Multi Strain Dynamics

Question 1

Define cross immunity

Answer 1

protection against a given pathogen thanks to immunity acquired from past exposure to a related pathogen

Question 2

In the multi strain dynamics lab, what did Parameter γ (gamma) represent?

Answer 2

the extent of cross immunity

Question 3

What do these values mean

𝛾 = 0

0 < 𝛾 < 1

𝛾 = 1

Answer 3

𝛾 = 0: no cross-immunity

0 < 𝛾 < 1: partial cross-immunity

𝛾 = 1: full cross-immunity

Question 4

In this lab, how do we define a strain?

Answer 4

instead of defining a strain by its entire genome, a strain is defined by the genetic loci that encode antigens against which the immune responses act

Question 5

1.1 & 1.2
What is the dynamic behavior of each strain in the model?

Answer 5

The dynamic behavior of each strain in the model is SIR-like, showing a series of epidemics followed by an equilibrium state.

Question 6

1.1 & 1.2
Why are the dynamics of each strain SIR-like in the model?

Answer 6

because the model contains a set of independently transmitting strains (strains do not interfere with each others dynamics), each with the same transmission rate and recovery rate parameters.

Question 7

1.1 & 1.2
Why do strains behave similarly in the model?

Answer 7

because the transmission rate and recovery rate parameters for each strain are the same. Any differences only arise due to different initial conditions for each strain.

Question 8

1.1 & 1.2
What is the compartmental model used to produce this plot?

Answer 8

top of page three

dZAX/dt - proportion protected to a particular strain

dWAX/dt - proportion partially protected to a particular strain

dYAX/dt - proportion infected by a particular strain

cross immunity parameter set to 0

Question 9

1.1 & 1.2
There are six strains in this model but we cannot see them all in the plot, why?

Answer 9

Their transmission dynamics are so similar that they are plotted on top of each other

Question 10

1.2b
What did running this instruction do?

extractYFinalConditions(simdata)

Answer 10

showed allelic sequences of each of the strains in the simulation
showed that all strains have the same prevalence at the end

Question 11

What is meant by prevalence?

Answer 11

proportion infected

Question 12

Define beta

Answer 12

transmission rate

Question 13

1.3
What are the dynamic consequences of making one strain more transmissible?

Answer 13

The change in beta should translate to a
change in R0.

Strain 2 now causes higher and more frequent epidemics at the start.

Strain 2 ends up with higher prevalence at
equilibrium.

Quantitatively the behaviours
are different, but qualitatively the same.

Question 14

1.4
Explain the dynamics of strain diversity

Answer 14

Least diverse ecosystem composition = one strain (S=0)
Most diverse = multiple strains all with the same maximal abundance (Smax)

maximum diversity is achieved regardless of total prevalence. Hence if at some point all strains have abundance 0.01 or 0.1 it does not make any difference to S, which will take value Smax in both cases.

Transient times - strains are still adjusting and will display recurrent epidemics. At this point diversity is less than Smax because soe strains are more abundant than others.
Late times - strains are equally abundant and diversity plateaus as the strains become constant at equilibrium

Question 15

What does Shannon Diversity Index Plot?

Answer 15

the amount of diversity in an ecosystem’s composition at a point in time

Question 16

2.1
What does this graph show?

Answer 16

Transmission Rates (beta) are set the same - 292
Cross immunity is very high - set to 0.95 (nearly 1 which would mean full cross immunity)

Question 17

2.1
The three strains have the sam R0 but show different levels of prevalence (proportion infected). What are these levels?

Answer 17

High prevalence (dominant strain)
Intermediate prevalence (subdominant strains)
Low prevalence (strains are excluded and run the risk of becoming extinct)

Question 18

2.1
If all strains have the same epidemiological parameters (beta, sigma and mu), what does this mean in terms of fitness?

Answer 18

None of the strains have an explicit fitness advantage over the other

Question 19

x

Answer 19

Once strain X (strain 6) becomes dominant, any strain sharing alleles at the same locus suffers from the high levels of herd immunity to X.

Question 20

In the presence of a dominant strain, why might some strains be driven to extinction?

Answer 20

x

Question 21

What happens to strains that don’t share alleles with the dominant strain?

Answer 21

they manage to co-circulate with the dominant strain

Question 22

Why might one of two strains co-circulating with a third dominant strain, never outdo (or dominate the present dominating strain)?

Answer 22

the two co-circulating strains share alleles and thus are busy comepting directly with each other for susceptible individuals.

