Illinois Archives - Matthew Gove Blog https://blog.matthewgove.com/tag/illinois/ Travel the World through Maps, Data, and Photography Tue, 03 Aug 2021 18:08:45 +0000 en-US hourly 1 https://wordpress.org/?v=6.1.5 https://blog.matthewgove.com/wp-content/uploads/2021/03/cropped-android-chrome-512x512-1-32x32.png Illinois Archives - Matthew Gove Blog https://blog.matthewgove.com/tag/illinois/ 32 32 15 COVID-Friendly Landscape Photography Adventures in the Eastern United States https://blog.matthewgove.com/2020/11/02/15-covid-friendly-landscape-photography-adventures-in-the-eastern-united-states/ Tue, 03 Nov 2020 00:06:53 +0000 https://blog.matthewgove.com/?p=1932 As COVID-19 cases continue spiraling out of control in the United States, taking care of your mental health will be critical this winter. One of the best ways to disconnect and escape from all the craziness is to get out in nature. What’s even better, is that you can do […]

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As COVID-19 cases continue spiraling out of control in the United States, taking care of your mental health will be critical this winter. One of the best ways to disconnect and escape from all the craziness is to get out in nature. What’s even better, is that you can do it all while observing the CDC guidelines for COVID safety.

Last week, we looked at 15 COVID-Friendly Landscape Photography Adventures in the Western United States. If you’re on the east coast, it’s your turn today. Let’s look at 15 COVID-friendly adventures in the Eastern United States that are proven to boost your mental health and refresh your soul.

A Word of Caution About Adventuring During the Pandemic

Just because we’re talking about fun adventures today does not mean it’s a green light to let loose. Don’t forget we’re still in the middle of a once-in-a-century pandemic. Please consider the following precautions to ensure your safety during the COVID crisis.

  • Stay close to home and stick to day trips.
  • Only travel with people you live with. This is not the time to invite all of your friends.
  • Obey all state and local COVID-19 restrictions, ordinances, and mandates.
  • Pack food, drinks, and hand sanitizer so you don’t need to interact with the public.
  • Don’t forget to be prepared for non-COVID hazards. Snow and ice can negatively impact many of these adventures.
  • Always check the weather forecast and road conditions when traveling during the winter.

Now, let’s kick those Covid blues and put your mental health on the fast track to happiness.

1. Historic Route 66 – Illinois, Missouri, and Oklahoma

Boost your mental health and soak in the freedom along Historic Route 66.
Heading east on Historic Route 66 near Tulsa, Oklahoma – July, 2013

Is there anything more American than getting your kicks on Route 66? The eastern half of Historic Route 66 runs connects Chicago and Oklahoma City. The route runs along what is currently Interstates 44 and 55. However, you’ll find a much more authentic experience if you get off the freeway and drive the original road.

You’ll find a wide diversity of landscapes along the way. From the rolling hills of eastern Oklahoma to Missouri’s Ozark Mountains to the agricultural plains in Illinois, there is no shortage of great photo opportunities.

2. Tamiami Trail – Florida

Getting on the water is the best way to lift your mental health and soothe your soul.
The Miami, Florida skyline provides a striking backdrop to sailboats racing on Biscayne Bay – March, 2010

Prior to the construction of Interstate 75, the Tamiami Trail was the only route connecting Tampa and Miami. You’ll find the best photo ops as the Tamiami Trail winds its way through the guts of the Everglades. Find a safe spot to pull off on the side of the road. Sit, watch, and enjoy the solitude. You’ll see alligators, birds, fish, lizards, and much more.

In addition, the many parks, preserves, and wildlife refuges on the west coast of the Florida peninsula make for excellent side trips. Just a few of my favorites include the JN “Ding” Darling National Wildlife Refuge on Sanibel Island, Big Cypress National Preserve east of Naples, and and the Terra Ceia State Park and Aquatic Preserve north of Bradenton. On the Miami side, stop off at the Everglades and Francis S. Taylor Wildlife Refuges for additional nature and landscape photo ops.

