​This model attempts to understand the behavior of average lifetime of companies in the S&P500 index. The reference mode for the model is a graph available at this link: https://static-cdn.blinkist.com/ebooks/Blinkracy-Blinkist.pdf (page 5) which was discussed in the System Thinking World Discussion forum.

Mergers & Acquisitions can be one of the reasons for older companies to be replaced with newer companies in the Index. With M&A of older companies, the empty slots are taken over by newer companies. However, overtime, these new companies themselves become old. With steady M&A, the stock of older companies decreases and stock of newer companies increases. The result is that average age of the companies in the S&P Index decreases.

The oscillations in the diagram, according to me, is due to oscillations in the M&A activity.

There are two negative feedback loops in the model. (1) As stock of new companies increases, the number of companies getting older increases which in turn decreases the stock. (2) As M&A increases, stock of older companies decreases which in turn decreases M&A activities.

Limits of the model

The model does not consider factors other than M&A in the increase in number of new companies in the Index. New companies themselves may have exceptional performance which will result in their inclusion in the Index. Changes in technology for example Information Technology can usher in new companies.

Assumptions

1. It is assumed that M&A results in addition of new companies to the Index. There could be other older companies too, which given the opportunity, can move into the Index. Emergence of new technologies brings in new companies.

Predator

dy/dt = δxy - γy

The predator population growth δxy depends on successful kills and the reproduction rate; however, delta is likely be different from beta. The loss rate, an exponential decay, of the predators {\displaystyle \displaystyle \gamma y}γy represents either natural death or emigration

Aztecs

Aztecas

Before addressing the specific case of the smallpox epidemic among the Aztecs, it is important to introduce the basic epidemiological model known as SIR (Susceptible – Infected – Recovered). This model helps explain how an infection spreads through a population over time by classifying people into three main categories:

• Susceptible (S): Individuals who have not yet been infected but are at risk.
• Infected (I): Individuals who have contracted the disease and can transmit it.
• Recovered (R): Individuals who are no longer contagious, either because they have developed immunity or have died.

​This model attempts to understand the behavior of average lifetime of companies in the S&P500 index. The reference mode for the model is a graph available at this link: https://static-cdn.blinkist.com/ebooks/Blinkracy-Blinkist.pdf (page 5) which was discussed in the System Thinking World Discussion forum.

Mergers & Acquisitions can be one of the reasons for older companies to be replaced with newer companies in the Index. With M&A of older companies, the empty slots are taken over by newer companies. However, overtime, these new companies themselves become old. With steady M&A, the stock of older companies decreases and stock of newer companies increases. The result is that average age of the companies in the S&P Index decreases.

The oscillations in the diagram, according to me, is due to oscillations in the M&A activity.

There are two negative feedback loops in the model. (1) As stock of new companies increases, the number of companies getting older increases which in turn decreases the stock. (2) As M&A increases, stock of older companies decreases which in turn decreases M&A activities.

Limits of the model

The model does not consider factors other than M&A in the increase in number of new companies in the Index. New companies themselves may have exceptional performance which will result in their inclusion in the Index. Changes in technology for example Information Technology can usher in new companies.

Assumptions

1. It is assumed that M&A results in addition of new companies to the Index. There could be other older companies too, which given the opportunity, can move into the Index. Emergence of new technologies brings in new companies.