On April 27, 2009, 18 cases of the flu virus, influenza A (H1N1), were detected

Question

On April 27, 2009, 18 cases of the flu virus, influenza A (H1N1), were detected by medical officials. A 'case' is when a person shows symptoms that occur four days after initial contact with the virus. 28 days after April 27 the number of detected cases per day was 541. The relationship between time (t, in days since the first person showed symptoms, independent variable) and the number of new cases per day (N, depender variable) was established to be linear on a log-log scale with a slope of 1.8. Write out the equation with values for slope and intercept. Identify which paramete are time, number of new cases per day, slope, and intercept. Give units for all parameters. What was the date that the first person came in contact with the virus? Assuming that the infection rate continues at the same rate, how many years after April 27, 2009 (to three decimal places) will it be when 1,000,000 cases a day are reported?

Explanation / Answer

x^7 = 541; x=2.46; Initially one person had the virus on on 21st Apr 2009. He gave to x persons. These x people showed the symptoms after 4 days on 24rd April 2009. Again these x people gave the virus to x persons . So, ()2 person will show the infection symptoms on 27th April 2009. These were further pass on infection to () persons each, who will show symptoms on 30 th April 2009 ()3. After 28 days 7 cycles will pass by. So, number of persons having the infection will be x^7 =541;

x = 2.46. This means initially one person gave the virus to 2.46 persons

The equation can be written as :- Final no. of people having the infection (X) = initial no. of people (x)time(t)/gestation period of virus(g)

lnx (X) = t/g

b) 21st april 2009

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