I only ran the models out until early May because we need to focus on what’s going to happen in the next two to three weeks, not what’s going to be happening several months in the future. Additionally, model forecasts get less accurate the further into the future you go. This run assumes current social distancing restrictions remain in place through mid-May and does not account for any additional surges or waves of the virus that may occur later this spring, this summer, or this fall.

Don’t forget, you can always get more information about the model and view detailed case data on my COVID-19 Dashboard. Additionally, I will write up a separate post about the mathematics, equations, and methodologies used in my coronavirus model, which I’m hoping to get posted in the next day or two. Stay tuned for additional discussions about each hot zone as more data comes in.

Alberta

Arizona

British Columbia

California

Connecticut

Florida

Georgia

Illinois

Louisiana

Maryland

Massachusetts

Michigan

New Jersey

New York

Ohio

Oklahoma

Ontario

Oregon

Pennsylvania

Québec

Rhode Island

South Dakota

Tennessee

Texas

U.S. Virgin Islands

Washington (State)

After several requests, I updated this post on 16 April, 2020 to include additional states and provinces, bringing the total to 26 plots instead of 24.

Top Photo: Palo Duro Canyon State Park – Amarillo, Texas – August, 2019

The post A Look at the Best-Fit COVID-19 Model Curves for 24 Key States and Provinces appeared first on Matthew Gove Blog.

Overview of SIR Model Output

Each city has four plots. The top row is the “working” model output, with the model curve best fit to the actual data. The bottom row is an experimental model output showing the effect of social distancing. In the “working” model runs on the top row, there are 5 lines on each plot. The middle line is the R Naught value that was reverse-engineered by fitting the model output to the actual data, and there are two lines on each side of the best-fit line showing different R Naught values in steps of 0.2.

Note: The y-axis on some of the experimental social distancing plots showing the total case count (bottom right plot for each city) is mislabeled. It should read “Total Cases”, not “Number of Infected”.

Finally, don’t forget that the plots below assume the R Naught values and the amount of social distancing remains constant throughout the entire time series. In reality, additional social distancing restrictions will dampen the curve and shift it to the right, while removing social distancing restrictions will cause the curve to accelerate and shift to the left.

Confidence in SIR Model Predictions

My confidence level in the “working”/top row model outputs is as follows:

• Predicting the apex of the outbreak: medium-high to high. The curves should at least be “in the ballpark.”
• Predicting the total number of cases: low to very low. With how fast things are changing right now and how fast new data is coming in, we just don’t know at this point. My gut feeling is that the case count projections in these model runs are likely high overall, but from a public health perspective, I would much rather have the model overestimate case counts than underestimate them.

Plots are in alphabetical order by city, with a table of additional cities at the bottom. Click on any plot to view it full size.

Boston, Massachusetts

Chicago, Illinois

Detroit, Michigan

Los Angeles, California

Montréal, Québec

New Orleans, Louisiana

New York, New York

Oklahoma City, Oklahoma

Ottawa, Ontario

Portland, Oregon

Phoenix, Arizona

San Francisco, California

Tampa, Florida

Toronto, Ontario

SIR Model Outputs for Additional Cities

Please note that this table contains outputs of just this single model run and does not necessarily reflect what my actual predictions are. I will be putting this table on my COVID-19 Pandemic Tracker later this week and regularly updating it there.

Data points I’m skeptical of in this output (with some comments):

• Chicago, IL: Case count is likely overestimated. I’m not sure why, but the most likely reason is good social distancing.
• Los Angeles, CA: Case count is likely overestimated due to California being better at social distancing than what was input into the model
• Seattle, WA: Peak date is incorrect due to the State of Washington’s 100th case occurring before John’s Hopkins began breaking down data by state.
• Washington, DC: Not enough data to accurately fit the curve
• Winnipeg, MB: Not enough data to accurately fit the curve

The post Complete Revised SIR Model Forecasts (8 April): USA and Canada appeared first on Matthew Gove Blog.

