The answer to this question is completely dependent on the context of infection. For instance, when you brush your teeth, you introduce bacteria from your mouth into your blood stream and become temporarily bacteremic. Fortunately, the immune system clears these bacteria quickly. In this daily event, thousands of bacteria enter the bloodstream. After brushing, bacteria in the blood were below 104 cfu/ml, as estimated by PCR, and exact numbers are nearly impossible to quantify (Lockhart et al. 2008).
In contrast, Ebolavirus replicates to ~107 – 108 virions/ml in the blood of non-human primates (Bente et al. 2009). The average person has ~5 liters of blood. Very conservatively, an Ebola survivor will have cleared ~5 x 1010 virions from just the blood. That’s 50 billion virions.
Keep in mind that this is also just a snapshot of a moment during infection. Viruses are constantly propagating, and a single virally infected cell can produce thousands of viral particles in a single day. It’s possible that over the course of a 2 week infection, 1011 – 1012 virions may be produced and cleared (it’s probably much higher). While this number is staggering, it somehow pales in comparison to the magnitude of the U.S. debt, which currently stands at ~$18 trillion, or $1.8 x 1013.
I also estimated the rough number of virions from the liver and spleen, two organs with significant ebola titer, and the total is nowhere near the magnitude of virions in the blood.* Additionally, ebola virus is being shed through mucosa and other bodily fluids. People generate ~ 4 liters of mucus daily in the gastrointestinal tract. I could not find an accurate estimate of Ebola viral titers in the mucus, but it’s unlikely to be near the levels of that in the blood. Granted, mucus could still contribute significantly to viral titer. There’s also the possibility that other organs harbor high titers of ebola virus, especially the gut.
*Approximately 104 – 105 virions/gram were detected in the liver and spleen using a mouse model for Ebola (Bray et al. 1996). Given that the average mass of a human liver is 1.5kg and a spleen is 140g (Molina et al. 2012), and using conservative estimates, about 1.6 x 107 virions from the spleen and liver alone, over 1000 times less than that from the blood.