Millionaire Mode

Mathematical Modeling: Healthcare and Medicine

Question 1 of 14

In a study of the spread of a contagious disease, the number of infected individuals is given by the differential equation $\frac{dI}{dt} = \beta I (1 - \frac{I}{N})$, where $\beta$ is the transmission rate, $I$ is the number of infected individuals, and $N$ is the total population. What is the general solution to this differential equation?

  1. $I(t) = N(1 - e^{-\beta t})$
  2. $I(t) = \frac{N}{1 + e^{-\beta t}}$
  3. $I(t) = \frac{N}{1 - e^{-\beta t}}$
  4. $I(t) = N e^{-\beta t}$

Prize Money

15₹7 Crores
14₹1 Crore
13₹50,00,000
12₹25,00,000
11₹12,50,000
10₹6,40,000
9₹3,20,000
8₹1,60,000
7₹80,000
6₹40,000
5₹20,000
4₹10,000
3₹5,000
2₹2,000
1₹1,000