Lecture 9. Dynamics 5: Stochasticity and Complexity Flashcards
What is the main difference between stochastic models and deterministic models?
Stochastic models look closer to reality, but more complex than deterministic models
What are the differences between simulations in a stochastic model?
The variability between the simulations are different
The peaks of infection in the simulations are different
No two epidemics are the same
What are the two forms of stochasticity?
Observational and demographic
What does observational stochasticity deal with?
Questions of miss-diagnoses, either false positives or false negatives, and therefore diagnostic sensitivity and specificity (observational noise)
What does demographic stochasticity deal with?
When events happen by chance, this has two consequences:
1) Any results obtained are subject to ‘Random Noise’
2) This ‘Random Noise’ is passed from one generation to the next. It is noise on the outcome, not noise on the observation
What is one huge result of demographic stochasticity?
Even when R₀ > 1 an infection can fail to invade by chance
R₀ is an average so it is unlikely that each infection causes an exact number of new cases
What is the probability that the first individual does not produce any secondary cases (recovery before anything else)?
γ/(β+γ) = 1/(1+R₀)
Starting with one case, what is the chance that the infection dies out before a major epidemic?
1/R₀
Starting with n cases, what is the chance that the infection dies out before a major epidemic?
(1/R₀)^n
What can cause extinctions of endemic infections?
When there are few infected individuals at the endemic equilibrium caused by:
Small population sizes
Low birth rates
Infections with low R₀
What is the most well-studied pattern of extinctions?
For measles in England and Wales before vaccination (1944-1970)
What is the critical community size/critical population size for measles and what does it mean?
500,000 is the critical community size for measles
For populations above around 500,000 we rarely see extinctions of measles
What are the two distinct elements that form critical community size?
Larger population sizes have more infected individuals and therefore there is less risk of the chains of transmission being
broken
Larger populations generally have more interactions with the outside world and therefore more imports of infection. Imports scale with population size
What is a metapopulation model?
Breaks a single large population into several distinct communities (or subpopulations)
These communities are linked by interactions
Each community has its own internal infection dynamics, which are influenced by the interaction between subpopulations
What are interactions between the wards based upon?
Interactions between the wards are based upon commuter. Actually sub-divide each ward into people who live in ward i but work in ward j.
Include the random movement of non-workers. This is a similar pattern to workers, but has more very short and very long range movements.
How do we insist that transmission (and movement of non-workers) is stochastic?
Using a tau-leap method with steps of half a day - to account for daytime and nighttime behaviour
What does tau-leap mean?
How long the time leaps are within the model
Why are models used?
Models are used because it is too dangerous to experiment with the real world
What are the main two uses of models?
To predict likely scenarios for early planning
To help decide between competing control strategies
What else must be considered beside models when deciding on the “best control measures”?
Economics, ethics and practicality
