key: cord-0816393-nax5jxsi
authors: Zhang, S.; Bi, G.; Yang, Y.; Qi, J.; Li, S.; Mao, X.; Peng, R.; Yang, P.
title: An Extended COVID-19 Epidemiological Model with Vaccination and Multiple Interventions for Controlling COVID-19 Outbreaks in the UK
date: 2021-03-12
journal: nan
DOI: 10.1101/2021.03.10.21252748
sha: 7427d041eda99ea63ba32b52615f7f888c6349f0
doc_id: 816393
cord_uid: nax5jxsi

There has been a second outbreak of the Coronavirus Disease (COVID-19) in the UK in 2019. In this situation, the United Kingdom re-implemented two blockade intervention strategies. Different from the first COVID outbreak, the second outbreak is accompanied by two new situations: 1) the emergence of a new variant strain that originated in September which is more infectious than the original strain, 2) and the official start of a vaccine in the UK started in mid-December. As the date for lifting the third blockade approaches, what kind of intervention measures will the UK continue to take: curb the spread of the COVID epidemic, reduce medical needs, and allow people to return to normal life and revitalize the national economy as quickly as possible. Targeting at this problem, this article conducted a feasibility study by defining the mathematical model SEMCVRD, and expanded the traditional SEIR (susceptible exposure to infectious disease recovery) model by adding two key features: the mixed infection of the mutant strain and the original strain, and the addition of Crowd of vaccinators. The model uses a public data set for fitting and evaluation. The data set contains daily new infections, new deaths, and daily vaccination in the UK from February 2020 to February 2021. Based on the simulation results, we have the following findings: 1) We simulated the mixed infection of the new mutant virus and the original virus in the UK, and found that under the hypothesis that the vaccine is effective against the new virus, we continue to promote the injection of vaccines within the society, which can effectively curb the spread and infection of new mutant viruses. We predicted that if UK could continuously implement insensitive suppression, COVID-19 epidemic would be able to control by 9th April 2021 and would be nearly ended by 1st May 2020. 2) With the increasing number of people vaccinated and immunized against the virus, the unblocking of the third blockade in the UK is coming. Using a phased and progressive unblocking intervention strategy with an intensity of 3 is our best choice at present. Under this strategy, the total number of infections in the UK will be limited to 4.2 million; and the total number of deaths in the UK is 135,000. People can return to normal life and social distancing after four months. The epidemic will nearly end in 6th June (The sign of the end: the number of new infections per day is less than 1,000, and the number of new deaths per day is less than 35). In addition, according to our prediction, under this kind of intervention, the UK will not experience a shortage of medical resources as it did in the first half of 2020. 3) In the case that it is possible to provide people with 600 thousand vaccinations(double the quantity now provided) every day, we can try a higher intensity (intensity 5) Phase intervention strategy to nearly end the epidemic earlier (25th May) and restore people's normal life and social distance.

capacity of vaccine companies, it is not enough to achieve universal vaccination in the UK. In addition, taking the vaccine developed by Pfizer-BioNTech as an example, it is not possible to achieve complete immunity to the COVID-19 virus after the first shot of the vaccine.

According to the study, in the interval between the first and second doses, the observed vaccine efficacy against Covid-19 was 52% and that for the first 7 days after dose 2 was 91%, while reaching full efficacy against disease with onset at least 7 days after dose 2. Therefore, it will take more time to achieve universal immunity in the UK. [4] [5] [6] In response to this issue, a feasibility study is conduct to explore a series of epidemiological situations by adopting different intervention strategies for the current information on the COVID-19 epidemic in the UK. [7] [8] By using mathematical transmission models, the data is used to estimate the proportion of the new and original strains in the UK infections and to classify a new population that represents vaccinators. By changing the intensity, timing, cycle and combination of various interventions, the feasibility of the UK to minimize the total number of infections and deaths and return to normal life and economic recovery as quickly as possible has been proved.

