WIP Clone of IM-9085 for multiscale frameworks based on ecography article. Vital Signs From NAP Toward Quality Measures for Population Health and the Leading Health Indicators Report  WHO NCD Framework picture and IHI Whole system measures 2.0 (Added Nov 2016)

Shows the ecological impact of population.

​Physical meaning of the equations

With these two terms the equation above can be interpreted as: the change in the prey's numbers is given by its own growth minus the rate at which it is preyed upon.

Predators

The predator equation becomes

dy/dt =  - 

In this equation, {\displaystyle \displaystyle \delta xy} represents the growth of the predator population. (Note the similarity to the predation rate; however, a different constant is used as the rate at which the predator population grows is not necessarily equal to the rate at which it consumes the prey). {\displaystyle \displaystyle \gamma y} represents the loss rate of the predators due to either natural death or emigration; it leads to an exponential decay in the absence of prey.

Hence the equation expresses the change in the predator population as growth fueled by the food supply, minus natural death.

The simulation integrates or sums (INTEG) the Nj population, with a change of Delta N in each generation, starting with an initial value of 5.Nj+1 = Nj  + mu (1- Nj / Nmax ) Nj

Delta Nj: is the “change in number of items” as we go from the present generation into the next generation. This is just the number of items born minus the number of items who have died.

mu: is the growth or birth rate parameter, similar to that in the exponential growth and decay model. However, as we extend our model it will no longer be the actual growth rate, but rather just a constant that tends to control the actual growth rate without being directly proportional to it.

F(Nj) = mu(1‐Nj/Nmax): is our model for the effective “growth rate”, a rate that decreases as the number of items approaches the maximum allowed by external factors such as food supply, disease or predation. (You can think of mu as the growth or birth rate in the absence of population pressure from other items.) We write this rate as F(Nj), which is a mathematical way of saying F is affected by the number of items, i.e., “F is a function of Nj”. It combines both growth and all the various environmental constraints on growth into a single function. This is a good approach to modeling; start with something that works (exponential growth) and then modify it incrementally, while still incorporating the working model.

Nj+1 = Nj + Delta Nj : This is a mathematical way to say, “The new number of items equals the old number of items plus the change in number of items”.

Nj/Nmax: is what fraction a population has reached of the maximum "carrying capacity" allowed by the external environment. We use this fraction to change the overall growth rate of the population. In the real world, as well as in our model, it is possible for a population to be greater than the maximum population (which is usually an average of many years), at least for a short period of time. This means that we can expect fluctuations in which Nj/Nmax is greater than 1.

​Physical meaning of the equations

With these two terms the equation above can be interpreted as: the change in the prey's numbers is given by its own growth minus the rate at which it is preyed upon.

Predators

The predator equation becomes

dy/dt =  - 

In this equation, {\displaystyle \displaystyle \delta xy} represents the growth of the predator population. (Note the similarity to the predation rate; however, a different constant is used as the rate at which the predator population grows is not necessarily equal to the rate at which it consumes the prey). {\displaystyle \displaystyle \gamma y} represents the loss rate of the predators due to either natural death or emigration; it leads to an exponential decay in the absence of prey.

Hence the equation expresses the change in the predator population as growth fueled by the food supply, minus natural death.

Simulation of how tiger population and anti poaching efforts effect the black market value of tiger organs.

​Physical meaning of the equations

With these two terms the equation above can be interpreted as: the change in the prey's numbers is given by its own growth minus the rate at which it is preyed upon.

Predators

The predator equation becomes

dy/dt =  - 

In this equation, {\displaystyle \displaystyle \delta xy} represents the growth of the predator population. (Note the similarity to the predation rate; however, a different constant is used as the rate at which the predator population grows is not necessarily equal to the rate at which it consumes the prey). {\displaystyle \displaystyle \gamma y} represents the loss rate of the predators due to either natural death or emigration; it leads to an exponential decay in the absence of prey.

Hence the equation expresses the change in the predator population as growth fueled by the food supply, minus natural death.

Simple BIDE model

​Physical meaning of the equations

With these two terms the equation above can be interpreted as: the change in the prey's numbers is given by its own growth minus the rate at which it is preyed upon.

