I'm asking the question for someone who is both diagnosed Babesiosis and Fibromyalgia by different practicians.
However the Babesiosis diagnosis seems weak because only based on a positive IgG (Immunoglobulin G) and a fibromyalgic syndrome.
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Here's a brief description of tests for babesiosis (PubMed, 2003):
A CBC [Complete Blood Count] is a useful screening test since anemia and thrombocytopenia are commonly observed and parasites may be visualized on blood smear. Conclusive diagnosis of this disease generally depends upon microscopic examination of thin blood smears. Babesia frequently are overlooked, however, because parasitemia tends to be sparse, often infecting fewer than 1% of erythrocytes early in the course of the illness. Identification of amplifiable babesial DNA by polymerase chain reaction (PCR) has comparable sensitivity and specificity to microscopic analysis of thin blood smear for detection of babesia in blood. Serologic testing provides useful supplementary evidence of infection because a robust antibody response characterizes human babesial infection, even at the time that parasitemia first becomes detectable.
There are many other conditions with musculoskeletal pain and fatigue that can be confused with fibromyalgia (various types of arthritis, myositis, etc.).
There is no laboratory test for fibromyalgia, so a diagnosis is by exclusion of other conditions (niams.nih.gov).
As far as I know Babesiosis is very similar to Paludism. The main parasite in the US, Babesiosis Microti, is supposed to be less agressive than Paludism agents. This is however quite insure with Babesia Divergent. The main parasite in Europe. There are way less reported cases in Europe and these are way more severe. However this could be because mild cases are ignored since the disease is rare in Europe.
Symptoms vary from nothing to repetitive severe flu like syndrome that can last a few weeks. The most severe - life threatening - cases are observed with asplenic and immunodepressed patients. The parasite attacks red blood cells and can, if in great numbers, cause anemia.
This type of flu like symptoms are more likely to be confused with a chronic fatigue syndrome than a Fibromyalgia. The main reason is that fatigue is generally more important than pain. The other is that it is not constant but relapsing.
However some Lyme doctors do not think the same way. But I did not find any evidence.