Question 23

What might explain two strains appearing on a plot at an intermediat prevalence (horizontal line in middle of graph)

Answer 23

the two strains do not share alleles with the dominant straina nd thus do not suffer from herd immunity generated by the dominant strain, however the two strains share alleles with each other and therefore compete for susceptible individuals. This means one of the two strains will never outdo the present most dominant strain.

Question 24

2.5
Why is strain diversity where there is high cross immunity generally smaller than observed under no cross-immunity(Q1)?

Answer 24

Diversity is lower at equilibrium compared to the scenario with no cross-immunity because 3 of the strains are actually “extinct”.

Question 25

2.5
Describe the shannon index plot under cross immunity

Answer 25

Diversity oscillates during the initial epidemic phase as the strains compete to dominate.
As the simulation converges to equilibrium, so does diversity.

Question 26

What was part 3 about?

Answer 26

Multi-strain dynamics with intermediate cross-immunity

Question 27

3.1
Explain the dynamics of the graph with strains that have the same beta (292) but intermediate cross immunity of 0.7
XX????

Answer 27

Chaotic strain structure - many strains circulate and typically replace each other over time

Observed dynamics are at an intermediate state between high and no cross immunity

Strains follow the SIR framework and create recurrent epidemics.

As one strain (A) creates an epidemic, other strains that share similar alleles suffer from herd immunity and are suppressed. However, because cross immunity isn’t high, this doesn’t lead to the stable dominance of that one strain (A).

XXX
The network of
immunological interactions (by which a strain is continuously suppressed by similar
strains) also stops it from actually generating very high population level immunity to
itself. Strains thus find it harder to burn out the available susceptibles, and as such
are kept in an intermediate state that avoids equilibrium.
XXXX?

Question 28

3 strain structure types (pathogen behaviours) and meanings

Answer 28

1. No Strain Structure - Strains have the same frequencies
2. Discrete Strain Structure - Strains have different frequencies but are constant at end of epidemic
3. Chaotic Strain Structure - Strains have different frequencies but never become constant

Question 29

Which strain structure type matches the pathogen behaviour of what pathogen

Answer 29

Influenza A resembles the chaotic strain structure

Question 30

How can knowledge of strain structures inform us about vaccination strategies?

Answer 30

Influenza A resembles the chaotic strain structure

CSS is unpredictable, many strains circulate and replace each other over time, unpredictable which strain will be dominant at any one point and create the next epidemic.

So influenza A vaccines are updated every 1-3 years and an assessment needs to be made about what strains should be incorporated into the vaccine before it is updated.

We vaccinate repeatedly every year because the CSS means new strains are constantly becoming dominant and then receding and being replaced by a different strain.

Question 31

3.4
Discuss differences in observed dynamics of influenza A in a host with a 70 year lifespan (humans) compared to a 10 year lifespan (ducks).

Answer 31

Humans - same dynamic as ducks much much slower

Ducks -

Shorter lifespan means that in a duck population there are more susceptible individuals at any one time.

Duck dynamics have higher peaks more regularly, they also have faster cycling.

This is due to host turn-over.

One immediate implication is that diversity is higher in ducks
than humans at any point in time, which hints at avian species’ role as natural reservoirs of Flu A genetic diversity.

Question 32

3.5
When is strain diversity highest?

Answer 32

When all strains co-circulate at similar prevalence (proportion infected)

Question 33

Explain why the diversity of strains with a chaotic strain structure MEASURED PER TIME STEP is generally much lower than those with no strain structure or discrete strain structure?

Answer 33

Per time step, meaured diversity of the strains appears very low.
This is because each epidemic is usually caused by a single strain. This strain never stabilises, instead it recedes and another new strain then dominates for a period of time.

Diversity oscillates in time and never reaches a stabilised value.

Holistically, the diversity plot simulation appears to show high diversity however measured per time step diversity is low.

Question 34

What is part 4 about?

Answer 34

Strain control under high cross immunity

Question 35

What can we expect shannon diversity index to be at a point in time when a population is dominated by a single strain

Answer 35

Single strain - low diversity index
Old strain recedes and new strain dominates - high diversity index as strain recedes and then low again as new strain dominates
Shannon diversity index exhibits a cyclical dynamic similar to the cyclical dynamics of multi-strain models

Question 36

Explain why vaccinating against one dominant strain may result in a previously rare strain replacing it and becoming dominant

Answer 36

X