## Model Thinking Part 3 – Coarsera

**Tipping Point**

- Can be direct cause which is something causes the tip — small action or event (small change in variable) has large impact on end state — this depends also on context
- Can be contextual (percolation model is example) which means something in context changes to permit tip – a slight change in the context (environment)can have a big impact on final state
- Between and within class — system can go within the class from one state to another or the system can go between states across systems

Note: 4 types of systems: equilibrium , periodic, random, complex

**Percolation Model** – physics model – water percolating down into ground is example

use a checker board model with filled in squares to show tipping point (59.27%) at which a process goes from start to finish (end) used in information flow, forest fire prediction, innovation flow, social model (context changes if more connections are made)

**Diffusion Model** – natural diffusion but no tipping point

W sub t (time) = W sub-t (time) (current state) + N * c(number * contact rate) * t (tau – transmission rate) * W sub-t (time) /N (people with disease / number) * (W sub-t (time) – N / N)

**SIS**– S (for susceptible), I (for infectious) and S (for susceptible). epidemiology — non-linear – diffusion model but person can get cured than reinfected — has a tipping point because people can be cured — this can alos apply to information

W sub t (time) = W sub-t (time) (current state) + N * c(number * contact rate) * t (tau – transmission rate) * W sub-t (time) /N (people with disease / number) * (W sub-t (time) – N / N) **– a [# of people cured)W (sub t) — **this can be simplified using standard algebra notation

Basic Reproduction Number is R sub 0 = ct/a then if R sub 0> 1 disease spreads , hence a tipping point

V = % vaccinated so R sub0(1 – V) = r sub 0 he< or equal to V nce 1 – 1/R sub 0 = number to vaccinate — must get to the number to vaccinate percentage (R sub 0) to create the tipping point needed to protect those people not vacinnated. If R sub 0 < or + 1, no spread of disease, but if / or > than 1, disease will spread

**Economic Models**

Real growth is growth – inflation