Network models to evaluate vaccine strategies towards herd immunity in COVID-19

Abstract

Vaccination remains a critical element in the eventual solution to the COVID-19 public health crisis. Many vaccines are already being mass produced and supplied in many countries. However, the COVID-19 vaccination programme will be the biggest in history. Reaching herd immunity will require an unprecedented mass immunisation campaign that will take several months and millions of dollars. Using different network models, COVID-19 pandemic dynamics of different countries can be recapitulated such as in Italy. Stochastic computational simulations highlight that peak epidemic sizes in a population strongly depend on the network structure. Assuming a vaccine efficacy of at least 80% in a mass vaccination program, at least 70% of a given population should be vaccinated to obtain herd immunity, independently of the network structure. If the vaccine efficacy reports lower levels of efficacy in practice, then the coverage of vaccination would be needed to be even higher. Simulations suggest that the "Ring of Vaccination" strategy, vaccinating susceptible contact and contact of contacts, would prevent new waves of COVID -19 meanwhile a high percent of the population is vaccinated.

Keywords: COVID-19; Epidemics; Mass vaccination; Networks; Ring of Vaccination; SARS-CoV-2; Vaccination.

Fig. 1

Model scheme. An illustration of infection spread with vaccination on a social network. Individuals in the social network are considered as nodes and contact between nodes exposed to the virus and those who do not have the virus can potentially lead to a transmission. Persons who are vaccinated are considered to be immune to infection. The epidemic state of each node is represented by a colour: Susceptible, $S$, (), Exposed, $E$, (), infectious, $I$, (), Vaccinated, $V$, () and Recovered, $R$, ().

Fig. 2

Infection cases between the network model simulation using $\beta (t)$ and Italian SARS-CoV-2 data from February 22 2020 to September 1 2020. The y-axis shows the infection cases. Parameter values used are $b_1=0.028,b_2=0.001,r_1=0.09,r_2=0.04,m_1=50,m_2=126$.

Fig. 3

Distribution of the final infectious cases in different timing for scenarios without vaccination in both networks. A population of N = 10⁶ individuals was generated and 100 simulations were run to simulate the epidemic in the course of one year. An individual was chosen randomly as patient zero for each run. Circles represent mean infection cases for each month connected by lines. (a): Erdos–Renyi network, (b): Barabasi-Albert network.

Fig. 4

Comparing infection peaks in both networks.

Fig. 5

Outcome for mass vaccination scenarios for each vaccine efficacy percentage on an Erdos–Renyi network. This shows the changes in mean infected cases over time under the different vaccine efficacies. In (a), (b), (c) and (d) vaccine efficacies are $40\%,60\%,80\%$ and $100\%$ respectively.

Fig. 6

Outcome for mass vaccination scenarios for each vaccine efficacy percentage on a Barabasi Albert network. This shows the changes in mean infected cases over time under the different vaccine efficacies. In (a), (b), (c) and (d) vaccine efficacies are $40\%,60\%,80\%$ and $100\%$ respectively.

Fig. 7

Comparing average proportion of unvaccinated individuals who got exposed in the course of the infection in both networks.

Fig. 8

Comparing average proportion of vaccinated individuals who got exposed in the course of the infection in both networks.

Fig. 9

Outcome for ring vaccination scenarios for each vaccine efficacy percentage on a Erdos-Renyi network. This shows the changes in mean infected cases over time when there is $1\%$ and $3\%$ prior exposed population in (a) and (b) respectively.

Fig. 10

Outcome for ring vaccination scenarios for each vaccine efficacy percentage on a Barabasi Albert network. This shows the changes in mean infected cases over time when there is $1\%$ and $3\%$ prior exposed population in (a) and (b) respectively.