Study On Discrete-random COVID-19 Epidemic Model With Prevention And Vaccination

In December 2019,an outbreak of COVID-19 broke out in Wuhan,China.In the early stage,due to people's insufficient understanding of the transmission mechanism and mode of the virus,as well as the significant increase of population mobility during the Spring Festival,the epidemic quickly spreads to all provinces and cities across the country.However,with the lockdown of Wuhan on January 23,2020 and the continuous strengthening of the prevention and control measures,the epidemic in all provinces,municipalities and autonomous regions of China has been effectively contained,gradually achieved phased results in the prevention and control,and the situation of the epidemic has been developing in a good direction in a short time.By March 2020,Tianjin,China,and Singapore had achieved remarkable results in COVID-19 prevention and control.However,after April,the epidemic in Singapore began to deteriorate,and Tianjin was still under control.In the face of such a completely opposite situation,it is of great practical significance to dig out the key points affecting epidemic prevention and control through comparative analysis of its internal influencing factors and simulation of its dynamic changes.Therefore,it is of great research value and application prospect to use the data to conduct mathematical modeling and analyze by changing the influencing factors to determine the key factors affecting the outbreak or secondary outbreak.Using detailed data from Tianjin,China,and Singapore,a discrete-random COVID-19 epidemic model was first constructed to depict the dynamic development of the epidemic.Parameter estimation,sensitivity analysis and calculating the effective reproduction number of the discrete-random model were developed to study the probability of imported cases inducing an outbreak in relation to different prevention and control efforts.Results show that the resumption of work and the reopening of schools will not lead to an outbreak if the effective reproduction number is lower than 1 and approaches 0 and tracking quarantine measures are strengthened.Once an outbreak occurs,if close contacts can be tracked and quarantined in time,the outbreak will be contained.If work is resumed and schools are re-opened with the effective reproduction number greater than 1,then it is more likely that a secondary outbreak will be generated.Also,the greater the number of undetected foreign imported cases and the weaker the prevention and control measures,the more serious the epidemic.Therefore,the key to prevention of a second outbreak is to return to work and to re-open schools only after the effective reproduction number is less than 1 for a period,and when tracking quarantine measures have been strengthened.Following the successful development of the COVID-19 vaccine,it is urgent and challenging to analyze how the upcoming mass vaccination in the population and the growing public desire to relax non-pharmaceutical interventions(i.e.,unlocking)interact to have an impact on the prevention and control of the COVID-19 pandemic.Based on the discrete-random dynamics model developed in the previous chapter,the vaccination term is introduced to analyze how much vaccination coverage is needed to avoid the second wave of the epidemic with different content of relaxing non-pharmaceutical interventions and imported cases.The analysis found significant differences in the effective vaccination coverage required to avoid a second outbreak between Tianjin,China,and Singapore.In particular,we predicted outbreaks in the two regions with different vaccination coverage,revealing that different levels of vaccination were effective in reducing the peak of a future wave.In addition,we found that low vaccination coverage can lead to subsequent multiple outbreaks once non-pharmaceutical interventions relaxed.Thus,there is a minimum vaccination coverage that depends on the intensity of non-pharmaceutical interventions in both regions,above which subsequent multiple outbreaks can be completely avoided and a dynamic balance between unlocking and vaccination can be achieved.In conclusion,vaccination programmes and coverage,designed and optimized for the specific characteristics of local epidemics,can gradually replace non-pharmaceutical interventions and eventually lead to normalisation of life.