Ranking the effectiveness of non-pharmaceutical interventions to counter COVID-19 in UK universities with vaccinated population

Abstract

Several universities around the world have resumed in-person teaching after successful vaccination campaigns have covered 70/80% of the population. In this study, we combine a new compartmental model with an optimal control formulation to discover, among different non-pharmaceutical interventions, the best prevention strategy to maximize on-campus activities while keeping spread under control. Composed of two interconnected Susceptible-Exposed-Infected-Quarantined-Recovered (SEIQR) structures, the model enables staff-to-staff infections, student-to-staff cross infections, student-to-student infections, and environment-to-individual infections. Then, we model input variables representing the implementation of different non-pharmaceutical interventions and formulate and solve optimal control problems for four desired scenarios: minimum number of cases, minimum intervention, minimum non-quarantine intervention, and minimum quarantine intervention. Our results reveal the particular significance of mask wearing and social distancing in universities with vaccinated population (with proportions according to UK data). The study also reveals that quarantining infected students has a higher importance than quarantining staff. In contrast, other measures such as environmental disinfection seems to be less important.

Figure 1

Model structure. Flow chart of five epidemic stages among students and staff in a university department: S, susceptible (including the vaccinated); E, exposed (asymptomatic); I, infected (symptomatic); Q, quarantined (hospitalized or mandatorily isolated); R, recovered. The subscript “y” stands for students while the subscript “s” denotes staff.

Figure 2

Prediction in the baseline scenario of no interventions. (a) Evolution of COVID-19 among students. (b) Evolution of COVID-19 among staff. Magnitudes are in proportion to the total number of students or staff.

Figure 3

Optimal trajectories for the minimum-case scenario. Optimal trajectories when the department spares no effort to contain the epidemic. (a) and (b) The epidemic evolution among students and staff, respectively. (c) The optimal strategies for mask wearing (${\kappa }_m$), social distancing (${\kappa }_d$), and environmental disinfection (${\kappa }_e$). (d) The optimal strategies for mandatory quarantine on infected students (${\kappa }_{\mathit{qy}}$) and infected staff (${\kappa }_{\mathit{qs}}$).

Figure 4

Optimal trajectories for the minimum intervention scenario. Optimal trajectories when the department would like to minimise the enforcement of control measures. (a) and (b) The epidemic evolution among students and staff, respectively. (c) The optimal strategies for mask wearing (${\kappa }_m$), social distancing (${\kappa }_d$), and environmental disinfection (${\kappa }_e$). (d) The optimal strategies for mandatory quarantine on infected students (${\kappa }_{\mathit{qy}}$) and infected staff (${\kappa }_{\mathit{qs}}$).

Figure 5

Optimal trajectories for minimum use of non-quarantine interventions. Optimal trajectories when the departments would like to minimise use of masks, social distancing and environmental disinfection. (a) and (b) The epidemic evolution among students and staff, respectively. (c) The optimal strategies for mask wearing (${\kappa }_m$), social distancing (${\kappa }_d$), and environmental disinfection (${\kappa }_e$). (d) The optimal strategies for mandatory quarantine on infected students (${\kappa }_{\mathit{qy}}$) and infected staff (${\kappa }_{\mathit{qs}}$).

Figure 6

Optimal trajectories for the minimum quarantine scenario. Optimal trajectories when the department would like to minimise the enforcement of mandatory quarantines. (a) and (b) The epidemic evolution among students and staff, respectively. (c) The optimal strategies for mask wearing (${\kappa }_m$), social distancing (${\kappa }_d$), and environmental disinfection (${\kappa }_e$). (d) The optimal strategies for mandatory quarantine on infected students (${\kappa }_{\mathit{qy}}$) and infected staff (${\kappa }_{\mathit{qs}}$).