3. Newfound Gap Road – North Carolina and Tennessee

Lift your spirits with the fresh mountain air of Great Smoky Mountains National Park.
Classic Great Smoky Mountains scenery on the Tennessee side of Newfound Gap – May, 2014

Newfound Gap Road runs through the heart of Great Smoky Mountains National Park. It connects Cherokee, North Carolina with Gatlinburg, Tennessee. Pull off at any of the turnouts to find classic mountain views, lush forest scenery, and refreshing rivers. The best views are at the summit of Newfound Gap, which sits right on the state line. Be aware though, it can be crowded there.

To get away from the crowds, consider hiking a short ways down the Appalachian Trail. In addition to a bit more solace, you’ll get views that most others won’t see. You can also find more great views along the road to Clingman’s Dome. However, Clingman’s Dome can be busy and the road often closes in the winter due to snow and ice.

Please check road conditions before going in the winter. The road is narrow, with many sharp curves and steep switchbacks. The summit of Newfound Gap is over 6,000 feet (1,830 meters) above sea level and often closes in the winter due to snow and ice. If you’re not comfortable driving in snow and ice, I recommend avoiding this route.

4. Kancamagus Highway – New Hampshire

Fall river scenery provides a calming experience along New Hampshire's Kancamagus Highway.
River scenery along New Hampshire’s Kancamagus Highway – October, 2015

The Kancamagus Highway runs through the heart of the White Mountain National Forest in the shadow of Mt. Washington. While northern New England is best known for its spectacular fall colors, the Kancamagus Highway offers beautiful photo ops year round.

While you’re in the area, I also highly recommend driving north up Interstate 93 to Franconia. You’ll be treated to breathtaking views of the White Mountains. On the east end of the Kancamagus, stop and photograph any of the many covered bridges in the Conway area.

For the more adventurous, take a drive up Mount Washington during the warmer months. At the summit, you’ll see where some of the most extreme weather in the world is observed and studied. Scientists measured a wind gust of 231 mph (372 km/h) at the summit of Mt. Washington on 12 April, 1934. That record stood as the strongest wind gust ever measured on earth until the 3 May, 1999 tornado in Oklahoma. Today, it still stands as the strongest non-tornadic wind gust ever recorded.

5. Great River Road – Arkansas and Tennessee

Scenery near the Great River Road in Tennessee.
Scenery near the Mississippi River in Tennessee – May, 2014

Why risk exposing yourself to COVID-19 on one of the Mississippi River cruises when you can drive it instead? While you can drive along the river for its entire length, the best scenery is in Tennessee and Arkansas, with southern Missouri close behind it. Travel at your own pace, stop for some great photo ops, and find a quiet place for a nice picnic lunch along the river.

6. Discovery Route – South Carolina

Drive the Discovery Route across South Carolina and let its southern hospitality boost your mental health.
Calming scenery along the Discovery Route near Charleston, South Carolina – February 2010

Come out and explore everything South Carolina has to offer. The Discovery Route runs from Walhalla, in the far northwest, to Charleston. Along the way, you’ll be presented with photo ops of mountains, oceans, agriculture, rivers, and more. Stop at any of the state’s roadside fruit stands for a treat you won’t soon forget. If you’re there in August or September, South Carolina’s peaches are absolutely to die for.

7. Old King’s Highway – Massachusetts

An on the water view of Nobska Lighthouse in Woods Hole, Massachusetts
Nobska Lighthouse in Woods Hole, Massachusetts – September, 2014

Get an in-depth and hands-on introduction to Cape Cod’s culture, food, and scenery. Starting at the Sagamore Bridge, follow US-6 to its eastern terminus in Provincetown. Get off and explore historic towns on Massachusetts Highway 6A. Pack a picnic and have lunch at one of the Cape’s many world-famous beaches. As an added bonus, Cape Cod is headed into its offseason right now, so you’ll avoid the summer crowds.

The highlight of the drive is the Cape Cod National Seashore. Stop off anywhere on the eastern shores of Cape Cod. You’ll find incredible aerial and beach-level photo ops of the seashore. Taking a calming walk on the beach and enjoying the fresh sea air is a great temporary escape from reality, too.

8. Delaware Water Gap – New Jersey and Pennsylvania

Boost your mental health and find your inner peace on the shores of the Delaware River.
A Tranquil Summer Afternoon at the Delaware Water Gap in New Jersey – August, 2009

The Delaware Water Gap is a breathtaking gap in the Appalachians where Interstate 80 crosses the Delaware River. While the area right around I-80 is popular due to its ease of access, the Delaware Water Gap National Recreation Area extends north most of the way to the New York state line. With so much room to spread out, there is no shortage of spots to tuck yourself away from crowds.

