The conventional method of following infections is to plot dependent variables (for example: parasitemia, fever, anemia, weight loss) versus time; this obscures some important relationships (). For example, it is simple to pick out the peak values and times for health and parasitemia, but the relationship between health and parasitemia is harder to see because the relationship changes continuously. We presume that parasite load drives changes in health, but we seldom monitor this directly.
Plotting data in the phase plane to better monitor infections.
What would happen if instead of taking the peak parasitemia and minimum health as a summary of an infection, we plotted health-by-microbe values at every time point 
? Imagine the individual depicted in . This patient is initially infected by a parasite, which produces a single large red lump on his hand. The parasite reproduces, creating more red lumps, but this doesn’t have a large effect on health. At some point the immune response turns on and the parasites are removed; the patient now suffers an immunity-driven loss of health, as indicated by his posture. Ultimately, the patient recovers his initial health and all of the parasites are cleared. This is a resilient system. By resilience, I mean the properties of a system that push it back to its original state following a perturbation. That we get better following an infection means that we are resilient.
Instead of plotting parameters versus time, I’ve plotted dependent parameters against each other in the phase plane as health-by-microbe number in . This produces a looping curve that better shows the relationship between health and microbe number across the whole infection. This relationship changes across the course of the infection: In the first portion, microbe load increases without affecting health. Next, both health and microbe numbers simultaneously crash. Finally, health increases and microbe numbers drop to zero.
Though all of the information is present in the original, this new type of plot reveals some properties that are hard to visualize from the timelines. It is clear that in this infection, microbes are not the direct cause of pathology; rather, the immune response is causing damage because there is no pathology until microbe clearance begins. The relationship that becomes very apparent out in this presentation is recovery; at some point during the infection the patient heals. Much of our research into microbial pathogenesis is directed towards limiting microbe growth or limiting pathology with the hope that if we don’t get severely ill then it will be easier to recover. This graphing approach highlights recovery and provides a quantitative method for measuring recovery.
This presentation is useful as a two-dimensional map and it is easy to overlook the hidden third property–velocity. The spacing of each data point indicates how quickly an individual passes through health-by-microbe space (). For example, it is easy to imagine two individuals that traverse the same health-by-microbe space but differ in their velocity and that it is the velocity that leads to different outcomes. A change in velocity (acceleration) during the course of the infection in an individual also provides useful information (). For example, when the rate of parasite growth decelerates, that suggests that antimicrobial effectors are being produced. Likewise, when health starts to accelerate in a positive direction, this suggests that repair mechanisms are being expressed. It is therefore important to study the velocity and acceleration of these curves in addition to the simple phase space depiction of infection.
The contribution of velocity to disease curves.
The disease curve shown in is drawn in two dimensions, but there is no theoretical limit to the number of dimensions that could be used. Physicians working in an intensive care unit might find this obvious as they monitor dozens of parameters when they coax a person’s health back to a survivable range. Those of us studying microbial pathogenesis in the lab tend not to look at all of these parameters at once, but by drawing even two-dimensional disease curves explicitly we can highlight processes that have been understudied.