A threshold value for the time delay to TB diagnosis

Abstract

Background: In many communities where TB occurs at high incidence, the major force driving the epidemic is transmission. It is plausible that the typical long delay from the onset of infectious disease to diagnosis and commencement of treatment is almost certainly the major factor contributing to the high rate of transmission.

Methodology/principal findings: This study is confined to communities which are epidemiologically relatively isolated and which have low HIV incidence. The consequences of delays to diagnosis are analyzed and the existence of a threshold delay value is demonstrated. It is shown that unless a sufficient number of cases are detected before this threshold, the epidemic will escalate. The method used for the analysis avoids the standard computer integration of systems of differential equations since the intention is to present a line of reasoning that reveals the essential dynamics of an epidemic in an intuitively clear way that is nevertheless quantitatively realistic.

Conclusions/significance: The analysis presented here shows that typical delays to diagnosis present a major obstacle to the control of a TB epidemic. Control can be achieved by optimizing the rapid identification of TB cases together with measures to increase the threshold value. A calculated and aggressive program is therefore necessary in order to bring about a reduction in the prevalence of TB in a community by decreasing the time to diagnosis in all its ramifications. Intervention strategies to increase the threshold value relative to the time to diagnosis and which thereby decrease disease incidence are discussed.

Figure 1. Different individuals belonging to a particular PCC each have their own non-coinciding PCC's.

Figure 2. The infectiousness index function, f, relating degree of infectiousness at time t days since the onset of disease in the primary member of the PCC.

Figure 3. The function, g, describing the number of susceptible people remaining in a PCC at time t days since the onset of disease in the primary member of the PCC.

Figure 4. Flow diagram for the cohort of infected people.

Figure 5. The horizontal line labeled Kappa (κ = 0.38) indicates the ceiling value for f (t)·g (t).

Figure 6. κ = (1+μ/r)/τ is a function of r and tau (τ), κ is plotted for values of r given by r, 0.8 r, 0.6 r and 0.5 r.