Taking a hike, going for a swim, and enjoying a relaxing afternoon on the boat are just a few of the many outdoor activities available at the Delaware Water Gap. Just choose your side of the river carefully, as river crossings are few and far between. Most of the recreation area is on the New Jersey side of the river, but the main north-south highway is on the Pennsylvania side.

9. Blue Ridge Parkway – Virginia and North Carolina

Does it get any better than crisp air and beautiful mountain views along the Blue Ridge Parkway
Late fall mountain views along the Blue Ridge Parkway in Virginia – November, 2014

The Blue Ridge Parkway is one of the most scenic and well-known drives east of the Mississippi River. Stretching from Waynesboro, Virginia to Cherokee, North Carolina, there are new scenic vistas around every turn. Explore side expeditions including hiking trails, waterfalls, mountain biking, wildflowers, camping and much more.

If that’s not enough, there are national parks at each end of the Blue Ridge Parkway. At its northern terminus, take in the magnificent sights at Shenandoah National Park. At the south end, explore the majestic mountains of Great Smoky Mountains National Park.

10. Rangeley Lakes Scenic Byway – Maine

Views from the Height of Land Overlook are incredibly underrated
Spectacular views from the Height of Land Overlook near Rangeley, Maine – October, 2015

Sitting in western Maine just a stone’s throw from both New Hampshire and Quebec, the Rangeley Lakes Scenic Byway is a true hidden gem. While the scenery is gorgeous any time of year, it is truly exceptional during the fall colors season. Make sure you stop at the Height of Land Overlook and take in the breathtaking views of Lake Mooselookmeguntic.

If you have additional time, find additional scenic scenery on Old Canada Road (US-201). Running from Skowhegan to the Canadian border, there are ample photo ops featuring mountains, rivers, forests, and more. Keep in mind that the US-Canada border is currently closed to all non-essential travel.

11. Panhandle Scenic Drive – Florida

Let the refreshing turquoise waters along Florida's Panhandle Scenic Drive put a smile on your face.
On-the-water perspective along the Panhandle Scenic Drive from Destin, Florida – March, 2012

If you’re looking for a relaxing beach getaway, Florida’s Panhandle Scenic Drive is for you. Take in the ocean, beaches, bays, and bayous as you make your way along US-98 between Apalachicola and the Alabama State Line. Once you get away from the population centers, you’ll pass through marshes, forests, and wildlife refuges.

Don’t be afraid to get off the beaten path a bit. For an even more unique escape, explore some of these areas in a boat. The entire coast of Florida is dotted with small islands that are only accessible by boat. What better way to boost your mental health than spending a day in the fresh salty air, away from civilization.

12. Talimena Scenic Byway – Oklahoma and Arkansas

Give your mental health a lift with crisp fresh mountain air and the best fall color viewing in Oklahoma
Fall colors along the Talimena Scenic Drive in Oklahoma – November, 2013

Stretching across the top of a mountain ridge at an elevation of 2,000 to 3,000 feet, the Talimena Scenic Drive is hands down the best place in Oklahoma to view fall foliage. Listed as one of America’s National Scenic Byways, the 100 kilometer (60 mile) drive winds through the beautiful Ouachita National Forest and the majestic Kiamichi Mountains, connecting Talihina, Oklahoma to Mena, Arkansas.

If you’ve ever driven the Blue Ridge Parkway, you’ll be right at home on the Talimena Scenic Byway. There are stunning aerial views of mountains, valleys, forests, and farmland around every corner. Find a quiet spot to pull off, have a picnic lunch, breathe the fresh mountain air, and watch the world go by. Your mental health will thank you.

Note: The Talimena Scenic Drive is not maintained in the winter. If there are concerns about snow and ice, please consider driving US-59 through the valley instead.

