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I am currently searching for population dynamics models. Concerning animal population growth, I have found the following so far :

Do you know any other mathematical models ? My aim is to simulate the dynamics of a human population and the aforementioned models are too simplistic for that, due to the lack of parameters.

Informatics models based on a system of rules like a cellular automata may be used for a more complex simulation. However, I would like to know if there is any mathematical equations for the dynamics of human population. I understand it is a difficult problem but surely much work must have been done on that.

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    Mathematical ecology by Pielou is a great book with a lot of information about this.2018-11-03

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There are "age-specific population models." In these, you divide the population into groups by age, then assume that with the passage of time each individual in a given age group has a certain probability of survivng into the next age group, and that the females in a given age group have, on average, such and so many babies. You may find something about them by searching for that term, or by searching for "the Leslie matrix".