The remainder of this paper is arranged as follows. The model is introduced in Section 2. In the Section 3, the materials and implementation of experiment are reported. Section 4 provides detailed experimental evaluation and discussion. The conclusion and future directions are given in Section 5.

We implemented a modified SEIR model, which called SECMVRD model to account for a dynamic Susceptible [9] [10] [11] [12] [13] For estimating healthcare needs, the infectious group was categorized into two sub-cases: Mild [M] and Critical [C] (mild cases did not require hospital beds and critical cases need hospital beds but possibly cannot get it due to shortage of health sources). [14] [15] [16] Meanwhile, the vaccinated population was divided the into two sub-cases: Vaccinated1 [V1] and Vaccinated2 [V1], where V1 is the population who has received the first dose of vaccine, and V2 is the population who has received the second dose of vaccine. 4 Conceptually, the modified modal is shown in Figure. 1. The parameters in this model are shown in Table. 1.

The model accounted for delays in symptom onset and reporting by including compartments to reflect transitions between reporting states and disease states, where 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. [17] [18] [19] If effectiveness of intervention in contain phase was not sufficiently strong, susceptible individuals may contract disease with a given rate when they come into contact with a portion of exposed population E. After an incubation period α1, the exposed individuals became the infectious population I at a ratio 1/α1.The incubation period was assumed to be 5.8 days. 20 Once exposed to infection, infectious population started from Mild cases M to Critical cases C at a ratio a, Critical cases led to deaths . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The copyright holder for this preprint this version posted March 12, 2021. ; https://doi.org/10.1101/2021.03.10.21252748 doi: medRxiv preprint at a ratio d; other infectious population finally recovered. [21] [22] It was assumed that COVID-19 can be initially detected in 2 days prior to symptom onset and persist for 7 days in mild cases and 14 days to severe cases. 23 The susceptible population S will be vaccinated from December. The number of susceptible populations v1 will be vaccinated daily (from S to V1). 21 days after the first vaccination, V2 people receive the second vaccination every day (from V1 to V2) Figure 1. Extended SEMCVRD model structure: The population is divided into the following eight classes: susceptible, exposed (and not yet symptomatic), infectious (symptomatic), mild (mild or moderate symptom), critical (severe symptom), vaccinated, deceased and recovered (i.e., isolated, recovered, or otherwise non-infectious).

In addition, one parameter was defined to measure changes in intervention intensity over time as Pt. which was presented by average number of contacts per person per day. It was assumed that transmission ratio β equals to the product of intervention intensity Pt and the probability of transmission (b) when infected. β1 and β2 respectively correspond to the infection rate of Infectious [I] and Exposed [E] (infected but asymptomatic). Intervention intensity was assumed within the interval [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] , gave with a relatively accurate estimation of COVID-19 breakouts. 24 The value of population density and population mobility in London and the UK were calibrated and different interventions were implemented to estimate the COVID infection situation.

Notably, four important features in our model differ with other SIR or SEIR models. 18, 20 The first one was that two direct relationships has been established 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. 25 They did not go to hospital for official COVID-19 tests but actually were infected. Without considering this issue, the estimation of total infections was greatly underestimated. 20 In order to measure portion of self-recovery population, . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The copyright holder for this preprint this version posted March 12, 2021. ; https://doi.org/10.1101/2021.03.10.21252748 doi: medRxiv preprint it was assumed that exposed individuals at home recovered in 3-5 days; mild case at home recovered in 7-10 days. But if their symptoms get worse, they will be transferred to hospital.

The second feature was to the consideration that the 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 deaths at home (non-hospital).

