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Learn More. Related Searches ternary plot. Thanks for helping keep SourceForge clean. X You seem to have CSS turned off. Briefly describe the problem required :. The latter factor puts a natural upper limit to the official number of cases and may thus provide a distorted picture of the extent of the outbreak.
Such a problem is particularly true in the developing world due to resource constraints on testing capacity Lee Alternative approaches have thus been proposed to address this flaw. For example, Delgado et al. Monitoring excess mortality above background levels is also proposed to estimate the accurate scale of the pandemic e. For example, patients with life-threatening conditions may be unable to get proper health care due to hospital congestion. In this paper, we propose an alternative approach to displaying epidemic data using a ternary diagram.
Such diagrams are commonly used in chemical engineering, chemistry, geology, and material science to provide graphical depictions of three-component mixtures; for example, notable process engineering applications include property integration El-Halwagi et al. The next section describes the logic of this approach. We discuss insights that can be drawn from the alternative display and then give conclusions and prospects for future work.
Our proposed visualization method is based on a ternary diagram. At any given time, the cumulative infected population can be regarded as a mixture of active cases A , recovered patients R , and deceased victims D. The fractions of A, R, and D in the total infected population can be plotted in a ternary diagram, as shown in Fig. The vertices A, R, and D correspond to states of the system where all patients are under treatment, recovered, or deceased, respectively.
The edges of the ternary diagram indicate states of the system where all patients fall into just two of the categories. For instance, the edge between vertices R and D corresponds to a population where all patients have either recovered or died. The interior of the ternary diagram signifies states where patients fall under all three categories. The proportion of patients in the interior is determined based on this location, as illustrated in Point 2 in Fig.
The rest are active cases undergoing treatment, as shown in the orange line. Figure 1 further illustrates the stylized trajectory of a generic outbreak. Each point in the ternary diagram represents the case distribution at a particular time however, the time dimension is not explicitly represented in the ternary diagram.
All outbreaks begin at vertex A Point 1 , corresponding to an early state before any of the patients recover or die. Furthermore, all outbreaks terminate along the edge between vertices R and D, a state at which all patients have either recovered or died, and none are left under treatment.
The trajectory of the outbreak between the logical initial and final states can be plotted based on case statistics; examples are Points 2, 3, and 4. Note that this approach is naturally scale-free since the progress is tracked based on ratios of patients in the three groups, rather than absolute headcount. The progression of an epidemic with undetected cases can also be illustrated in Fig.
The presence of undetected cases can only be estimated indirectly, as they are, by definition, not directly observed. For example, the true extent of COVID is generally thought to be greater than official figures based on estimates based on surplus death statistics Russell et al.
Two ternary plots are presented here; one follows the trajectory for the estimated actual number of cases, and the other follows the recorded cases. Each point represents a specific time in the epidemic.
This is compared to the conventional epidemic curve, where the number of active cases is plotted against time. Three points are used as reference for the comparison of the two diagrams: one point is on the time where the number of active cases starts to rise, another is when the number of active cases peaks, and the last one is when the epidemic ends.
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