Applying network theory to epidemics: control measures for Mycoplasma pneumoniae outbreaks

Abstract

We introduce a novel mathematical approach to investigating the spread and control of communicable infections in closed communities. Mycoplasma pneumoniae is a major cause of bacterial pneumonia in the United States. Outbreaks of illness attributable to mycoplasma commonly occur in closed or semi-closed communities. These outbreaks are difficult to contain because of delays in outbreak detection, the long incubation period of the bacterium, and an incomplete understanding of the effectiveness of infection control strategies. Our model explicitly captures the patterns of interactions among patients and caregivers in an institution with multiple wards. Analysis of this contact network predicts that, despite the relatively low prevalence of mycoplasma pneumonia found among caregivers, the patterns of caregiver activity and the extent to which they are protected against infection may be fundamental to the control and prevention of mycoplasma outbreaks. In particular, the most effective interventions are those that reduce the diversity of interactions between caregivers and patients.

Figure 1

Health-care institution network. Each vertex represents a patient, caregiver, or ward, and edges between person and place vertices indicate that a patient resides in a ward or a caregiver works in a ward.

Figure 2

Future transmission diagram I, summing all possible future transmissions stemming from a caregiver who works in an infected ward.

Figure 3

Future transmission diagram II, summing all possible future transmissions stemming from a ward in which an infected caregiver works.

Figure 4

Epidemic thresholds. Each line assumes a different value for μ_c(the average number of wards per caregiver), and graphs the combination of τ_c and τ_w(transmission parameters) above which the population crosses the epidemic threshold. From top to bottom, the lines represent μ_c= 1, μ_c= 2, μ_c= 3, μ_c= 4, and μ_c= 5 .

Figure 5

Size of epidemic. Predicted and actual number of caregivers and wards affected in an outbreak. These predictions assume that the transmission rate from caregivers to wards is τ_c = 0.6 and from wards to caregivers is τ_w= 0.06.

Figure 6

Simulated outbreak sizes. Frequency distributions of the numbers of wards and caregivers affected in 1,000 epidemic simulations are shown for μ_c= 1,2,3.

Figure 7

Comparing derivations to simulation. This graph compares the analytical predictions to the size of a simulated outbreak averaged over 1,000 simulations for each value of μ_c.

Figure 8

Distribution of transmission rates and ward sizes in the psychiatric institution.

Figure 9

Simulated spread of Mycobacterium pneumoniae among patients within a ward.