Agent based network modelling of COVID-19 disease dynamics and vaccination uptake in a New South Wales Country Township

TL;DR

The paper investigates how multi-dose vaccination interacts with a scale-free contact network to shape COVID-19 dynamics in a hypothetical NSW town (N=$10^4$). By embedding an SEURV-type compartment model within a Barabási–Albert network and simulating a phased Pfizer vaccination program up to three doses, the study shows that while three doses can contain, they do not eradicate, the disease, leading to endemic cycles whose amplitude and period depend on natural immunity waning and its heterogeneity. It also demonstrates a robust cross-correlation between infection among high-degree hubs and overall infection, with hubs serving as early predictors of outbreaks, and shows that higher vaccination coverage reduces the predictive lag. These findings highlight the interplay between network topology, vaccination uptake, and disease dynamics, offering insights for vaccination strategies in remote communities and similar settings. The framework can be adapted to other towns by calibrating parameters to local demographics and contact patterns.

Abstract

We employ an agent-based contact network model to study the relationship between vaccine uptake and disease dynamics in a hypothetical country town from New South Wales, Australia, undergoing a COVID-19 epidemic, over a period of three years. We model the contact network in this hypothetical township of N = 10000 people as a scale-free network, and simulate the spread of COVID-19 and vaccination program using disease and vaccination uptake parameters typically observed in such a NSW town. We simulate the spread of the ancestral variant of COVID-19 in this town, and study the disease dynamics while the town maintains limited but non-negligible contact with the rest of the country which is assumed to be undergoing a severe COVID-19 epidemic. We also simulate a maximum three doses of Pfizer Comirnaty vaccine being administered in this town, with limited vaccine supply at first which gradually increases, and analyse how the vaccination uptake affects the disease dynamics in this town, which is captured using an extended compartmental model with epidemic parameters typical for a COVID-19 epidemic in Australia. Our results show that, in such a township, three vaccination doses are sufficient to contain but not eradicate COVID-19, and the disease essentially becomes endemic. We also show that the average degree of infected nodes (the average number of contacts for infected people) predicts the proportion of infected people. Therefore, if the hubs (people with a relatively high number of contacts) are disproportionately infected, this indicates an oncoming peak of the infection, though the lag time thereof depends on the maximum number of vaccines administered to the populace. Overall, our analysis provides interesting insights in understanding the interplay between network topology, vaccination levels, and COVID-19 disease dynamics in a typical remote NSW country town.

Figures (5)

• Figure 1: The SIRV Compartmental Model for COVID-19 disease dynamics (similar to the one in Abou-Ismail et al Abou-Ismail2020), consisting Susceptible ($S$), Exposed ($E$), Quarantined ($U$), Recovered ($R$), and Vaccinated ($V$) compartments. Three doses of vaccination are assumed, the second and the third being administered 28 and 208 days after the first. The transmission rate is $\beta$, recovery rate is $\delta$, the rate of becoming susceptible after disease is $\gamma$, the vaccination rates are $\alpha_i$ for $i^{th}$ vaccination, calculated as a proportion of people who took the previous vaccine, and the rate of vaccination immunity wearing off from $i^{th}$ vaccination is $\phi_i$.
• Figure 2: Infectious disease dynamics of COVID-19 in the NSW township of 10,000 people when a) zero b) one c) two d) three vaccines are administered. Second and third vaccines are administered 28 and 208 days after the first, respectively. The proportion of Susceptible ($S$), Infected ($I = E + U$) and Vaccinated ($V$) people in the population are shown. Endemic cycles are observed in no vaccine or single vaccine scenarios, whereas the disease is largely contained when three vaccines are administered, even with limited contact with the outside world where the infection still spreads freely. Vaccine uptake rates are $\alpha_1=\;\alpha_2=\;\alpha_3=\;0.9$. People who have recovered from COVID-19 are assumed to retain natural immunity for 180 days Nature2020, and the endemic circles in the case of no vaccine are the result of this temporary natural immunity conferred by the disease.
• Figure 3: Infectious disease dynamics of COVID-19 in the NSW township of 10,000 people when a) no vaccine b) one vaccine c) two vaccines d) three vaccines are administered. Second and third vaccines are administered 28 and 208 days after the first, respectively. The proportion of susceptible ($S$), Infected ($I = E + U$) and Vaccinated ($V$) people in the population are shown. Vaccine uptake rates are $\alpha_1\;=\;\alpha_2\;=\;\alpha_3\;=\;0.9$. In this case, the period of natural immunity conferred by contracting the disease varies such that a) people who have had no vaccine and no previous COVID-19 infection retain natural immunity for 140 days, people who have had one or more vaccines retain natural immunity for 180 days, people who have had previous COVID-19 infection retain natural immunity for 180 days, and people who have had one or more vaccination and previous COVID-19 infection retain natural immunity for 200 days. Compare this with \ref{['fig:doses_i']} where everyone who recovered from COVID-19 is assumed to have natural immunity for 180 days, regardless of previous history or vaccination status.
• Figure 4: $\left\langle k\right\rangle_I$ and $I$ compared over time for a) no vaccine b) one vaccine c) two vaccines d) three vaccines. Blue bars represent the average degree of infected population $\left\langle k\right\rangle_I$, and the orange line represents the proportion of infected population $I$. There is clear cross-correlation between the two time series, with a time lag. The results correspond to simulations shown in \ref{['fig:doses_i']}.
• Figure 5: Cross-correlation coefficient $\rho$ against lag time for the time series $\left\langle k\right\rangle_I$ and $I$ for the four distinct cases: a) zero b) one c) two d) three vaccines. In all cases, there is strong cross-correlation which peaks for a lag time between 25 and 12 days. (A negative lag time indicates $\left\langle k\right\rangle_I$ leads $I$. Since we are interested in predicting $I$, not $\left\langle k\right\rangle_I$, we only consider negative values for the lag-time.)