Problem I. 143. (November 2006)
I. 143. The spread of an epidemic in a city of population 0<V<1 million is modelled. The following is known about affected people:
- the latency period is 0<L<15 days during which infected people are asymptomatic and do their daily routine work
- infected but still asymptomatic people meet other people, so each infected person infects 0<F<10 other people each day on the average, who should be considered infected from the next day
- after the latency period, each infected person stays at home for 0<B<15 days and avoids contact with others
- once a patient is recovered, he or she begins working again, but can not infect others and can not be infected in the future
- the epidemic originated from a single person, entering the city on the first day of the latency period (that is, he or she was infected on the previous day)
- sooner or later everyone in the city gets infected. The epidemic ends when everyone is recovered.
Prepare your spreadsheet with input parameters V, L, B and F
- giving the number of days (J) the epidemic lasted
- giving on which day (O) the city had the maximum number of infected people, and how many of them (H) stayed at home then
- plotting the number of latent, ill and recovered people, in the same diagram, from the outbreak to the end of the epidemic.
The spreadsheet in default format and with default extension (e.g. i143.xls, i143.xsc, ...) should be submitted.
One of the sheets should contain
- the names and modifiable values of the parameters of the epidemic in cells A1:B4
- the answers to the questions above in cells C1:D3
- other cells should contain the actual computations.
Another sheet should contain a diagram showing the evolution of the epidemic.
Deadline expired on December 15, 2006.
Sorry, the solution is available only in Hungarian. Google translation
20 students sent a solution. 10 points: Balambér Dávid, Czigler András, Fehér András, Györök Péter, Kiss Dániel Miklós, Kovács 129 Péter, Ócsvári Ádám, Ridinger Tamás, Szoldatics András, Véges Márton, Vincze János. 9 points: Gombos Gergely, Polgárfi Bálint. 8 points: 1 student. 7 points: 1 student. 6 points: 1 student. 5 points: 2 students. 2 points: 1 student. 1 point: 1 student.