Birth–death process

Imagine you are standing in front of a big box filled with colorful balls. Here, each ball represents a person, and you are standing right outside this box, where you can see the balls coming in and going out.

Now, let's say that every time a ball comes into the box, it represents a person being born. Likewise, every time a ball disappears from the box, it represents a person dying.

This process of balls coming and going is called a birth-death process. It's a way of keeping track of how many people are coming into and leaving a system over time.

The rate at which balls come into the box (people being born) and the rate at which balls disappear (people dying) can be different. For example, if more people are being born than are dying, the number of balls in the box (the population) is growing. On the other hand, if more people are dying than are being born, the population is shrinking.

Additionally, we can add other factors to this process. For instance, we can have balls leave the box for reasons other than death, like emigration.

Overall, a birth-death process is a simple way to keep track of how a population changes over time. It's like your own little world with colorful balls, where you can see how people are born, grow up, and eventually pass away.