As of April 1st, 2020, the ongoing global epidemic outbreak of coronavirus disease 2019 has spread to at least 146 countries and territories on 6 continents, resulted in 896 thousands confirmed case and over 45 thousands people. 1 In the UK, COVID-19 infection and death reached 29478 and 2352, with a mortality ratio nearly 7.9%. 1 For effectively controlling COVID19-breaks, most countries have implemented two non-pharmaceutical interventions: suppression strategy like immediate lockdowns in some cities at epicentre of outbreak; or mitigation that slows down but not stopping epidemic for reducing peak healthcare demand. 2.3.4 
Evidence before this study Suppression and mitigation are two common interventions for controlling infectious disease outbreaks. Previous works show rapid suppression is able to immediately reduce infections to low levels by eliminating human-to-human transmission, but needs consistent maintenance; mitigation does not interrupt transmission completely and tolerates some increase of infections, but minimises health and economic impacts of viral spread. 3 While current planning in many countries is focused on implementing either suppression or mitigation, it is not clear how and when to take which level of interventions for control COVID-19 breakouts to certain country in light of balancing its healthcare demands and economic impacts.
We used a mathematical model to access the feasibility of multiple intervention to control COVID-19 outbreaks in the UK. Our model distinguished self-recovered populations, infection with mild and critical cases for estimating healthcare demand. It combined available evidence from available data source in Wuhan. We estimated how suppression, mitigation and multiple rolling interventions impact on controlling outbreaks in London and non-London regions of the UK. We provided an evidence verification point that implementing suppression in London and rolling intervention with high intensity in non-London regions is probably an optimal strategy to control COVID-19 breakouts in the UK with minimised deaths and economic impacts.
The effectiveness and impact of suppression and mitigation to control outbreaks of COVID-19 depends on intervention intensity and duration, which remain unclear at the present time. Using the current best understanding of this model, implementing consistent suppression in London for 100 days and 3 weeks rolling intervention with intensity between 3 and 5 in other regions potentially limit the total deaths in the UK to 33.8 thousand. Future research on how to quantify and measure intervention activities could improve precision on control estimates.
However, both above interventions have apparent pros and cons; the effectiveness of any one intervention in isolation is limited. 4. Taking an example of controlling the COVID-19 epidemic in Wuhan, suppression strategy with extremely high intensity (the highest state of emergency) were token by China government from 23 nd January 2020 for 50 days, resulting prevention of over 700 thousand national infectious case. 5 However, China's first quarter gross domestic product is estimated to a year-on-year contraction to 9 percent. 6 In most scenarios, it is difficult to conduct an optimal intervention that minimises both growing infections and economic loss in ongoing COVID-19 breakouts.
The effectiveness of intervention strategies is accessed by decline of daily reproduction parameter R t , that used to measure a transmission potential of a disease. The R t of COVID-19 is estimated to be 2.5 -3.2. 7,8.9.10 Its implementation hinges on two parameters: intervention intensity presented by average-number contacts per person, and intervention duration counted by weeks. 11 The practical impacts of applying intervention strategies to certain country are varied in light of many factors including population density, human mobility, health resources, culture issues, etc. It is crucial but hard to know how and when to take which level of interventions tailored to the specific situation in each country.
Targeting at this problem, we aimed to conduct a feasibility study that explored a range of epidemiological scenarios by taking different intervention strategies on current information about COVID-19 outbreaks in the UK.
We assessed the effectiveness of multiple interventions to control outbreaks using a mathematical transmission model accounting for available and required healthcare resources by distinguishing self-recovered populations, infection with mild and critical cases. By varying the intensity, timing point, period and combinations of multiple interventions, we show how viable it is for the UK to minimise the total number of infections and deaths, delay and reduce peak of healthcare demand.
We implemented a modified SEIR model to account for a where Mild cases did not require hospital beds; Critical cases need hospital beds but possibly cannot get it due to shortage of health sources. Conceptually, the modified modal is shown in Fig.2 .
The model accounted for delays in symptom onset and reporting by including compartments to reflect transitions between reporting states and disease states. Here, this modal assumed that S is initial susceptible population of certain region; and incorporated an initial intervention of surveillance and isolation of cases in contain phase by a parameter β. 14.15 If effectiveness of intervention in contain phase was not sufficiently strong, susceptible individuals may contract disease with a given rate when in contact with a portion of exposed population E. After an incubation period p, the exposed individuals became the infectious population I at a ratio α. The incubation period was assumed to be 5.8 days. 8 Once exposed to infection, infectious population started from Mild cases M to Critical cases C at a ratio a, Critical cases led to deaths at a ratio d; other infectious population finally recovered.
