Electronic – Alternating between two LEDS using BJTs and SPST Switch

The 555 can either source or sink quite a considerable amount of current (like 200mA). Thus the transistor shown in the circuit isn't necessary (IMHO) for something like an LED. You can connect one LED from + to the output and another from output to GND. Like this:

Note - I've a feeling that the 555 doesn't have a high value that's equal to Vcc but slightly less than it. Which means that when LED2 is on, LED1 might be a little on too (anyone?)

Proteus VSM (Virtual System Modeling) does not operate in real-time, at least not on even very high end desktop computers. The simulation is very processor-intensive, as you would notice if you brought up Windows Task Manager while the simulation is running. Depending on your computer's capabilities and the number of active simulation elements in your design, the actual simulation speed varies widely.

One way to estimate how much slower than real-time the simulator works, is to incorporate a loop (not a timer ISR) in your simulated microcontroller code, that flips some GPIO once every so many counts. Let's say we set this period to be around a tenth of a second in real-time, by counting clock cycles of code.

So, if the simulation flips that bit once every 20 seconds, the simulation is running at 1/200th of real-time.

Add a couple of active simulation elements to the design, then run the simulation again and watch the bit-flipping, to see how much slower it gets.

That being said, there isn't actually any practical way to achieve true real-time simulation of any non-trivial Proteus design, with present-day consumer hardware. By throwing enough processing power at it, perhaps by overclocking your PC massively, real-time might be feasible, but I wouldn't hold my breath on it.