Disclaimer: As I’ve mentioned many times before, I claim zero knowledge about anything in the medical field, including infectious disease. These analyses are based solely on my expertise in mathematical modeling.

An Important Note on Making Predictions From Mathematical Models

One of the most common uses of mathematical models to make predictions in day-to-day life is weather forecasting. Luckily, meteorology happens to be a field in which I do have extensive knowledge. When forecasting any type of weather, it’s important to look at multiple models. Do not make any predictions based solely on any one model. In an ideal world, the models are all in agreement. In reality, you need to use your knowledge and expertise to gauge how much weight to give each model when you make your prediction. The same principle applies to the current pandemic.

Additionally, from a purely mathematical standpoint, all outbreaks follow roughly the same bell-shaped curve when plotted over time. Different types of outbreaks can use vastly different equations in their models. While I do not have much experience with outbreaks of infectious disease, I have worked with and extensively studied outbreaks of tornadoes and severe weather during my time as a meteorology student at the University of Oklahoma. We can apply that knowledge when making predictions about the current COVID-19 outbreak.

Adding a Social Distancing Factor to the SIR Model

I have been running a lot of possible scenarios in Python using the Susceptible – Infected – Removed, or SIR model. I recenly covered the mathematics of the model, so I’m not going to state all of that again. You just need to know that the model is based on a system of three ordinary differential equations.

With the help of my uncle, who also has a lot of experience with mathematical models, we set out to add a parameter, which we’ll call f, to the SIR model. f represents the percentage of the population who are strictly complying with social distancing guidelines.

Accounting for Social Distancing in the Model

To incorporate f into the SIR model, we need to look at the terms that are modeling the contacts between the infected and susceptible people. The rate of contact would be reduced by (1 – f)² because the fraction of both the susceptible and infected population interacting would be reduced by a factor of (1 – f). The removed (recovered/dead) population would not be affected by the social distancing parameter. Therefore, the differential equations for the susceptible and infected population would then become:

We are still working on fine-tuning these equations, but this is what we’re going with for now.

Estimating a Baseline Infection Rate

The final piece of the puzzle is to set the baseline for beta. That baseline is the infection rate assuming 0% social distancing compliance. In other words, beta is the number of infecting contacts per day between an infected and susceptible person. Beta is also part of the equation that calculates R Naught.

Since I only plan to model the effect of social distancing at the city level, I simply scaled beta based on the city’s population density to set the baseline infection rate. Cities with higher population densities would have a higher rate of infection than those with lower population densities. COVID-19 is spreading much faster in New York or Chicago than it is in Topeka, Kansas or Bismarck, North Dakota.

The scaled baseline for the infection rate at 0% social distancing compliance is simply:

where d is the population density in units of people per square kilometer. The “plus one” is because some small cities in Alaska have population densities of less than 10 people per square kilometer. Low population densities result in very small and unrealistic beta and R Naught values. It’s not an exact science, so the equation will be tweaked as we go along.

Limitations of the SIR Model

Not surprisingly, mathematical models are only as good as the assumptions that they make. The COVID-19 models make plenty of them. Some of the assumptions and limitations the SIR model (plus our revisions) make include, but are not limited to:

• Uniform population density across the entity being modeled. This means the SIR model predicts outbreaks in individual cities much more accurately than it does in states and countries.
• Population remains constant – i.e. people are not being born or dying of causes other than the disease. The SIR model has terms to account for birth and death rates, but its effect on the model is negligible. I don’t have birth and death rates in my database, so we will simply set those terms to zero.
• R Naught and the percentage of people social distancing are constant throughout the outbreak of the disease. This can cause both the peak of the outbreak and the date of that peak to be either over- or under-estimated.

Outputs From Our Revised SIR Model

We now have enough data from the United States, Canada, and Australia. Let’s fit the model output to each state’s existing curve. We can then use that output to model major cities in each state.

