The birth–death process is a special case of continuous-time Markov process where the states represent the current size of a population and where the transitions are limited to births and deaths. Birth–death processes have many applications in demography

Demography

Demography is the statistical study of human population. It can be a very general science that can be applied to any kind of dynamic human population, that is, one that changes over time or space...

, queueing theory

Queueing theory

Queueing theory is the mathematical study of waiting lines, or queues. The theory enables mathematical analysis of several related processes, including arriving at the queue, waiting in the queue , and being served at the front of the queue...

, performance engineering

Performance Engineering

Performance engineering within systems engineering, encompasses the set of roles, skills, activities, practices, tools, and deliverables applied at every phase of the Systems Development Life Cycle which ensures that a solution will be designed, implemented, and operationally supported to meet the...

, or in biology

Biology

Biology is a natural science concerned with the study of life and living organisms, including their structure, function, growth, origin, evolution, distribution, and taxonomy. Biology is a vast subject containing many subdivisions, topics, and disciplines...

, for example to study the evolution of bacteria

Bacteria

Bacteria are a large domain of prokaryotic microorganisms. Typically a few micrometres in length, bacteria have a wide range of shapes, ranging from spheres to rods and spirals...

.

When a birth occurs, the process goes from state n to n + 1.