For instance, in Wuhan, taking an immediate suppression intervention on 23 rd January 2020 increased serious society anxiety and led to a higher mortality rate. In order to accurately quantify deaths, our model considered percentage of elder people in the UK at a ratio occupancy of available National Health System (NHS) hospital beds over time at a ratios Ht and their availability for COVID-19 critical cases at a ratio Jt. It was assumed that critical cases at non-hospital places led to deaths in 4 days; elderly people in critical condition at hospital led to deaths in 14 days and non-elderly people in critical condition at hospital led to deaths in 21 days. 24 The third feature was to consider the outbreak of a new variant of COVID-19 in the UK in September 2020. The strain probably The fourth feature was to consider the special circumstances of the UK starting vaccination in December 2020. Based on the existing vaccine information, it can be known that the vaccine is administered in two doses, so two different vaccinated populations V1 and V2 was assumed. According to statistics on the official website of the UK, the model simulates an increase in the number of two different groups of people who are vaccinated each day. In the two vaccination stages, the population has different immunity, which is represented by parameters e1, e2. 2

Following previous assumptions, the implementation of dynamic transmission of our modified SEIR model follows steps as below:

. CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted March 12, 2021. ; . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted March 12, 2021. ; https://doi.org/10.1101/2021.03.10.21252748 doi: medRxiv preprint

Here parameter 1 is the transmission rate from E to M (1/ 1 (incubation period)), Parameter 2 is the transmission rate from M to C (1/ 2 (average period from M to C)).

Parameter 1 is the transmission rate from E to R (1/ ɤ 1 (average period from E to R)), parameter 2 is the transmission rate from M to R (1/ ɤ 2 (average period from M to R)), parameter 3 is the transmission rate from NH to R (1/ ɤ 3 (average period from NH to R)), parameter 4 is the transmission rate of older people from IH to R (1/ ɤ 4 (average period of older people from IH to R)), parameter 5 is the transmission rate of non-older people from IH to R (1/ ɤ 5 (average period of non-older people from IH to R)).

Parameter 1 is the transmission rate from NH to R (1/ 1 (average period from NH to D)), parameter 2 is the transmission rate of older people from IH to R (1/ 2 (average period of older people from IH to D)), parameter 3 is the transmission rate of non-older people from IH to R (1/ 3 (average period of non-older people from IH to D)).

The SEMCVRD model is explored to simulate the COVID-19 infection in the UK starting in August. Before August, the epidemic in the UK had been brought under control and stabilized. We simulated the outbreak of the second COVID-19 epidemic in the UK that started in August 2020 and included two special cases during the period: 1) There are at least three new variant strains in the UK and they are more infectious than the original strain. The mutant strain considered in the experimental simulation accounts for the majority of all strains of the mutant infection in the UK. 2) The official start of a vaccination programme in the UK started in mid-December 2020. Different interventions . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted March 12, 2021. ; https://doi.org/10.1101/2021.03.10.21252748 doi: medRxiv preprint were simulated and implemented to estimate how to control the COVID-19 epidemic in the UK after the third lockdown was lifted. A total of four types of interventions were simulated, each of which contains a different situation. The initial populations were given as UK (66.49 million). The parameter P representing average number of contacts per person per day was given as 15 to the UK.

The suppression intensity was given to reduce unaltered internal mobility of a region, where: M = 3. 29 As shown in Figure 2 As of 2 nd December 2020, when the lockdown was lifted, the number of new infections per day has dropped to 14,607, which fully reflects the effectiveness of the suppression intervention measures. However, after the lift on 2 nd December 2020, the curve rose soon, forming the next outbreak. It can be found that the early release of intensity may increase the risk of a second outbreak. As a result, the UK implemented the third lockdown strategy on 5 th January 2021. With the start of vaccination in mid-December, the COVID-19 epidemic was effectively contained, and the number of new infections per day also declined exponentially.

We estimate that the total number of infections in the UK, including exposed and infectious people, will actually reach 3,889,216, accounting for almost 0.58% of the UK population before the intensive suppression measures are lifted on 8 th March 2021 (the 220 th day).

We predicted that if UK could continuously implement insensitive suppression, COVID-19 epidemic would be able to control by 9 th April 2021 (the 252 nd day) and would be nearly ended by 1 st May 2020 (the 274 th day). In this case, the total deaths by the end on 16 th July 2020 in the UK would be about 131,746. However, it is not capable estimate the date when people return to normal life under this intervention.

