How to make my algorithm depends on time?

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I used MATLAB to simulate the cascading failure of two interdependent networks/Layers (I generated the two layers based on small world - watts strogatz algorithm).

My code works fine but it is not time dependent. I want to have time steps, for example, the initial attack on one node happens at t1 then after some time the next vulnerable nodes get failed at different time t2 and so on for the other failure events. My code emulates only telecommunication nodes ( all events happen instantaneously), I want it to work for other logistic networks, say social networks for example, where the timestamp for every event might be in minutes or hours. Your thoughts and ideas would appreciated.

Note: I can provide my code if this helps.

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