I’ve included model outputs from a few cities in the United States, and will include more in a separate post. When looking at the model outputs, you want to focus on general trends. Do not look at specific dates or case counts. Instead, focus on something happening in periods such as “mid-April” or “early May” instead of “April 15th” or “May 1st”.

Our Revised SIR Model’s Assumptions

Don’t forget that our revised SIR model assumes a constant level of social distancing. We are just starting to see the effects of stricter social distancing show up in the data set. As a result, the model will likely underestimate the amount of social distancing being done. Therefore, it will overestimate the number of cases. I’ve included curves for several R Naught values both less than and greater than the R Naught values that I reverse engineered by fitting the model curve to the existing data.

The revised SIR model seems to do a decent job predicting the apex of the outbreak. I have checked the apexes on the first plot you see below in each city against what health officials in Arizona, New York, Michigan, Massachusetts, and Louisiana have said. They’re at least “in the ballpark” with what health officials are saying. The social distancing plot is primarily to drive home the importance of social distancing and flattening the curve during the pandemic.

Speaking of social distancing, don’t forget about assumptions. The plots below assume the amount of social distancing remains constant throughout the entire time series. In reality, additional social distancing restrictions will dampen the curve and shift it to the right. Removing social distancing restrictions will cause the curve to accelerate and shift to the left.

Confidence Levels in the Model

My confidence level in these model outputs is as follows:

• Predicting the apex of the outbreak: medium-high to high. The curves should at least be “in the ballpark.”
• Predicting the total number of cases: low to very low. With how fast things are changing right now and how fast new data is coming in, we just don’t know at this point. My gut feeling is that the case count projections in these model runs may be high. From a public health perspective, I would much rather have the model overestimate case counts than underestimate them.

With regards to the projected case counts, look at the how the University of Washington model has been all over the place over the past week. That is how the model tells us it doesn’t know. We can’t make any meaningful forecasts from it at least until it starts to stabilize from day to day. This would be like trying to make a forecast and issue warnings for a hurricane using a model that keeps flip-flopping between the hurricane making landfall in Houston and making landfall in Miami.

View the full output from our revised SIR model for most major cities in the United States and Canada.

New York, NY

New Orleans, LA

Detroit, MI

Plots for additional cities will be posted in a separate post.

Looking at the University of Washington Model

A model developed by the University of Washington has made headlines over the past several weeks. It is one of the most trusted models out there for predicting the pandemic (at least in the United States). However, I worry that too many people are focusing only on this one model and are not considering what other models are forecasting.

Like every model, the University of Washington model makes its fair share of assumptions:

• The model accounts for social distancing restrictions, such as closing businesses and schools and issuing stay-at-home orders. However, it does not address how social distancing restrictions are lifted. It assumes that Americans continue to practice full social distancing practices through at least sometime between June 1 and August 1.
• The model does not account for any resurgences or additional waves that may occur later this summer or fall.
• The model does not account for hospital staff shortages due to being out sick, running out of supplies, or any other reason.
• It is also important to note that the University of Washington model forecasts deaths and hospital usage. It does not predict the total number of cases.

I believe that this is probably the most accurate model out there right now. My gut instinct is that because of the assumptions, it may slightly underestimate both the hospital needs and death counts.

Also note that the plots below are for hospital needs. It looks like 20 to 25 percent of all COVID-19 cases require hospitalization. Multiply the y-axis values by 4 to 5 to get the approximate number of cases the model is predicting.

My Predictions

Because of the fluidity of the situation and how fast everything seems to be changing, focusing my predictions on exact numbers will only contribute to the spread of misinformation. Instead, I will be focused on general trends, as I discussed earlier. These predictions are based on the two models I discussed in this post, as well as several others.

