So this question is a math question having to do with me calculating the rate of population growth starting from a population of 100,000. I have already gotten the first 3 steps done (sex ratio, ratio of cycle time, and pregnancy ratio) after a week among those in the fertile timeframe (calculating the ratio amongst the entire female population, which is what I'm after, should be relatively easy afterwards).

[SIZE="5"]Monthly Cycle numbers[/SIZE]

Here is the cycle ratio:

$2_{early}:2_{fertile}:1_{late}$

And the numbers:

$20,000_{early}:20,000_{fertile}:10,000_{late}$

Now, let's divide the early into 2 groups, pre-fertile, and safe and assume there is a 50/50 split between those 2 groups. Let's also assume that all the people in the fertile group are in the late group after a week, all those that are in the late group, are in the safe group after a week and so on. This suggests a cycle length of $4$, but let me verify it.

After a week:

$10,000_{safe}:10,000_{pre-fertile}:10,000_{fertile}:20,000_{late}$

After 2 weeks:

$20,000_{safe}:10,000_{pre-fertile}:10,000_{fertile}: 10,000_{late}$

After 3 weeks:

$10,000_{safe}:20,000_{pre-fertile}:10,000_{fertile}:10,000_{late}$

Yep, cycle length of $4$ is confirmed. To get the pregnancy ratio after a month of trying for pregnancy, I need the exact division which is a tad more complicated.

[SIZE="5"]Figuring out pregnancy ratio[/SIZE]

The ratio amongst the people in the fertile window of people who become pregnant is $2:3$ or $40\%$ Anti-miscarriage meds only work at or after 4 weeks has passed. Their effectiveness is $60\%$ at 4 weeks and $70\%$ at 5 weeks. It is 100% effective at 6 weeks. Here are the miscarriage rates:

- 3 weeks: 30.9%

- 4 weeks: 35.4%

- 5 weeks: 26.9%

So for the first week, $8,000$ become pregnant and the other $12,000$ in the fertile window go on to be in the late group. Ratio is $8,000_{pregnant}:42,000_{non-pregnant}$ which simplifies to $4:21$ or in terms of percents, $16\%$ of the female population.

After a week, another $4,000$ become pregnant. However, 30.9% of those from the starting week have a miscarriage. That is $2472$ people who miscarried, fewer than the number that became pregnant. Now the number is at $9,528$ pregnancies.

After another week, another $4,000$ become pregnant. 30.9% of those from the previous week miscarry. On top of that, 40% of the predicted 35.4% miscarry. So that is $1,236 + 783 = 2019$ miscarriages. This is fewer than those that become pregnant so there is an overall increase again. Now $11,509$ people are pregnant

After a third week, another $4,000$ become pregnant. 30.9% of those from the previous week, 40% of 35.4% of those that became pregnant the week before last, and 30% of 26.9% of those that became pregnant on the starting week miscarry. This adds up to $1,236 + 566 + 346 = 2,148$ miscarriages. Now $13,361$ people are pregnant.

After a fourth week, another $8,800$ become pregnant. At this point, there is no more push to become pregnant so the miscarriage calculations will get simpler from here. Here are the numbers for the miscarriages: $177 + 391 + 1236 = 1804$ miscarriages. Now, this is way less than the number that became pregnant so the total number of pregnancies now is $20,357$

Fifth week:

$2,719 + 391 + 192 = 3,302$ miscarriages

$17,055$ pregnancies

Sixth week:

$192 + 861 = 1,053$ miscarriages

$16,002$ pregnancies

Seventh week:

$421$ miscarriages

The final number of pregnancies is $15,581$ pregnancies

Percentage pregnant is $31.2\%$ which is approximately a $3:10$ ratio

Did I do my calculations correctly or did I make a mistake somewhere in the sea of multiplication, addition, and subtraction to calculate the miscarriage and pregnancy numbers week by week?

NOTE: My calculations assume no fertility after the miscarriage for several months, no other causes of fetal death besides spontaneous abortion(otherwise known as a miscarriage), and no maternal death while pregnant so despite matching the percent of the population that become pregnant after 1 try very closely, it might not be a realistic percentage for after 2-4 tries. Also, it is only this step, calculating the number of pregnancies that I need you to verify. Calculating how many are twins, etc. I should be able to do fine on my own.