Exogenous re-infection and the dynamics of tuberculosis epidemics: local effects in a network model of transmission

Abstract

Infection with Mycobacterium tuberculosis leads to tuberculosis (TB) disease by one of the three possible routes: primary progression after a recent infection; re-activation of a latent infection; or exogenous re-infection of a previously infected individual. Recent studies show that optimal TB control strategies may vary depending on the predominant route to disease in a specific population. It is therefore important for public health policy makers to understand the relative frequency of each type of TB within specific epidemiological scenarios. Although molecular epidemiologic tools have been used to estimate the relative contribution of recent transmission and re-activation to the burden of TB disease, it is not possible to use these techniques to distinguish between primary disease and re-infection on a population level. Current estimates of the contribution of re-infection therefore rely on mathematical models which identify the parameters most consistent with epidemiological data; these studies find that exogenous re-infection is important only when TB incidence is high. A basic assumption of these models is that people in a population are all equally likely to come into contact with an infectious case. However, theoretical studies demonstrate that the social and spatial structure can strongly influence the dynamics of infectious disease transmission. Here, we use a network model of TB transmission to evaluate the impact of non-homogeneous mixing on the relative contribution of re-infection over realistic epidemic trajectories. In contrast to the findings of previous models, our results suggest that re-infection may be important in communities where the average disease incidence is moderate or low as the force of infection can be unevenly distributed in the population. These results have important implications for the development of TB control strategies.

Figure 1

Graphs with two different D values. (a,c) D=1. (b,d) D=10. Clustering coefficients (C) are calculated using the formula in appendix A. While the degree distribution and average number of contacts for each of these graphs are similar, the average length of each of these connections is much higher on the D=10 graph (note that different length-scales are used for c and d). To allow better visualization of the networks, these graphs have 300 individuals and n (average degree)=8; graphs used for the simulations have 100 000 individuals and n=15.

Figure 2

Disease model transitions. (a) Infection model. Individuals are born into the susceptible state (S); if infected they move into a state of latency (L) from which they suffer primary progression to disease (vertical grey bars) for the first 5 years after infection, endogenous re-activation (diagonal black bars) if they progress to disease more than 5 years after an infection (or re-infection) event or exogenous re-infection (dark grey) if they progress to disease within 5 years after a re-infection event. Individuals in the diseased state (I) are infectious until they are either cured by drugs and move to the recovered state (R) (in our simulations this happens only after drugs become available in 1950), they self-recover and return to latency (arrows not shown), or they die. (b) Routes to disease. Progression for a hypothetical individual who is infected three times over the course of his life. The height of the bars represents the probability of progression to disease (by each route) as a function of time.

Figure 3

Simulations. (a) TB incidence and (b) ARI on graphs with D=2 (dashed orange) and D=10 (solid blue) with 100 000 individuals and parameter values as listed in table 1. Snapshots showing 10 000 individuals during epidemics at (c, e) high and (d,f) low incidence on graphs of (c,d) D=2 and (e,f) D=10. Grey pixels are unoccupied spaces, blue pixels represent individuals who are susceptible to infection and yellow pixels represent individuals with latent infection. Even at incidence levels considered high for TB epidemics, infectious individuals (red) are not present in large enough numbers to be seen easily at this resolution and edges are not shown in this representation as they were in the much smaller network depicted in figure 1a,b. Clustering of those with latent infection is evident in the more local graph at low levels of incidence (d), but not easily detected at higher incidence (c) or on the more global graph at any time in the epidemic (e,f).

Figure 4

Importance of exogenous activation at different incidence levels and values of D. D has a substantial effect on estimates of the fraction of disease due to exogenous re-infection at low levels of TB incidence, but less impact at higher levels of disease occurrence.