Expectations for the United States and Canada

• Nearly every city and state in the United States will reach its apex within the next 4 to 5 weeks. I’m still working on projections for Canada.
• At the end of the pandemic, total case counts in every major city in both the US and Canada will be in the tens of thousands, if not more. New York City is currently just shy of 80,000 cases.
• Total or cumulative case counts for the both the United States and Canada will be in the millions. I think Canada can still keep their case count below 1 million with proper social distancing. That ship has long since sailed for the US.
  • For perspective, let’s use the Centers for Disease Control’s recent prediction of 80,000 deaths in the United States. Using the current death rate based on data from the past week, it works out to about 2.5 to 3.5 million total cases in the US.
  • In Canada, the Government of Ontario recently released a study projecting at least 15,000 deaths in the province. Using the same calculation as above, that works out to 500,000 to 750,000 cases in Ontario alone.
• New cases will be reported in both the US and Canada every day through at least late June/early July. Expect government mandated social distancing protocols to remain in effect through at least the end of May in most states/provinces. These restrictions include stay-at-home orders, closures of restaurants, schools, and other places of gathering, etc.
• The outbreak in Canada will have a flatter curve and grow slower than the outbreak in the United States. As a result, Canada will peak later than the outbreak in the US.
• Don’t forget that like weather forecasting, the models get less accurate the further into the future you get. I will be posting routine updates as new case data comes in.

One Final Thought

When a hurricane makes landfall, it ravages the coast with the eye wall – the most powerful part of the storm – before the calm of the eye passes over. Inside the eye, winds drop down close to zero, the sun comes out, and it looks like a beautiful day. In the first half of the 20th century, before weather radar became mainstream, coastal residents commonly mistook being inside the eye to mean the storm was over. They then went back to their normal lives. As a result, they were then blindsided when the back side of the eye wall came ripping ashore like a buzzsaw. They didn’t realize that they still had the whole second half of the hurricane to go. Such a mistake undoubtedly caused numerous injuries and deaths that should have been preventable.

Don’t Repeat Past Mistakes

I am a bit concerned that a lot of people will be making the same mistake by going back to their normal lives once their city and state hits the apex of the pandemic. Like the eye of a hurricane, the apex is only the half-way point. You still need to come down the back side of the curve. Look at any of the plots above. In fact, the apex is likely not even the half-way point. It almost always takes longer to come down the back of the curve than it does to go up the front of it. Expect the Stay at Home orders to remain in place for at least 4 to 6 weeks after your state passes its apex. We will likely be into June before we can even begin to think about going back to our normal lives.

Look, I understand the cabin fever is real. You want to go see your friends and loved ones. Be patient and be smart. We don’t need any more people dying from this virus than already are.

The post Latest SIR Model Outlooks: COVID-19 Pandemic appeared first on Matthew Gove Blog.

From Indianapolis, I set my sights on crossing the border into Canada for my second stopover of the trip. I’ll be spending a few days at my uncle’s house in Washago, Ontario, which is near Toronto. My original plan was to not have to cross the border on the weekend. Alas, it was a Sunday and I wasn’t about to wait around in Indianapolis. I got off to an early start to avoid getting caught in traffic. Many weekend warriors return home from Canada on Sunday afternoon. My Global Entry card allows expedited entry into the US, but does not get me anything crossing the border into Canada.

The Detroit-Windsor Border Crossing to Canada

The most direct route to my uncle’s house is to cross from Detroit, Michigan into Windsor, Ontario. That crossing is one of the busiest ports of entry on the entire US – Canada border. After crossing from Ohio into Michigan, it felt like it took forever getting up to Detroit, despite it only being about 45 miles. All while watching the wait times on the CBSA (Canada Border Services Agency) website get longer and longer.

The Ambassador Bridge is the direct link between I-75 in Michigan and the 401 in Ontario. By the time I started coming into the southern suburbs of Detroit, the wait at the Ambassador Bridge was close to an hour and a half going into Canada.

Time to go to Plan B: the Detroit-Windsor Tunnel

I was very happy, and a bit surprised, to see that the wait times at the tunnel were only about 10 minutes. The route to the entrance to the tunnel is disturbingly well signed. Navigating the streets of downtown Detroit was a breeze. After a short jaunt through the tunnel (a little under 1 km), you pop out in another country.

