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.