We assumed that COVID-19 can be initially detected in 2 days prior to symptom onset and persist for 7 days in moderate cases and 14 days to severe cases. 19 Figure 2 : Extended SEMCR model structure: The population is divided into the following six classes: susceptible, exposed (and not yet symptomatic), infectious (symptomatic), mild (mild or moderate symptom), critical (severee symptom), death and recovered (i.e, isolated, recovered, or otherwise non-infectious).
Notably, two important features in our model differ with other SIR or SEIR models. 12.13 The first one was that we built two direct relationships between Exposed and Recovered population, Infections with mild symptoms and Recovered population. It was based on an observation of COVID-19 breakouts in Wuhan that a large portion (like 42.5% in Wuhan) of self-recovered population were asymptomatic or mild symptomatic. 14 They did not go to hospital for official COVID-19 tests but actually were infected. Without considering this issue, the estimation of total infections were greatly underestimated. 13 In order to measure portion of self-recovery population, we assumed that exposed individuals at home recovered in 3.5 days; mild case at home recovered in 7 days. 19 The second feature was to consider shortage of health sources (hospital beds) in the early breakouts of COVID-19 might lead to more deaths, because some severe or critical cases cannot be accommodated in time and led to death at home (non-hospital). For instance, in Wuhan, taking an immediate suppression intervention on 23 rd Jan 2020 increased serious society anxiety and led to a higher mortality rate. In order to accurately quantify deaths, our modal considered percentage of elder people in the UK at a ratio O, occupancy of available NHS hospital beds over time at a ratios H t and their availability for COVID-19 critical cases at a ratio J t . We assumed that critical cases at non-hospital places led to death in 4 days; elderly people in critical condition at hospital led to death in 14 days, and non-elderly people in critical condition at hospital led to death in 21 days. 19 One parameter was defined to measure intervention intensity over time as M t . which was presented by average number of contacts per person per day. We assumed that transmission ratio β equals to the product of intervention intensity M t and the probability of transmission (b) when exposed (i.e., β= mb). In Wuhan, intervention intensity was assumed within [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] , and gave with a relatively accurate estimation of COVID-19 breakouts. 13 We calibrated its value with respect to the population density and human mobility in London and the UK, and estimated outcomes of COVID-2019 outbreaks by implementing different interventions.
All data and code required to reproduce the analysis is available online at: https://github.com/TurtleZZH/Comparison-of-Multiple-
Considering that COVID-19 breakouts in Wuhan nearly ended by taking suppression intervention, our model was first fitted and calibrated with data on cases of COVID-19 author/funder, who has granted medRxiv a license to display the preprint in perpetuity.
The copyright holder for this preprint (which was not peer-reviewed) is the . https://doi.org/10.1101/2020.04.05.20054429 doi: medRxiv preprint in Wuhan. 13 In Fig.1 Using Wuhan's data, our estimation was close to the practical trend of outbreaks in Wuhan, and gave similar results to other works. 13 . 22 We tested that transmission rate from I to S is about 0.157; transmission rate from E to S is about 0.787. 13 The incubation period was assumed to be 6 days. 8 As for other parameters, we followed the COVID-19 official report from WHO 19 , and gave a medium estimation on average durations related from infectious, to mild or critical case, and death or recovery were shown in Table. 1.
Regard as the percentage of elderly people in the UK, it was assumed as 18%. 21 The total number of NHS hospital beds was given as 167589 with an initial occupied ratio up to 85%. 22 Considering that UK government began to release NHS hospital beds after COVID-19 breakouts, we assumed the occupied ratio reduced to 80% and would further fall to 40% by April 04, 2020. Accounting for other serious disease cases requiring NHS hospital beds in the early breakout of COVID-19, we assumed that a ratio of available hospital beds for COVID-19 critical cases was initially at 80%, and gradually raised to 100%.
The intervention intensity was related to the population density and human mobility. We gave an initialization to 
Due to difference of population density between London and other regions in the UK, we observed a fact that the accumulative infections in London was about one third of the total infectious population in the UK. 22 We separately combined the calibrated model with data on the cases of COVID-19 in London, the UK (non-London) and the UK during February 2020 and March 2020 to estimate the total number of infections and deaths, and also peak time and value of healthcare demand by applying different interventions. In contain stage, we assumed a strategy of isolation contacts were taken in the UK from 6 th Feb 2020 to 12 th March 2020, the effectiveness of isolation of cases and contacts was assumed as 94% in London and 88% in non-London regions.
