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In India, the newspapers are reporting that without lockdown $1$ person will infect $406$ persons in $30$ days. The newspapers are also reporting that the Mathematical factor for this growth is $1.5$ to $4$. I tried to figure this out by plugging in the details in the compounding formula, and I found that the factor should be $6.65$. What am I doing wrong?

I tried to solve the problem in the following way:

$$\left(1 + \frac{6.65}{30}\right)^{30} \approx 406.$$

user729424
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user40011
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2 Answers2

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Remember the general form of the exponential equation

$$ab^x = y$$

Since our starting value is $1$, we set $a = 1.$ Now, if we let $x$ represent time (in days), we can set $x=30$, since $406$ people are infected every 30 days. Thus, we solve the equation

$$b^{30}=406$$ $$b = 406^{1/30}$$ $$\approx 1.22166$$

Thus we have

$$1.22166^x = y$$

N. Bar
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  • Thanks. But why are the modellers pegging the factor between 1.5 and 4. Are there any other factors kicking in, like probability of infection etc? I know that this is not an epidemiology section. But would appreciate if someone could answer. – user40011 Apr 09 '20 at 16:46
  • Well, the $R_0$ factor is much more complicated than the general exponential growth equation. While this equation only takes in one data point (406 people have 30 days), $R_0$ takes into account vaccinations, contact period, and vaccinations. See this – N. Bar Apr 09 '20 at 19:53
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You are dividing 6.65 people by 30, which doesn't make sense. You do that for interest rates, an interest rate of 6.65 per month compounded daily, we divide 6.65 by 30, then pay that amount each day. Not applicable for disease transmission. The $R_0$ factor is not "people per month", so we do not get "people per day" by dividing $R_0/30$.

GEdgar
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