Modeling the End of Monkeypox

Jared Leibowich

The journalistic and public health response to the US monkeypox outbreak was noisy and contentious. What tools do we have for predicting its spread?

COVID-19 upended our daily lives, but for me the most anxiety-provoking part of the early pandemic was the uncertainty over how the next weeks and months would unfold: How severe was SARS-CoV-2? How contagious? Where was the next hot spot? And when would it be over? Watching the news only brought me more stress: experts couldn’t seem to make up their minds about what was happening, let alone how things might play out. In trying to resolve these questions for myself, I became obsessed with forecasting. I created an account on Good Judgment Open, a public platform where forecasters share their predictions. Trying to answer the site’s COVID-19 questions helped keep me sane while dealing with the uncertainties of pandemic life. The site’s founder, Philip Tetlock, is well known for identifying, evaluating, and analyzing “super forecasters” — those in the top 2% of forecasting ability. But these forecasting skills are not innate. I attribute my success in forecasting to the heuristics I’ve learned from thinking about hundreds of questions, as well as Tetlock’s book (co-written with journalist Dan Gardner) Superforecasting. In this article, I’ll demonstrate how the skills I learned forecasting COVID-19 helped me think about the spread of monkeypox in the United States — what factors went into my estimates, and where I made adjustments along the way.

Background on Monkeypox

Monkeypox is a zoonotic disease originally found in a variety of mammals, with symptoms like a milder version of smallpox. It is transmitted between humans primarily through exposure to infected bodily fluids or contaminated objects.  Pockets of transmission have been recorded since at least the 1970s in Central and West Africa, but the 2022 outbreak represents the first incidence of widespread community transmission in Europe or America. The first confirmed case was reported to the WHO on May 7, but the virus was likely circulating throughout April, and perhaps even as early as March. Spain, Portugal, and the United States each confirmed cases on May 18, with many other countries to follow suit through May and June. As of this writing on September 14, cases have been confirmed in over 100 countries. 


Nearly all of these cases are among men. More than 95% of cases in which data are available are among gay, bisexual, and other men who have sex with men (MSM). The preponderance of cases among MSM suggests that monkeypox is currently spreading like a sexually transmitted infection. Discussing a virus that overwhelmingly affects MSM risks reinforcing stereotypes that MSM are diseased and therefore disgusting — a form of stigma which has had devastating consequences during the HIV/AIDS epidemic. Journalists and public health experts spent the summer debating whether to de-emphasize group risk or engage in more pointed public health messaging. I won’t address that debate here, but my position is that understanding how the disease spreads and who it impacts is necessary for predicting its progress and mounting an adequate public health response.

Kyle Ellingson

My Forecasting Process in Early August

Forecasting websites generally provide well-formed questions, but it’s worth knowing what goes into generating them. Valuable questions tend to be ones where there are clear parameters: a discrete time period with a beginning and end, unambiguous wording, and specific sources for how a question will be resolved. For this article, I chose to forecast the following question:

How many confirmed cases of monkeypox will there be in the United States by January 1st, 2023? The question will resolve with official CDC data for confirmed cases by January 1st.

In making my prediction, I looked at several critical pieces of information. First, in recognizing that the current strain of monkeypox operated more closely to an STI than other infectious diseases, I guessed that its spread would not extend beyond sexual transmission with men unless there was a significant mutation in the virus. This assumption dramatically narrows the susceptible population, putting a cap on my predicted case counts.

Second, I drew inspiration from Youyang Gu, a data scientist who pivoted from his day job early in the pandemic to model the spread of COVID-19. Gu’s model was unique among early COVID-19 projections because it incorporated only one data input: daily deaths. From this statistic, Gu calculated parameters like reproduction number and infection mortality rate using machine learning. Gu’s projections were more accurate than other models with more complicated inputs in the early stages of the pandemic. My approach was not nearly as sophisticated, and didn’t apply machine learning (I used back-of-the-envelope calculations). Still, I felt confident I could make a decent forecast with only accurate data on monkeypox case rates.


Alas, such data has not been available. I made my first forecast in early August. The EU and UK were a few weeks ahead in their outbreaks, so I looked there to project trends in the United States. Here, I was hampered by inadequate data and poor reporting. Daily case counts early in the outbreak were not being released in real time. It was clear that between May and July cases had grown exponentially, but beyond that, reporting lags and high variance in day-to-day results  made it difficult to extrapolate clear trends.

