I can't find much re: arthritis but this paper covers allergies and some more general auto-immune diseases.
There appears to be some support for the hypothesis in the form of animal models and epidemiological data but the interventions appear to do poorly in clinical trials.
Iatrogenic Helminth Infections: A Good or a Bad Idea?
Given the contradictory findings highlighted above, it is not surprising that the iatrogenic administration of helminths—labeled as a safe, efficacious treatment strategy for inflammatory and autoimmune diseases—has met with mostly mixed or negative results.
For asthma or allergic rhinitis, there appears to be no benefit from administration of parasitic helminths. Specifically for asthma, in a randomized control trial, no benefit of hookworm larval administration was observed . Additionally, three randomized trials, one using T. suis eggs  and the other two using hookworm [58,60], failed to show any therapeutic benefit against grass pollen–induced allergic rhinitis, allergic rhinoconjunctivitis, or asthma. In fact, in two of these three trials, patients suffered from gastrointestinal symptoms as a result of the helminth infection. An additional Cochrane review evaluating the efficacy of helminth therapy for allergic rhinitis management found that participants receiving helminth therapy showed no improvement in rhinitis symptoms or number of well days but did have increased adverse events, including local pruritus and gastrointestinal symptoms such as abdominal pain, flatulence, and diarrhea .
For IBD and celiac disease, therapy has focused on using the pig whipworm T. suis or the human hookworm Necator americanus. Regarding the former, two open-label studies by Summers et al. showed that T. suis therapy for the treatment of IBD correlated to a remission rate of around 70%, helping ignite the excitement of helminth therapy in human beings [62,63]. In the follow-up placebo-controlled, double-blind, randomized trial, there was an improvement in ulcerative colitis disease severity but no significant improvement in the rates of remissions . Two subsequent Phase 2 clinical trials in the US, with 250 patients (TRUST-1, trial identifier NCT01576471), and Europe, with 240 patients (FALK, trial identifier NCT01279577), using T. suis eggs for moderate-to-severe Crohn’s disease were terminated in 2013 because of a lack of efficacy, which was determined by both a measure of disease activity index and remission rates [65,66]. A 2014 Cochrane review that evaluated the safety and efficacy of T. suis therapy to induce inflammatory bowel disease remission found insufficient evidence, secondary to small studies and low-quality evidence, to support the use of helminth therapy . Although these trials do not show significant short or long-term adverse events to T. suis therapy, when given up to 7,500 ova, there are continued concerns of safety. Of particular concern is aberrant migration, which is well known to occur with many helminth species when in unnatural hosts . Additionally, zoonotic helminths have been noted for their propensity to be particularly inflammatory when in humans . These concerns, along with limited efficacy, have influenced investigators to explore human helminth-derived molecules and N. americanus, which has a well-defined natural lifecycle within humans [68,70]. For Crohn’s disease, after 45 weeks of N. americanus infection, one study showed no statistically significant decrease in disease activity index among patients . A second study using N. americanus larvae for the treatment of 20 patients with celiac disease showed a reduction in IFN-γ and IL-17 inflammatory cytokines in duodenal biopsies but no improvements in clinical symptoms among those with hookworm treatment . More recently, in a preliminary study, combination therapy of N. americanus and gluten microchallenge showed improved gluten tolerance in eight celiac disease patients in an open-label, nonplacebo controlled study (66). It was further suggested that hookworm challenge infections might exert such effects by reversing microbial dysbiosis . Although the authors of the celiac study acknowledge that conclusions from the study are preliminary because of the sample size and lack of controls, they argue that further investigation into combination therapy should be considered .
Helminth therapy has been tried as a treatment for MS after the observation was made that 12 patients with MS and concomitant natural intestinal helminth infection in Argentina had a reduction in the number of relapses and lower MRI activity in comparison to uninfected MS patients . Building on this promising finding, a Phase 1 clinical trial of T. suis egg was administered to 5 MS patients during a three-month period and showed a mild reduction in the number of new gadolinium-enhancing lesions, but there were no changes in neurological symptoms, nor was there a placebo-controlled comparison .
The failed therapeutic potential of helminth treatment in humans has been surprising to some scientists. As highlighted above, there have been several animal studies that demonstrate an immunosuppressive role of helminths. Further, human epidemiological studies have suggested a protective role for helminths against autoimmune and inflammatory conditions. However, many of these studies identified delayed or diminished development of allergic or autoimmune responses when helminth treatment was used prophylactically, with few studies that demonstrate a clear therapeutic advantage in already established conditions . Furthermore, nearly all of the animal studies used helminth doses significantly higher than would be viewed as safe in humans, which perhaps explains why successful trials in humans were limited .
While initially promising, the treatments with parasitic worms have tended not to work terribly well in practice.