13. Merritt Parkway – Connecticut

The Merritt Parkway is a great getaway from the hustle and bustle of Interstate 95.
Scenery along the Merritt Parkway near Norwalk, Connecticut – August, 2006

You may think it’s hard to partake in COVID-friendly adventures in such a densely populated area that is so close to New York City. Advertised as the Gateway to New England, the Merritt Parkway was the first limited access divided highway in Connecticut. It is one of the oldest scenic parkways in the United States.

Even though there are not a lot of places to tuck yourself away from the crowds, it’s still a great scenic adventure that will give you a great escape from the hustle and bustle of the city.

14. Historic National Road – Illinois, Indiana, and Ohio

The Historic National Road is full of rich farmland, lush forests, and scenic plains.
Rich Farmland near the Historic National Road in Indiana – August, 2019

The Historic National Road is a bit of a journey back in time through the Heartland of America. While you can choose the modern route on Interstate 70, why not break the monotony of the freeway? Much like Route 66, you can still drive the original Historic National Road, US-40, today.

The Historic National Road stretches from St. Louis nearly all the way to Pittsburgh. You’ll get plenty of photo ops as you pass through forests, plains, farmland, small towns, big cities, and much more.

15. Green Mountains Scenic Tour – Vermont and New Hampshire

A scenic drive through the Green Mountains is one of the best in New England.
Soggy Green Mountain Views from Interstate 91 near Newport, Vermont – August, 2019

There’s something special about the tranquility and quaintness of northern New England. That’s especially true in Vermont’s Northeast Kingdom. Start at the Canadian Border in Derby Line, Vermont and wind your way south along US-5. You’ll pass through the heart of northern New England’s rich history and culture.

You’ll have a choice when you get to St. Johnsbury, Vermont. Continue south along US-5 to take in the scenery right along the Vermont side of the Connecticut River. Alternatively, get on Interstate 93, hop across the river, and explore New Hampshire’s beautiful White Mountains and national forests. Rest assured that regardless of which option you choose, you’ll return home feeling relaxed and refreshed.

Note: While the US-Canada border is currently closed, I highly recommend that you go check out the national parks near Magog and Sherbrooke, Québec once the COVID crisis ends.

Conclusion

During the COVID crisis, it’s more important than ever to take care of your mental health. Getting out in the sunshine and fresh air to take in beautiful scenery is proven to be one of the best ways not only to boost your mental health, but make yourself feel good overall. Recharge your batteries and refresh your soul. Take proper COVID precautions, and you should have a fun and safe adventure.

Top Photo: A Sunny Winter Day at Woodneck Beach
Falmouth, Massachusetts – January, 2015

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A Look at the Best-Fit COVID-19 Model Curves for 24 Key States and Provinces https://blog.matthewgove.com/2020/04/15/a-look-at-the-best-fit-covid-19-model-curves-for-24-key-states-and-provinces/ Wed, 15 Apr 2020 23:53:25 +0000 https://blog.matthewgove.com/?p=1194 Below you will find the latest state and provincial projections from the 15 April model run of my COVID-19 model for the US and Canada. I have included states and provinces that are in “hot” areas in both countries, as well as places where I have friends, family, and other […]

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Below you will find the latest state and provincial projections from the 15 April model run of my COVID-19 model for the US and Canada. I have included states and provinces that are in “hot” areas in both countries, as well as places where I have friends, family, and other loved ones. I alphabetized the plots by state or province name. The thick blue line represents the actual or observed data, and the other lines indicate the model predictions.

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

COVID-19 Model: Alberta

Arizona

COVID-19 Model: Arizona

British Columbia

COVID-19 Model: British Columbia

California

COVID-19 Model: California

Connecticut

COVID-19 Model: Connecticut

Florida

COVID-19 Model: Florida

Georgia

COVID-19 Model: Georgia

Illinois

COVID-19 Model: Illinois

Louisiana

COVID-19 Model: Louisiana

Maryland

COVID-19 Model: Maryland

Massachusetts

COVID-19 Model: Massachusetts

Michigan

COVID-19 Model: Michigan

New Jersey

COVID-19 Model: New Jersey

New York

COVID-19 Model: New York

Ohio

COVID-19 Model: Ohio

Oklahoma

Oklahoma

Ontario

Ontario

Oregon

Oregon

Pennsylvania

Pennsylvania

Québec

Quebec

Rhode Island

Rhode Island

South Dakota

South Dakota

Tennessee

Tennessee

Texas

Texas

U.S. Virgin Islands

US Virgin Islands

Washington (State)