The main question I hoped to answer was when the US could expect to exit the exponential growth phase. This seemed to happen in the EU and UK in mid-August, roughly 14 weeks after the outbreak began, but sporadic reporting made it difficult to say for certain.

Monkeypox: Daily cases reported (7-day average)
Source: World Health Organization. Available at Our World in Data
Monkeypox: Cumulative confirmed cases, Sep 13, 2022
Source: World Health Organization. Available at Our World in Data
Monkeypox vaccine administration in the U.S. Sep 13, 2022
Total JYNNEOS Vaccine Doses Administered and Reported to CDC
Source: CDC

This left me with the American data. On June 3rd, 2022, there were 32 confirmed cases of monkeypox in the United States. By July 3rd, that had grown to 563 confirmed cases, and by August 3rd, there were 6,599 confirmed cases. 1

I assumed that, given the scattered public health response and lower awareness of the virus, June case counts were somewhat unreliable and likely under-counted, so I chose to only look at July to August spread, which saw an 11.7x increase in cases. I assumed that this rate of growth might decrease slightly as public awareness of monkeypox increased, but would likely remain exponential. Rounding down the growth rate slightly to 10x and using the early August numbers gave me an idea of how many cases there would be by September 3 — about 66,000. I revised this downwards again based on my guess that America might exit the exponential phase in late August, leaving me with an estimate of 50,000 confirmed cases by the end of the month.

After this, I considered what would happen after America exited the exponential phase. Would new cases taper until there were basically none, or would there be a steady, linear rate of growth in total case numbers? Looking at Europe gave little indication. There, cases appeared to be potentially decreasing from exponential growth, but there was little indication of what would happen next.

My best guess was that new cases would taper off as risky contact between MSM decreased and vaccinations increased. I also thought cases would decrease as quickly as they increased, but I had low confidence in this assessment. Regardless, if the exponential peak occurred at 50,000 confirmed cases, I estimated that 100,000 confirmed cases by the end of the year might be likely, assuming that the exponential peak marks the halfway point in the outbreak and that cases would decrease at roughly the same rate as they had increased.

As you may already be aware, my initial forecast in August was somewhat off.

The Importance of Flexibility

An important lesson I have learned from my last few years of forecasting is to be willing to challenge my own expectations. Striking the right balance between under- and over-reacting to new evidence requires patience and humility; it’s always important to own errors. Personally, the way that COVID-19 has spread since 2020 left me primed to be fearful of pandemics breaking out. This biased me towards thinking that the monkeypox outbreak might turn into a full-blown pandemic.

Because I’d spent so much time thinking about COVID-19, I didn’t consider all the ways that the two viruses might be different. And amidst all of the debate about how to talk sensitively but truthfully about the spread of monkeypox within the MSM community, I likely didn’t weight a few key facts strongly enough.

First, it’s very likely that a substantial proportion of the spread occurred at organized sex parties. A leading theory traces the widespread outbreak in May to several parties in Spain and Belgium. In Late July, the World Health Organization cautioned MSM to reduce the number of sexual partners, reconsider sex with new partners, and exchange contact information with new partners to enable follow-up. Many event organizers followed suit by temporarily suspending parties throughout the United States. In short, despite the debates about the muddled public health response, men who are most at risk appear to have changed their behavior in response. 

I underestimated how quickly this would happen. This is where comparisons to COVID-19 limited the accuracy of my first forecast. MSM as a group, particularly those who frequent sex parties, have substantially more experience in risk management around a sexually transmitted pandemic than the general population. STI testing, along with other forms of risk prevention like PrEP, are embedded in MSM communities. Moreover, activism and organizing experience gained from decades of battling HIV also played a role; MSM were quick in organizing to demand testing and vaccination access. It’s also possible that politics played a role. We’re all by now well-aware of the politically and ideologically divided response to COVID-19: masks, lockdowns, vaccinations. Gay men skew heavily left compared to the general population, and political affiliation is shown to modify perceived risk (at least to COVID-19); it’s possible that extends to monkeypox.

In addition, public health authorities have rapidly scaled up vaccine administration despite the initially limited supply of vaccines. In early August, the Food and Drug Administration expanded its emergency use authorization to allow health care workers to administer the vaccine intradermally, or between layers of the skin. Compared to traditional administration through subcutaneous injection —into the fat layer beneath the skin — intradermal injections use ⅕ the dose. This allowed the 400,000 vials in the national stockpile to provide closer to 2 million shots. As of this writing, over 500,000 doses have been administered, 2 though demand has been steadily decreasing since mid-August.

