There are only 4 people in my math C class, including my teacher. We were given the question below and asked to find the answer, unfortunately we all have different answers. What is the answer to the following question?
A contagious virus infection is incurable and proves fatal 4 weeks after exposure. A person exposed to the virus becomes contagious agter 2 weeks. Each virus sufferer infects just one person each week during the contagious period. One just-infected person introduces the virus to Australia. How many people will be infected by the virus after 20 weeks.
As it is ambiguous whether or not another is infected at the start or end, both scenarios should be created (start of week and end).
A preferable answer would contain both the total amount deceased and the current amount of infected people.
We start in week 1 with the one newly-infected person. In week 2 we still have just that one infected person.
In week 3 the models start to diverge. For the "start of week" model, we still have the first infected person, but this is also the first full week of infection for a second person.
After that, at the start of each week one new individual is infected for each one who was infected just two weeks previously, and one for each who was infected just three weeks previously. So week number $n$ is the first full week of infection for $a_n$ individuals where $a_n = a_{n-2} + a_{n-3},$ $a_1 = 1,\ a_2 = 0,$ and $a_3 = 1.$ This is Sequence A182097 from the On-Line Encyclopedia of Integer Sequences.
For the "end of week" model, it takes exactly one week longer for each new infection to contribute to the total, that is, we have $b_n$ newly-infected individuals in week $n$ where $b_1 = 1,\ b_2 = b_3 = 0,\ b_4 = 1,$ and $b_n = b_{n-3} + b_{n-4}$ for $n > 4.$ I did not find this sequence in the OEIS.
Either recurrence can be solved by brute-force calculation for the first $20$ weeks. For the first model, the total number of individuals that have been infected (either still living or dead) at any point during that week is $\sum_{n=1}^{20} a_n,$ whereas the number who have died is $\sum_{n=1}^{16} a_n.$ The number still alive is $a_{17}+a_{18}+a_{19}+a_{20}.$ For the second model, simply use $b_n$ instead of $a_n$ in these calculations.
This math problem has an uncomfortable relationship to current events.