Epidemic Threshold In Campus Environment

One of the core contents of epidemic transmission research is the epidemic threshold.When the effective reproduction number is below the threshold,society is in a healthy state,and vice versa,society is in a disease state.The dynamic simulations of epidemics are usually based on continuous time models.However,in recent years,discrete time models have attracted a lot of attention.On the other hand,non-pharmaceutical interventions are the main measures to curb the spread of the epidemic,such as isolating patients from close contacts,wearing masks,maintaining social distancing,conducting accounting and nucleic acid testing,and so on.University campuses are densely populated and have a high risk of infection.Nowadays,there is no determined conclusion on the effectiveness of non-pharmaceutical interventions(NPIs)in the campus environment.Therefore,it is a meaningful work to propose models to give quantitative evaluations.Firstly,the phenomenon of critical slowing down in discrete-time epidemic models is studied.When the effective reproduction number approaches the threshold,the duration of the epidemic will become longer,which can serve as an early warning signal for the transition from social health to disease.We show in the discrete-time SIS and SIR models,the peak duration of the epidemic occurred at the threshold of the contact rate.Compared with the SIR model,the variation of duration of the epidemic is sharper in the SIS model at epidemic threshold,which has significant warning effect.Secondly,in residential universities,students attend classes according to curriculum schedule,and mainly pack into classrooms,dining halls and dorms.NPIs can be easily realized by using larger classroom,adopting staggered dining hours,decreasing the number of students per dorm and so on.Considering the reality of university campuses,under mean field approximation and based on discrete-time SIR and SIS models,the impact of these NPIs measures on epidemic thresholds is quantitatively evaluated.Finally,an individual time-varying contact network model is proposed to simulate the campus environment.Based on the discrete-time SIR and SIS model and Monte Carlo method,we study the influences of NIPs include varying the seat occupancy rate in class rooms,the seat occupancy rate in dinning halls and the number of students per dorm.We find the NPI that using larger classroom plays important roles in raising the epidemic threshold and reducing the outbreak size.