As the title says, my father alleges that this graph shows that masks have increased COVID-19 rates. Does the graph prove this relationship, or is this just a faulty correlation?
The old saying correlation does not equal causation applies here. In this case the correlation assumed by the question is that masks cause more transmission i.e. Mask mandate -> transmission + infection.
However, there is another correlation that could be the opposite of the assumed, with the causal relationship being that with increased transmission (and subsequent infections) you get a mask mandate to try to limit spread. For this relationship: transmission + infection -> mask mandate. This equation and the one in the first paragraph are not the same!
If you look closely at the graphs, if it were masks causing the transmission, you would expect the increases to happen after masks mandates were put in place, and for the transmission to continue and increase throughout the period during which mask mandates were in place. You would not expect to see the same rate of infection before the masks were used - note the two other times when mask mandates introduced on April 10 and July 17, you can see an obvious increase in cases before each mask mandate was introduced. Also note the shape of the curve in the period between May 8 and June 15 where the number of cases increases for a while, then reduces until mask mandates were removed on June 15. In addition, after the return of mask mandates on July 17, the curve slope doesn't change after the mask mandate was put in place, instead the rate of infection is more or less constant between early July and early August. Lastly on this point, if masks did increase the spread, you would expect in each case, after the mandate was introduced, that the curve would have a slope something like the one on the extreme right of the graph. This is patently not so, so it can't be the masks causing it.
What is shown in December 2021 and Jan 2022 is the effect of the highly transmissible Omicron variant. This has a reproduction number (R0) of about 3-times that of the Delta variant1. Delta has a R0 of about 5 (range 3.2-8.0 in the literature)2, compared to the original SARS-CoV-2, which had an R0 of about 3. This means that if you had Delta you would, on average, infect about 5 other people. With Omicron, you could be infecting up to 15 people. Masks alone don't work in this case, you also need people to comply with all the other public health measures that are available, such as hand washing, physical distancing, limiting time in close proximity, "isolation bubbles" etc., to be able to limit spread.
Masks have been proven to limit spread of SARS-CoV-23, and mask mandates result in greater levels of mask wearing than you might get otherwise4,5. Thus, the conclusion that mask mandates might be introduced when there is increased spread of SARS-CoV-2 is a logical one to make, and the opposite causal relationship is highly unlikely.
Note: The references provided are not the only ones around, there are tons of others showing the same things. I only took the first ones that popped up in my quick searches. The only ones that weren't first links coming up were for the R0 values (refs 1, 2).
1: Suzuki, R., Yamasoba, D., Kimura, I. et al. Attenuated fusogenicity and pathogenicity of SARS-CoV-2 Omicron variant. Nature (2022). https://doi.org/10.1038/s41586-022-04462-1
2: Khan NA, Al-Thani H, El-Menyar A. The emergence of new SARS-CoV-2 variant (Omicron) and increasing calls for COVID-19 vaccine boosters-The debate continues. Travel Med Infect Dis. 2022;45:102246. doi:10.1016/j.tmaid.2021.102246
3: Jeremy Howard, Austin Huang, Zhiyuan Li, Zeynep Tufekci, Vladimir Zdimal, Helene-Mari van der Westhuizen, Arne von Delft, Amy Price, Lex Fridman, Lei-Han Tang, Viola Tang, Gregory L. Watson, Christina E. Bax, Reshama Shaikh, Frederik Questier, Danny Hernandez, Larry F. Chu, Christina M. Ramirez, Anne W. Rimoin. An evidence review of face masks against COVID-19. Proceedings of the National Academy of Sciences Jan 2021, 118 (4) e2014564118 https://doi.org/10.1073/pnas.2014564118
4: Scott et al., The introduction of a mandatory mask policy was associated with significantly reduced COVID-19 cases in a major metropolitan city. PLOSone July 21 2021. https://doi.org/10.1371/journal.pone.0253510
5: Wadud Z, Rahman SM, Enam A. Face mask mandates and risk compensation: an analysis of mobility data during the COVID-19 pandemic in BangladeshBMJ Global Health 2022;7:e006803. https://doi.org/10.1136/bmjgh-2021-006803