Exploring community competition under different viral emergence probability conditions

b11902021 張嘉崴

Model Design

Every individual has moving speed \(v_i\) and fecundity \(f_i\)

Reproduction

Predation

Reproduction

\Delta N = N(r-1)(1 - \frac{N}{K})
v = v_i + \epsilon_v \,\,\ f = f_i + \epsilon_f
\epsilon \sim \mathcal{N}(0,\sigma^2) \,, i \sim X_R
P(X_R=i) = \frac{e^{cf_i}}{\sum_{j=1}^{N} e^{cf_j}}

(no trade-off)

Reproduction

\Delta N = N(1.1-1)(1 - \frac{N}{2000})
v = v_i + \epsilon_v \,\,\ f = f_i + \epsilon_f
\epsilon \sim \mathcal{N}(0,0.2) \,, i \sim X_R
P(X_R=i) = \frac{e^{0.3f_i}}{\sum_{j=1}^{N} e^{0.3f_j}}

(no trade-off)

w/ trade-off

v = v_i + \epsilon_v \,\,\ f = - v

Predation

\Delta N =d \cdot N
P(X_P=i) = \frac{e^{-cv_i}}{\sum_{j=1}^{N} e^{-cv_j}}

Predation

\Delta N =0.05 \cdot N
P(X_P=i) = \frac{e^{-0.3v_i}}{\sum_{j=1}^{N} e^{-0.3v_j}}

No Trade-off

Trade-off

Conclusion

  • Mean of traits both shift right
  • Moving speed is a more important trait.
  • In no trade-off, there's sudden jump.
  • In trade-off, mean moving speed fluctuates

Intro

Why didn't the Aztec Empire eradicate Europe?

Why didn't the Aztec Empire's

viruses eradicate Europe?

  • population?
  • difference in military forces?
  • difference in tamable livestock.

Why didn't the Aztec Empire's

viruses eradicate Europe?

More livestocks

Higher probability of new viruses that can pass between humans emerge

The community with

stronger viruses wins

Really?

The community with

stronger viruses wins

Really?

001010

011000

The hamming distance should be 2

My vague blueprint

Make 2 communities A and B

Add tons of viruses/mutations with different susceptibilities, fatalities, transmission rate ... into A

Drop a fraction of people in A into B

How to mutate?

How to simulate the effect of mutation on the viruses' abilities to transmit, to kill...?

Method

Experiment Design

M_1
M_2

Higher prob. new virus

M_1
M_2
M_2
M_1

Model Design

  • Consists of nodes
  • Individual Based (virus's perspective)
  • SIR Model
  • Evolutionary
v_0
v_1
v_2
v_3
M

Node Design

for i in range(year):
    human_reproduce()
    human_move()
    virus_simulation()
    virus_infection()
    add_new_virus()
  • Number of Susceptable/Infected/Recovered Humans
  • Fatality Traits
  • A set of viruses
    • Fatality Traits
    • Infection Traits
v

1. Human Reproduction

n =n_s + n_i + n_r \\ n_s \leftarrow n_s + kn_r + rn(1-\frac{n}{K})
n_0 = 1000, K = 2000, k = 0.3

2. Human Move

v_0
v_1
v_2
v_3

3. Virus kill/stay/recover

Every virus has a vector/scalar \(g_a\)

Every node has one vector/scalar \(g_b\)

c = \frac{1}{2} \left(\frac{g_a g_b}{|g_a||g_b|} + 1\right)
c - \epsilon \,/\, 2\epsilon \,/\,(1-c) - \epsilon
c = \frac{1}{1 + e ^{t (g_b-g_a)}}

4. Virus infection

  • Calculate the infection rate by SIR model
  • Decide which viruses will replicate by their infection traits \(I\)
p_j = \frac{e^{aI_j}}{\sum e^{aI_k}}

Result

I'm unable to find connection between

"Viral Emergence Probability" and

"Wiping out the other community"

Example Run

Higher probability

of virus emergence

10 new viruses/iter

Lower probability

of virus emergence

1 new virus/iter

Average

over 3 Runs

  • Equilibrium reached after 100 iterations

 

  • H. population is lower due to new viruses

 

  • After swapping viruses, no significant changes

With Elo

  • Less variance
  • Only little spike at 500th iteration
  • After swapping viruses, no significant changes

Viruses kills before it can replicate.

Especially with high ELO difference

 

The longer an infected human live,

the higher chance the virus passes on.

Observations

Best virus strategy: stay as long as possible, don't kill your host

Becomes a flu

More livestocks

Higher probability of new viruses that can pass between humans emerge

The community with

stronger viruses wins

Really?

My model cannot explain this

Possible Solutions?

Consider properties related to smallpox?

Detach fatality and incubation

Q&A

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