Fun Fact: The Detroit/Windsor border crossing is the only spot on the main part of the US – Canada border (i.e. excluding Alaska) where you can go south from the US into Canada

What to Expect at Canadian Customs

The process for entering Canada is very similar to entering the US. Restrictions on what you can bring into Canada are very similar to what you can bring into the US. When you pull up to the primary checkpoint, give the CBSA agent your passport. US passport cards also work entering Canada at land and sea ports of entry. Answer their questions truthfully, and be transparent. Don’t try to hide anything. Some things they may ask about include, but are certainly not limited to:

• The purpose and duration of your visit to Canada; where you plan to go
• If you’re carrying meat products or fresh produce
• If you’re carrying any weapons (guns, knives, etc) or drugs
• If you’re carrying any alcohol
• If you have medication or prescription drugs
• Do you have any past criminal convictions? If the answer to this question is yes, you will likely be denied entry into Canada unless you file the proper paperwork ahead of time

Onward into Canada

After a short 10 or so minute wait in line and a brief, friendly stop at the primary customs checkpoint, I was on the streets of Windsor. I ended up leading myself a bit astray trying to get around a couple street closures. When you leave the customs area, you’re actually facing back towards Detroit. I didn’t realize that, but I quickly got my bearings straight. Once I put the Detroit skyline in the rear view mirror, it was a quick and painless drive to get out to the 401.

Other than a half-hour delay due to an accident in a construction zone, I had a smooth run up the 401 to my uncle’s house. That accident was amazingly the only slow-down on the entire trip, other than a few short at customs. I know my uncle has some hiking and canoeing planned and I’m really looking forward to being able to do it when everything’s not buried under 2 feet of snow.

Funny Addendum to this Leg of the Trip

One pattern I noticed on this trip is that whenever I crossed an international border, something really funny and unexpected happened. This one happened at the first gas station I stopped at in Canada. I swiped my credit card at the pump and entered my zip code. I was getting ready to select the fuel type and put the nozzle in the filler to fill the tank when the pump asked another question that caught me completely off guard.

How much fuel do you wish to purchase?

The kicker was that you could only select a dollar amount, you couldn’t select a volume. And there was no “Fill It Up” option. Now I start doing the math in my head that I’ve done time and time again. The tank was a little over 1/4 full. I knew pretty much the exact number of gallons I needed to fill it up. From there, it’s easy to figure out how many dollars it is.

The Metric System Unexpectedly Got the Best of Me

I looked up at the price on the electric sign in front of the gas station and it immediately dawned on me that my math had gone awry. Oh crap, I’m in Canada. Those prices are in liters, not gallons. I start to do the conversion in my head. By now, it had thrown me enough curveballs to slightly knock me off my game. I’m trying to do the (very) approximate conversion of 1 gallon = 4 liters minus a little bit in my head, but the numbers just weren’t coming out right. For some reason the fact that I was paying in Canadian Dollars instead of US Dollars thre my logic off. The currency type was irrelevant because it stayed the same throughout the calculation.

Now, here’s where the rational person would pull out a calculator to do the conversion, but I don’t admit defeat that easily. After a few more attempts at the conversion and getting unnecessarily thrown off by an exchange rate that I didn’t know (or need), I got a number that sort of made sense and sort of didn’t. I had been on the road all day (remember this day started back in Indianapolis) and eventually just said “Screw It” and picked my best guess at the dollar amount: $50 Canadian.

It’s Better to Be Lucky than Good

After pumping the gas and completing the transaction, I got back in the truck to see how I did on the calculation. Much to my surprise, I absolutely nailed the guess. The needle on the fuel gauge was just above “F”, prompting a quick impromptu celebration before getting back on the road for the last few kilometers to my uncle’s house. The ensuing times I bought gas in Canada on this trip I came in “guns-a-blazing” and ready to do the math correctly. I was both happy and a tad disappointed when I discovered those pumps all had a “Fill It Up” option.

The post Crossing the Border into Canada: What You Need to Know appeared first on Matthew Gove Blog.