Predators

The predator equation becomes

dy/dt =  - 

In this equation, {\displaystyle \displaystyle \delta xy} represents the growth of the predator population. (Note the similarity to the predation rate; however, a different constant is used as the rate at which the predator population grows is not necessarily equal to the rate at which it consumes the prey). {\displaystyle \displaystyle \gamma y} represents the loss rate of the predators due to either natural death or emigration; it leads to an exponential decay in the absence of prey.

Hence the equation expresses the change in the predator population as growth fueled by the food supply, minus natural death.

Een dynamisch model over een prooi predator relatie tussen verschillende populaties onder invloed van abiotische factoren.

​Physical meaning of the equations

With these two terms the equation above can be interpreted as: the change in the prey's numbers is given by its own growth minus the rate at which it is preyed upon.

Predators

The predator equation becomes

dy/dt =  - 

In this equation, {\displaystyle \displaystyle \delta xy} represents the growth of the predator population. (Note the similarity to the predation rate; however, a different constant is used as the rate at which the predator population grows is not necessarily equal to the rate at which it consumes the prey). {\displaystyle \displaystyle \gamma y} represents the loss rate of the predators due to either natural death or emigration; it leads to an exponential decay in the absence of prey.

Hence the equation expresses the change in the predator population as growth fueled by the food supply, minus natural death.

This model is under construction, not at all ready, don't use it for any purposes (my suggestion ☺) yet.

Simulation of how tiger population and anti poaching efforts effect the black market value of tiger organs.

​Physical meaning of the equations

With these two terms the equation above can be interpreted as: the change in the prey's numbers is given by its own growth minus the rate at which it is preyed upon.

Predators

The predator equation becomes

dy/dt =  - 

In this equation, {\displaystyle \displaystyle \delta xy} represents the growth of the predator population. (Note the similarity to the predation rate; however, a different constant is used as the rate at which the predator population grows is not necessarily equal to the rate at which it consumes the prey). {\displaystyle \displaystyle \gamma y} represents the loss rate of the predators due to either natural death or emigration; it leads to an exponential decay in the absence of prey.

Hence the equation expresses the change in the predator population as growth fueled by the food supply, minus natural death.

This is a basic population estimator. Default values approximate recent data for the United States.

​Physical meaning of the equations

With these two terms the equation above can be interpreted as: the change in the prey's numbers is given by its own growth minus the rate at which it is preyed upon.

Predators

The predator equation becomes

dy/dt =  - 

In this equation, {\displaystyle \displaystyle \delta xy} represents the growth of the predator population. (Note the similarity to the predation rate; however, a different constant is used as the rate at which the predator population grows is not necessarily equal to the rate at which it consumes the prey). {\displaystyle \displaystyle \gamma y} represents the loss rate of the predators due to either natural death or emigration; it leads to an exponential decay in the absence of prey.

Hence the equation expresses the change in the predator population as growth fueled by the food supply, minus natural death.

Shows the ecological impact of population.

This is a simulator of natural resource depletion.

​Physical meaning of the equations

With these two terms the equation above can be interpreted as: the change in the prey's numbers is given by its own growth minus the rate at which it is preyed upon.

Predators

The predator equation becomes

dy/dt =  - 

In this equation, {\displaystyle \displaystyle \delta xy} represents the growth of the predator population. (Note the similarity to the predation rate; however, a different constant is used as the rate at which the predator population grows is not necessarily equal to the rate at which it consumes the prey). {\displaystyle \displaystyle \gamma y} represents the loss rate of the predators due to either natural death or emigration; it leads to an exponential decay in the absence of prey.

Hence the equation expresses the change in the predator population as growth fueled by the food supply, minus natural death.

Koala populations in South East Queensland have been plummeting for decades and is only speeding up. Here is a Systems Dynamics model of key factors that increase and decrease the Koala population in SEQ. 

David De Marco

​Physical meaning of the equations

With these two terms the equation above can be interpreted as: the change in the prey's numbers is given by its own growth minus the rate at which it is preyed upon.

Predators

The predator equation becomes

dy/dt =  - 

In this equation, {\displaystyle \displaystyle \delta xy} represents the growth of the predator population. (Note the similarity to the predation rate; however, a different constant is used as the rate at which the predator population grows is not necessarily equal to the rate at which it consumes the prey). {\displaystyle \displaystyle \gamma y} represents the loss rate of the predators due to either natural death or emigration; it leads to an exponential decay in the absence of prey.

Hence the equation expresses the change in the predator population as growth fueled by the food supply, minus natural death.

Simulation of Population