My failure to give enough weight to these two facts highlights an important lesson in forecasting: spend time with the subject matter. There’s no point trying to make predictions with only cursory knowledge of the question you’re forecasting. In hindsight, these two factors were major variables; if anything, I’m surprised that my underweighting of these factors didn’t lead to my forecast being more inaccurate. I think it’s important not to build an overly complicated model (as this can lead to greater errors along the way), but it helps to brainstorm about any potential factors that might play a role. I am of the opinion that writing down all of your ideas, no matter how far-fetched, is valuable to the forecasting process. Choosing not to filter enables creativity — which to me is also among the most enjoyable parts of forecasting.

My Adjusted Forecast

As of this writing, I assume that CDC’s case trends are more accurate. They are now being updated weekly. The 7-day moving average appears to have peaked around August 10 at 461, but remained above 400 through almost all of the month. On September 9th, there were roughly 21,500 confirmed cases of monkeypox in America. 3 The level of new cases per week peaked around the first week of August at roughly 2,500 cases, then remained the same through the month. At the time of this writing on September 9th, the number of new cases each week is beginning to decline.

In my updated September forecast, I took the halfway point of the three weeks around the peak when cases flattened (August 14th) to use as a halfway point in total confirmed cases: 13,500 confirmed cases. Once again, I assume that the halfway point in time in which cases have flattened serves as a midpoint in the outbreak, and that cases will decline at roughly the same rate as they have increased. Doubling this case count gives me 27,000 cases, but because I expect there will continue to be a low rate of transmission in the tail end of the outbreak, I will increase my estimate to 30,000 confirmed cases by the end of 2022. Furthermore, I predict the outbreak will have mostly subsided by the middle of November, assuming that the 2.5 months it took for cases to reach peak transmission will be mirrored by 2.5 months for cases to decline to very low levels of transmission.

Conclusion

There are a lot of assumptions behind my forecast. Most significantly, I assume that the current monkeypox strain will not mutate into a more contagious form before the end of 2022. If a new strain arose which made transmission much easier, then cases might once again start to increase exponentially. But while forecasting COVID-19 taught me to be humble about how a virus will evolve over time, a significant monkeypox mutation seems unlikely. SARS-CoV-2 is a single-stranded RNA virus — a sloppy replicator with a high mutation rate. Monkeypox, in contrast, is a DNA virus, and does not mutate as freely. Even so, research suggests that monkeypox is mutating much more frequently than expected — 50 times in the past four years, compared to once per year for the average pox virus. So far, it’s unclear if these mutations have actually made monkeypox more infectious, but public health authorities should have contingency plans in place if the strain does mutate into a more contagious or virulent form, and there should be in-depth monitoring of the viral genetic sequence for confirmed cases, as we’ve done with COVID-19.


The monkeypox outbreak may have been preventable. Tests and vaccines were on hand before the outbreak reached US soil, and local authorities were initially slow to respond to demand. Understaffed state and local health departments and a fragmented reporting system has hampered coordination between those authorities and the CDC — and as I’ve said, impeded early attempts to forecast the outbreak.

Despite all this, the monkeypox outbreak has been less severe than I initially predicted. Modeling COVID-19 was difficult for many reasons. The virus continues to evolve. Vaccine efficacy has ebbed with new variants. Our response to the pandemic — human behavior — was perhaps the most difficult variable of all to model. The biggest uncertainty in my model was when the monkeypox outbreak would exit exponential growth, and it happened much earlier than I expected. I attribute that relatively fast decline in cases to the organizing and advocacy of the MSM community. After two and a half years of COVID-19, that sort of unified action was difficult to predict.

  1. Due to lags in reporting, these numbers have been updated since the writing of this article on September 13. As of October 5, updated data show 66 confirmed cases on June 3rd, 1,219 cases on July 3rd, and 9,933 cases on August 3rd.
  2. As of October 4, 873,000 doses have been administered.
  3. As of October 5, the 7-day moving average reported on August 10 was 427; the peak 7-day moving average occurred on August 6 at 441. On September 9, there were 22,843 confirmed cases. The mean 7-day moving average for the month of August was just under 400.

Published November 2022

Jared Leibowich is a forecaster for Samotsvety and the Swift Centre. He placed 1st out of 7,000 for the In the News 2021 Good Judgment competition and is currently ranked 1st for the In the News 2022 competition. He can be reached at jleibowich@gmail.com