. Parameters: λ , recruitment by births, β , force of infection, µ , death rate of humans, α , disease induced deaths in humans due to active tuberculosis, 1 α , disease induced deaths in humans due to MDR tuberculosis, γ , recovery rate of infected humans from active tuberculosis, δ , recovery rate of infected humans from MDR tuberculosis, h λ ,  , rate at which the exposed become infectious, σ , rate at which the infected with active tuberculosis become resistant ρ , rate at which recovered humans become susceptible.…”

“…Proof To establish the global stability of the endemic equilibrium, Φ , we construct the lyapunov function 1 :…”

“…To test the sensitivity of our system to the disease induced death rate 1 α of the resistant individuals ES R and the disease induced death rate α of the infected I, we draw a 3-D curve (Figure 4) perturbing the system using this expression 1 α α η = + where η is a small positive value. Figure 4 shows that when η increases then 1 α the death rate of the resistant increases implying the decrease in R as the result of increasing deaths in I and ES R .…”

“…Tuberculosis is an airborne disease caused by Mycobacterium tuberculosis (Mtb) bacteria [1]. It is an ancient Figure 1.…”