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

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Complete Revised SIR Model Forecasts (8 April): USA and Canada https://blog.matthewgove.com/2020/04/08/revised-sir-model-forecasts-8-april-usa-and-canada/ Thu, 09 Apr 2020 00:00:50 +0000 https://blog.matthewgove.com/?p=1098 Here is a full look at the outputs from our revised SIR model. I have included plots from hot spots in both the US and Canada as well as cities where I have friends, family, and loved ones. I can run these simulations for just about any city in the […]

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Here is a full look at the outputs from our revised SIR model. I have included plots from hot spots in both the US and Canada as well as cities where I have friends, family, and loved ones. I can run these simulations for just about any city in the world, so if you have any cities you want to see, leave me a message in the comments or contact me directly.

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
CityState or ProvinceApex DateTotal Cases @ ApexInfected @ Apex
AtlantaGeorgiaLate April to Early May10,000 to 100,00010,000 to 100,000
BostonMassachusettsLate April to Early May50,000 to 200,00010,000 to 50,000
CalgaryAlbertaEarly June10,000 to 100,00010,000 to 50,000
ChicagoIllinoisMid-to-Late April100,000 to 500,000100,000 to 200,000
DallasTexasEarly May100,000 to 500,00050,000 to 100,000
DenverColoradoEarly-to-Mid May10,000 to 100,00010,000 to 50,000
DetroitMichiganMid-to-Late April50,000 to 100,00010,000 to 100,000
EdmontonAlbertaLate May to Early June10,000 to 100,00010,000 to 50,000
HoustonTexasEarly May100,000 to 500,00050,000 to 150,000
Los AngelesCaliforniaEarly May100,000 to 1,000,000100,000 to 500,000
MiamiFloridaLate April10,000 to 100,00010,000 to 50,000
MontréalQuébecLate April to Early May100,000 to 500,00010,000 to 100,000
New OrleansLouisianaMid-to-Late April10,000 to 100,00010,000 to 50,000
New YorkNew YorkMid-April100,000 to 1,000,000100,000 to 700,000
Oklahoma CityOklahomaEarly-to-Mid May10,000 to 100,00010,000 to 50,000
OttawaOntarioMid May50,000 to 200,00010,000 to 50,000
PhiladelphiaPennsylvaniaLate April to Early May50,000 to 500,00050,000 to 100,000
PhoenixArizonaMid May10,000 to 200,00010,000 to 100,000
PortlandOregonLate May to Early June10,000 to 100,0005,000 to 50,000
SeattleWashingtonLate April to Early May10,000 to 100,00010,000 to 50,000
San FranciscoCaliforniaLate April to Early May50,000 to 200,00010,000 to 50,000
TampaFloridaMid-to-Late April10,000 to 100,00010,000 to 50,000
TorontoOntarioMid-to-Late May100,000 to 500,00050,000 to 200,000
VancouverBritish ColumbiaEarly to Mid June10,000 to 100,0005,000 to 50,000
WashingtonDistrict of ColumbiaLate May to Early June10,000 to 100,00010,000 to 50,000
WinnipegManitobaLate June to Early July10,000 to 100,0001,000 to 20,000

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America, Please Don’t Quarantine Yourself From Knowledge https://blog.matthewgove.com/2020/03/18/america-please-dont-quarantine-yourself-from-knowledge/ Thu, 19 Mar 2020 04:32:04 +0000 https://blog.matthewgove.com/?p=975 During one of the New England Patriots’ recent runs to a Super Bowl victory, head coach Bill Belichick put it pretty well: “Do Your Job.” Everybody in the organization, from the owners all the way down to the team’s interns, had a job to do in order for the team […]

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During one of the New England Patriots’ recent runs to a Super Bowl victory, head coach Bill Belichick put it pretty well: “Do Your Job.” Everybody in the organization, from the owners all the way down to the team’s interns, had a job to do in order for the team to win the Super Bowl. Anyone not doing their job is doing nothing but getting in the way of the team’s success.