The key tuning operation was to adjust intensity level of M t over time. We assumed that suppression intensity was given to reduce unaltered internal mobility of a region, where: M = 3. Mitigation intensity was given a wide given range [4] [5] [6] [7] [8] [9] [10] [11] [12] author/funder, who has granted medRxiv a license to display the preprint in perpetuity.
The copyright holder for this preprint (which was not peer-reviewed) is the . https://doi.org/10.1101/2020.04.05.20054429 doi: medRxiv preprint 
We estimated that suppression with intensity M = 3 was author/funder, who has granted medRxiv a license to display the preprint in perpetuity.
The copyright holder for this preprint (which was not peer-reviewed) is the . https://doi.org/10.1101/2020.04.05.20054429 doi: medRxiv preprint probably because suppression applied in Wuhan (the 32 nd day) was 3 days earlier than London (the 35 th day). It implied that earlier suppression could reduce infections significantly, but may lead to an earlier peak time of healthcare demand.
We estimated that the predicted R t of London, non-London and the UK dramatically raised in the first 7 days to 2.5 above, and varied from the 2 nd days (February 8 th 2020) to from the 46 th day (March 23 th 2020), with values ranging from 2.5 to 3.2. Notably, non-London regions had slightly higher value of R than London during these days. 
We simulated that mitigation with low, moderate and high The results showed that mitigation strategies were able to delay the peak of COVID-19 breakouts but ineffective to reduce daily infectious populations. We estimated that the peak of daily infectious population was reduced to Above simulations appeared similar trends as findings, 4 taking mitigation intervention in the UK enabled reducing impacts of an epidemic by flattening the curve, reducing peak incidence and overall death. While total infectious population may increase over a longer period, the final mortality ratio may be minimised at the end. But as similar as taking suppression, mitigation need to remain in place for as much of the epidemic period as possible.
We simulated two possible situations in London and the UK by implementing rolling interventions as shown in Fig.   4 . We assumed that all regions in the UK implemented an author/funder, who has granted medRxiv a license to display the preprint in perpetuity.
The copyright holder for this preprint (which was not peer-reviewed) is the . https://doi.org/10.1101/2020.04.05.20054429 doi: medRxiv preprint 
We simulated other possible rolling interventions with varied period (2, 3 and 4 weeks) and intensity (M = 4, 5 and 6), as shown in Table. author/funder, who has granted medRxiv a license to display the preprint in perpetuity.
The copyright holder for this preprint (which was not peer-reviewed) is the . https://doi.org/10.1101/2020.04.05.20054429 doi: medRxiv preprint
We considered the length of intervention in the UK impacting on social and economic. Maintaining a period of suppression in London, it was possible to control the outbreaks at the 100 th -150 th day that minimized economic loss to the greatest extent. Due to lower population density and less human mobility of non-London regions, 3 weeks rolling intervention was appropriated to non-London regions for balancing the total infections and economic loss, but the length of this strategy was extended to 300 days.
Aiming at a balance of infections, deaths and economic loss, we simulated and evaluated how and when to take which intensity level of interventions was a feasible way to control the COVID-19 outbreak in the UK. We found rolling intervention between suppression and mitigation with high intensity could be an effective and efficient choice to limit the total deaths of the UK to 33-38 thousand but maintain essential mobility for avoiding huge economic lose and society anxiety in a long period. Fig.1 . Therefore, we concluded that taking rolling intervention was more suitable to the UK.
Notably, the total infections estimated in our model was measured by Exposed population (asymptomatic), which might be largely greater than other works only estimating Infectious population (symptomatic). We found that a large portion of self-recovered population were asymptomatic or mild symptomatic in the COVID-19 breakouts in Wuhan (occupied about 42%-60% of the total infectious population). These people might think they had been healthy at home because they did not go to hospital for COVID-19 tests. It was one important issue that some SEIR model predicted infectious population in Wuhan that 10 times over than confirmed cases. 12 Our results show that taking rolling intervention is one optimal strategy to effectively and efficiently control COVID-19 outbreaks in the UK. This strategy potentially reduces the overall infections and deaths; delays and reduces peak healthcare demand. In future, our model will be extended to investigate how to optimise the timing and strength of intervention to reduce COVID-19 morality and specific healthcare demand.