Table of Contents

• Section 1. Frank's Story
• 1: The story
• 2: Biological interlude
• Section 2. How the meningitis population grows
• 3: How many meningococci can kill you?
• 4: Build the basic growth equation
• 5: Draw exponential growth
• Section 3. So why isn't Frank dead already?
• 6: How long has poor Frank got?
• 7: All we need now is data
• 8: Looking at data
• 9: Log transform straightens out exponential growth
• 10: Do ALL curves get "straightened" by taking the log?
• 11: Phases of bacterial growth
• Section 4. How can we tell when the population is growing exponentially?
• 12: A test for exponential growth
• 13: And the answer is...
• 14: No way its growing that fast!
• 15: Some more practice
• 16: In search of ... the exact doubling time
• 17: Finding doubling time with messy numbers
• 18: Logs = Exponent-busters
• 19: Let's bust some exponents
• 20: Let's bust some exponents
• 21: Extended problem #1: Exponential growth ends (with a whimper)
• Section 5. Back to Frank
• 22: Extended Problem #2: How long DOES poor Frank have?

The story...

Frank was a college sophomore.  He lived in the dorm, and aside from being a pretty good student, he was an avid sports fan- both watching and playing.  He and his roommate Sven often took a study break on Saturdays to play some kind of game.  Sven, who came from Sweden, loved to play soccer.   Frank played football in high school, but he was pretty much game for any kind of sport.

One sunny Sunday right after lunch, Frank and Sven decided to organize a pickup game of flag football.    They got enough guys to agree to play, and it turned out to be a really competitive game.  After about ten minutes of play, they all agreed to take a quick water break.  Frank reached for his bottle of water, glad that he had been careful to write his name on it with a Sharpie this week.  Last week he had chugged down the remains of Sven’s water, pouring a little bit on his head and face to cool down, before he realized his mistake.  He was a little grossed out, but fortunately Sven was a pretty healthy guy and didn’t have a cold or the flu.

The next play was a long pass, and several of the players on his team went flying down the field to catch it.  Unfortunately Frank was paying so much attention to the trajectory of the ball that he didn’t notice the other guy’s elbow until it connected with his nose.    They made Frank lay down so that they could get the bleeding stopped, and then made sure his nose hadn’t been broken.  Frank decided he’d better take it easy the rest of the day, so he headed back to his room to lie down.  Sven went along just to make sure Frank was OK.  After about half an hour, Frank fell asleep.

Sven woke him up at six o’clock so that he wouldn’t miss dinner.  Frank went to dinner despite the headache.  He realized he’d been clocked pretty hard, so he wasn’t surprised at either the headache or the bruises that were beginning to show on his face.  He ate his dinner, then went back to his room, took a couple of aspirin and made it an early night.

At about three o’clock in the morning, Frank woke up feeling worse.  He was feeling feverish, which was confirmed when Sven put a hand on his forehead and told him he felt really warm.  The medical center didn’t open until seven the next morning, so Frank figured he’d have to wait a few hours before he could see a doctor.  When he sat up he noticed that his neck was really stiff. 

He thought it might be a good idea to check out the internet to see if he could get some advice on how to treat this until he could get some help at the medical center, so he had Sven bring up WebMD on his laptop.  He typed in “headache stiff neck fever” to search for his symptoms.  The first hit to come up was “Neck Problems and Injuries”.  He hadn’t really considered that he might have hurt his neck in the collision, but that was certainly a possibility, so they clicked on the link.  It said that you could get an acute neck injury from falling or sports accidents, so Frank lay back down, thinking maybe this was all much more serious than he had thought, and that maybe he should call an ambulance.

Of course, it was likely that if it was a neck injury at all, he probably had just sprained or strained something since it took so long to develop, so he stopped panicking.  Sven kept reading the article, and on page two of that entry it gave other possible causes of the headache and stiff neck.  They quickly ruled out arthritis- Frank was only 19 years old and arthritis doesn’t have a sudden onset like this.  The next choice was meningitis, but Frank had gotten the meningococcal vaccine before he came to campus.  Another choice was the flu, but his headache had came on much more suddenly than the flu usually does, and nobody on their floor was sick.  Convinced it was just a response to the collision, they waited a few hours and headed for the medical center.

By the time Frank got to the medical center, he started to notice a splotchy rash forming all over his body.  He was starting to feel dizzy, nauseous, and the lights were starting to bother his eyes.  He pulled his jacket over his head until it was his turn to be seen by the doctor.   After telling the doctor the list of symptoms, and explaining the really nasty bruise on his face from the collision and nosebleed, the doctor asked if he had had the meningococcal vaccine.  When he said that he had, the doctor asked him if he had close contact with anybody from another country.  He pointed out that his roommate and best friend came from Sweden.

The doctor immediately prescribed penicillin and got Frank admitted to the hospital for treatment of meningococcal meningitis.  Frank was pretty confused as to how he could get meningitis when he’d had the vaccine, but while the paramedics were getting Frank prepared for transfer to the stretcher, the doctor explained that there are several "serogroups" of the bacteria that cause meningococcal meningitis, and that not all of them are covered by the vaccine.  In fact, a form that is common in Sweden, serogroup B, is not covered by any currently available vaccine.