You can say the same thing about the COVID-19 pandemic. We all have a job to do to beat this thing. Every single one of us. Please use common sense, stay informed, and heed the warnings, guidance, and orders from your local, state, and federal government. Just like Hurricane and Tornado Warnings, there is a reason they are issuing warnings right now. Let’s have a look at why.

A New Type of Model: The SIR Model

Last week, we took a look at modeling the COVID-19 pandemic in the United States using Gaussian functions. Gaussian functions are also known as bell curves. Not surprisingly, there are more accurate ways to model a pandemic like this than with bell curves. Today, we are going to look at different scenarios using the SIR (Susceptible, Infected, Resistant) model. The SIR model is a simple model that uses a system of three differential equations to specifically model disease outbreaks.

SIR Model Differential Equations

The relationship between the equations is:

SIR Model Equation Relationships

Getting into how to solve the differential equations is a discussion for another time. In English, the equations and variables describe:

  • S(t) – The number of susceptible people (people who have not yet contracted the disease) over time
  • I(t) – The number of infected people (people who are currently sick) over time
  • R(t) – The number of resistant people (people who have either recovered or died) over time. The model assumes that recovered people cannot get sick a second time.
    • Note: In the model outputs below, I have broken R(t) down into recovered and dead.
  • β – controls how often a susceptible-infected contact results in a new infection
  • γ – The rate an infected person recovers and moves into the resistant phase

Introduction to R Naught

Now, you’re probably wondering where the “R naught” parameter comes in. R naught, denoted as R0, is the reproduction number. It is just a fancy way to say the average number of susceptible people to which an infected person spreads the disease. For example, if R naught is 3, it means that one infected person spreads the disease to an average of 3 other people over the course of their illness. We’ll define R naught as:

R0 = β / γ

Now, before we jump into the model, let’s have a look at the model inputs. Within the model, we need to define the population N. The population of the United States is about 330 million. We also need to define the average duration of infection, which according to the CDC is about 14 days. The initial conditions for each equation [S(t), I(t), and R(t)] were set so the numbers mirror the actual data of the outbreak in the United States so far.

The only input to the model is the R naught parameter. While we will be running the model for different scenarios, we’ll start with what the US Federal Government currently defines for R naught: R0 = 2.3. Keep in mind that these figures assume R0 is constant, while in the real world R0 is changing constantly.

A Few Short-Term SIR Model Predictions for the United States

First, a couple of short-term predictions from the SIR model, again assuming a constant R0.

United States Forecast with R Naught = 2.3, through early April
United States Forecast with R Naught = 2.3, through mid-May

Before we plot everything out over the course of the pandemic, I need to point out a few very important things:

  • The plot (and the above plots) assumes R0 stays constant at 2.3. In the real world, R0 is constantly changing.
  • Because R0 stays constant, it means that this scenario does not account for preventative measures, such as restrictions on large crowds, restaurant and bar closings, travel bans, and shelter-in-place orders.
  • This is a worst-case scenario and the odds of this actually playing out are very slim.
SIR Model Forecast for the United States, with R Naught = 2.3

Flattening the Curve

Flattening the curve. You hear it all over the news. What does it mean? If you leave the virus unchecked, it will grow exponentially and quickly overwhelm the hospital system when all of the sick patients show up at once. Instead, health authorities want to slow down the rate the disease is spreading and spread the sick patients out over time so hospitals can handle the volume of patients.

So how do we slow down the rate the disease is spreading? Simply lower the value of R naught. Okay, in the real world it’s quite a bit more complicated. Federal, state, and local governments across the country are putting measures in place to slow down the spread of the virus and reduce R naught, which may include:

  • Bans on large gatherings
  • Quarantines and Self-Isolation
  • Closing of schools, restaurants, bars, museums, and other public places where people tend to gather
  • Cancellations of Events
  • Closing Borders and Travel Bans
  • Shelter In Place Orders and Lockdowns

Still don’t believe me that flattening the curve works? Have a look at the following figure. I ran the SIR model several times with identical parameters, only varying the R naught values. Like the above examples, R naught remains constant for each run. These are just hypothetical scenarios and are not any kind of indication that anything like this will actually play out in the real world.

SIR Model for different R Naught scenarios in the United States

By reducing the R0 value from 2.6 down to 1.6, the number of infected people at the peak of the outbreak drops from 80 million down to about 25 million. For those of you that are mathematically challenged, that’s about 2/3, or 67% fewer infected people at the peak of the outbreak.

