To find the percentage of the original population that will die from the infection in four months, an iterative calculation shows that approximately 63.6% of the population will succumb to the disease.
To calculate the percentage of the original population that will die in the next four months, we can break it down month by month. Initially, everyone is healthy, so the first month, 80% become ill and none die because the death rate only applies to those who are already ill. The second month, 80% of the remaining 20% healthy individuals become ill (which is 16% of the original population), while 30% of the previously infected 80% die. This process is repeated for four months.
First month: 0% die, 80% ill
Second month: 30% of 80% die, 16% more become ill
Third month: 30% of the remaining ill (96%) die
Fourth month: 30% of the remaining ill (after second and third month deaths) die
The exact calculation requires iterative steps as follows:
- After the first month: 0% dead, 80% ill, 20% healthy.
- After the second month: 0.30 x 80% = 24% dead, 0.80 x 20% = 16% more fall ill, so 64% (80%-24%) + 16% = 80% are now ill.
- After the third month: 0.30 x 80% = 24% of the remaining ill die, totaling 48% dead so far, and all remaining are now ill (since 80% of the last 4% healthy fall ill).
- After the fourth month: 0.30 x the remaining ill (52%) die; this is 15.6%.
To find the final total percentage of deaths, we add 24% + 24% + 15.6% = 63.6%. Thus, the percentage of the original population that will die in the next four months is 63.6%.