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This problem involves the application of the **Kermack-McKendrick SIR model** for epidemiological dynamics, and asks to predict the number of infected individuals after 500 days using **Euler's method** with a step size of 0.1.

The model consists of the following system of ordinary differential equations:

\[
\frac{dS}{dt} = -\frac{r S(t) I(t)}{N}
\]
\[
\frac{dI}{dt} = \frac{r S(t) I(t)}{N} - \gamma I(t)
\]
\[
\frac{dR}{dt} = \gamma I(t)
\]

Given:
- Population \( N = 1,000,000 \)
- Initial susceptible individuals \( S(0) = 900,000 \)
- Initial infected individuals \( I(0) = 2 \)
- Initial removed individuals \( R(0) = 0 \)
- Infection rate \( r = 0.9 \)
- Recovery/death rate \( \gamma = 0.3 \)
- Time period \( t = 500 \) days
- Step size \( h = 0.1 \)

We will use **Euler's method** to estimate the values of \( S(t) \), \( I(t) \), and \( R(t) \) iteratively by updating the values for each time step based on the system of equations. Let's set up the simulation.

I'll calculate this using Python to give you the projections.

In 500 days, how many infected individuals will there be using Euler's method with a step size of 0.1, given a population of 1,000,000, an initial susceptible population of 900,000, 2 initial infected individuals, an infection rate of 0.9, and a recovery/death rate of 0.3?

This problem involves applying the Kermack-McKendrick SIR model to project the number of infected individuals in a population of 1,000,000 after 500 days using Euler's method with a step size of 0.1. Starting with 900,000 susceptible individuals, 2 infected individuals, and rates of 0.9 for infection and 0.3 for recovery or death, we calculate the progression of the epidemic.

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