Modeling the Changing R Naught Values

The easiest way to model the changing R naught values is to use piecewise functions to solve the differential equations. That just means we will assign different values of R naught for different values of time (t in the differential equations at the top of this post). If you’ve ever done numerical analysis or numerical integration, you’ve probably come across piecewise functions at some point, but that’s a discussion for another day.

So how does this all translate to the real world? Consider a scenario that we’ve seen in a lot of countries so far in this pandemic. The virus spreads undetected within the community at the start of the outbreak. Then, federal, state, and local authorities put increasingly restrictive measures into place. Restrictions start with bans on large gatherings. They then escalate to closing down restaurants, bars, and other public places. Finally, officials order a mandatory shelter-in-place or lockdown.

To illustrate this visually, I modeled a hypothetical scenario where the virus starts with R0 = 2.3. It spreads undetected for about 45 days at the onset of the outbreak. The government orders restrictions, scaling down R Naught until the issuance of a shelter-in-place order. In this scenario, it takes about a month to go from issuing the first restriction to a full lockdown. In the real world, the restrictions are implemented much faster than that. For example, it took Italy 12 days to go from just a handful of cases to the entire country under lockdown. It took Spain 9 days to do the same.

SIR model of a possible COVID-19 outbreak in the United States with vs without preventative measures

Looking at the Real World

This is where it gets tricky. Because the United States is so big and diverse, let’s look at ten major cities instead. Different states, counties, and cities have enacted different bans to combat the virus, making it nearly impossible to accurately use this model at a national level. For example, the shelter-in-place that was just issued for the San Francisco Bay area is not going to affect what’s going on in Seattle, Chicago, or New York.

A Few Things to Keep in Mind

  • These models consider the population of each metro area, which include the main city plus all of its suburbs.
  • The R0 values on the plots are fixed for each run. In the real world, the R0 values will start high and then drop as restrictions are enacted.
  • The high number of undetected or asymptomatic cases will help keep the R0 value of COVID-19 high.
  • The “Peak” label in the legends refers to the number of infected people at the peak of the outbreak for that scenario.
  • You want to focus on the number of infected people at the peak of each scenario. Do not worry about the exact dates of the peaks of the outbreaks.
    • As you look at those peak values, think of how you can help with social distancing to reduce R0.
  • The current R0 value of the coronavirus in the United States is about 2.3, according to the federal government. That means that every infected person spreads the disease to an average of 2.3 other people. For comparison, the seasonal flu has an R0 value of 1.3.
  • I don’t know what the hospital capacity is in each city, but for reference New York State (read: the whole state, not just NYC) has 54,000 hospital beds and 3,100 ICU beds.
  • When the city of Wuhan, China enacted their total lockdown in January, the R0 value dropped from 2.35 to 1.05 in less than a week. You won’t see R0 drops this drastic in the United States. However, the goal to get R0 as low as possible remains the same.

SIR Model Outputs for Several US Cities

COVID-19 Forecast for Seattle, WA
COVID-19 Forecast for San Francisco, CA
COVID-19 Forecast for New York City, NY
COVID-19 Forecast for Boston, MA
COVID-19 Forecast for Chicago, IL
COVID-19 Forecast for Los Angeles, CA
COVID-19 Forecast for Phoenix, AZ
COVID-19 Forecast for Dallas, TX
COVID-19 Forecast for Miami, FL

Conclusion

For this pandemic, I will say the same thing I say before just about every major weather disaster. Please heed your local, state, and federal government’s warnings. I can’t stress this enough. In a weather disaster, you’re only putting your own life at stake by being stupid. In a pandemic, you’re putting the lives of every one else who’s around you at stake as well.

I understand we are a society that rewards stupidity. If we all work together, there is still time to slow this thing down, but that window will slam shut in just a matter of a few days. All quarantining yourself from knowledge and common sense does is keep that critical R0 value high and put more lives at risk. I’ll leave you with one final plot of COVID-19 data comparing the US cases to Italy’s. This is actual data and is not generated by any models. Stay tuned for more updates.

The post America, Please Don’t Quarantine Yourself From Knowledge appeared first on Matthew Gove Blog.

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