Results

Network heterogeneity affects disease spread dynamics and viral evolution

Effective Reproduction Number

There are clear trends indicating a positive correlation between degree variance and effective 𝑅0, suggesting that this variance causes the emergence of potential superspreaders with many connections, increasing transmissibility potential. Clustering, coefficient, on the other hand, seems to have a negative correlation with effective 𝑅0; this makes sense when considering more clustered networks are more likely to have bridges that cut off sections of the network when disconnected, which would be the case when a node enters the D state and becomes unable to spread the disease.

Notably, strain 2 showed higher effective 𝑅0 even though strain 3 has a higher transmissibility. This is likely due to the fact that 𝑅0 was calculated at the moment each new strain first appeared. Strain 3 has a lower susceptible population to infect once it appears than earlier strains, and it must also compete with its predecessors; meanwhile, strain 2 only competes with strain 1 at first and has a higher available population to infect.

Probability of fixation of each new strain

Degree variance did not appear to influence the probability of fixation of different strains in any meaningful way. Clustering coefficient did seem to have a stronger effect, particularly with the highest values: with our highest clustering coefficient, none of the strains achieved fixation, meaning that none of the previous strains fully died out. This is in part because the evolution of the disease was much slower in highly clustered networks, but also because clustering can lead to isolated regions of the network. If pools of different strains are cut of from each other, this essentially ends competition between them and instantiates smaller networks with each one that then develop independently. It is therefore evident that clustering promotes coexistence between strains, and reduces the probability of one taking over the rest through winner-takes-all dynamics.

Peak Time

Peak time did not appear to exhibit a meaningful relationship with degree variance. However, an increase in clustering coefficient did delay the onset of the epidemic’s peak; this can be attributed to networks with a higher clustering coefficient having effective 𝑅0 values which are lower, but still greater than one. The result is a smaller-scale outbreak that nonetheless doesn’t quickly die out.

Epidemic Size

Epidemic size and peak infection show a very tight correlation, which is to be expected. They both seem to vary inversely with both heterogeneity measures, weakly with degree variance and somewhat more strongly with clustering coefficient. The latter is coherent with the other results we have observed thus far; high clustering coefficients create more isolation between segments of the network, increasing the likelihood of the disease being cut off from potential hosts. The opposite relationship exhibited between degree variance with these metrics as with effective 𝑅0 could be due to a mismatch between the theoretical 𝑅0 estimate and the experimental epidemic size and peak infection, or due to the low resolution of our experiment. This is certainly a potential avenue for further research.

Viral evolution furthers heterogeneity in human networks due to higher mortality

Mortality due to viral epidemic creates heterogeneity within the contact patterns of humans which leads to changing disease dynamics. The percolation threshold of the entire network is higher for a lattice network compared to a fully connected homogeneous network

Homogeneous regular lattice network

Heterogeneous Networks - Increased clustering via rewiring

Heterogeneous Networks - Increased variance in degree distribution

Disease Spread Dynamics across ranges of percolation thresholds (network property) and transmissibility (virus property)

Effective reproduction number

Beyond a critical value of the percolation threshold, a highly transmissible virus has high epidemic potential even when the percolation threshold is low (Figure 13). This means that the network heterogeneity does not interfere with theoretical predictions in cases of highly transmissible viruses.

Epidemic Size and Peak Infection - Increasing transmissibilities for a given percolation threshold increases the epidemic potential and peak infection.

SID dynamics across human contact network topologies

Here, we see that Variant 3 quickly starts to dominate the population even before the other two variants cease to exist. Once the die out, there is not much increase in the infections from variant 3 since the presence of the two variants accelerated cases by variant 3 through mutation within the individual.

Heterogeneous contact networks

Clustering coefficient = 0.5

Clustering coefficient = 0.34

Clustering coefficient = 0.05

Effect of local clustering on infection dynamics: We note that as the clustering coefficient increases, there is more grouping of individuals into clusters and thus the infection spread is cutoff from potential super spreaders since a individuals die of the disease and that could potentially cut off the the virus' access to that cluster.

Degree distribution (variance = 4.46)

Degree distribution (variance = 8.76)

Degree distribution (variance = 30.35)

Effect of having more spread in degree: Here, we note that for all 3 networks have the same mean degree of 4 and different variance as shown. A higher variance in the degrees indicate the presence of certain hub nodes that have potential to spread the infections faster than others (super-spreaders). This phenomenon is clearly indicated in the plot on right end (variance=30.35) the infection curves of variants 1 and 2 having narrower peaks and variant 3 having a higher peak infection value.

Real-world contact networks

U.S. High School contact network Influence network from Timik.pl (virtual world network in Poland)

US High School network: This network is a highly dense network and thus the infection thrives ireespective of the variant. The transmissibility difference, mutation and the selective advantage separate out the peaks of infection of the 3 variants.

Influence network: This network is a fairly sparse network indicating friendship connections in the virtual world restricted to Poland. The sparse nature explains the broader peaks of the infection curves in comparison to the US High school network.

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