Low-intensity, medium-intensity and high-intensity (P = 6, 8, 10) mitigation interventions in the UK on the 220 th day (8 th March 2021) were simulated when the UK lockdown was lifted for the third time, as shown in Figure 3 . 29 The simulation results show that the mitigation strategy can delay the COVID-19 epidemic in the UK, but there will still be the next peak of the epidemic in the future, which cannot reduce the total infected population. Compared with suppression, after the mitigation measures taken by the UK on 8 th March 2021, the number of new infections per day has fallen more slowly, which means that the number of infections in the UK is still increasing.

. CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The result appeared a similar trend as findings, taking mitigation intervention in the UK enabled reducing impacts of an epidemic by flattening the curve, reducing peak incidence and overall deaths. While total infectious population may increase over a longer period, the final mortality ratio may be minimized at the end. But as same as taking suppression, mitigation need to remain in place for as much of the epidemic period as possible.

Two possible situations were simulated in UK by implementing phase interventions as shown in Figure. 2) Since the third time the British lockdown was lifted, in all regions, the number of contacts P increased by 3 each month, and the lockdown was gradually lifted.

The simulation results in Figure 4 show that after the third lock-in was lifted, the 2-3 intensity phase intervention in the UK led to increased volatility and 2 or 3 infection peaks (the overall trend is still declining, and there is no obvious rebound) until the end of the epidemic. Compared with mitigation interventions, the total number of infections and deaths in the UK is not much different. In the phased intervention of intensity 2 and intensity 3, the total number of infections and deaths were 4,116,879 and 4,263,684, 133,192 and 135,339. The total number of deaths is about 2.3% to 6% higher than the results of the strong interventions carried out throughout the UK. Compared with suppression interventions that cannot accurately predict when people can return to a normal life , premature and high-intensity opening may lead to the recurrence of epidemics, phase intervention strategies that can predict the recovery time are obviously a better choice.

The end time of the epidemic with intensity 2 and intensity 3 phase intervention strategies is approximately: 29 th April 2021 (the 272 th day) and 6 th June 2021 (the 310 th day), and the time for people to return to normal social distance would be about: 6 months later and 4 months later . The number of deaths and infections of the two different intensity phase intervention strategies are similar, but the intervention strategy of intensity 3 can restore people to normal life two months earlier than the intervention strategy of intensity 2 (See Table 2 for details). This would be a great advantage for economic recovery.

. CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted March 12, 2021 

Recommended a vaccine intervention: suppose that the number of vaccines provided for domestic use in the UK doubles after the third British lockdown is lifted on 8 th March 2021. Combined with the previous phase intervention measures, a joint simulation is carried out to achieve an optimal intervention state. . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted March 12, 2021. ; https://doi.org/10.1101/2021.03.10.21252748 doi: medRxiv preprint is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted March 12, 2021. ;  In this case, an intensity 5 phase intervention strategy can be implemented. The implementation of a phase intervention strategy with an intensity of 5 will result in increased volatility and 2 infection peaks. The end of the epidemic will be around 25 th May 2021 (the 298 th day), and people will also return to normal social distance at the end of May. The overall number of infections and deaths are: 4,259,272 and 135,340.

Vaccine intervention strategies are heuristics to disengage us from focusing on social distance or the number of contacts. From another perspective, consider better interventions so that people can return to normal life and the country's economic recovery faster.

In addition to the intervention strategies in the previous cases, intervention strategies in other possible situations are also simulated.

The initial intervention intensity is different (P = 6, 8, 10, 12) or the increased intervention intensity is different (intensity 2, 3, 4, 5 and 6), as shown in Table 2 . First of all, this paper introduces the impact of different intervention strategies of mitigation intervention strategy. When the initial intensity is greater than or equal to 10, although it can effectively delay the epidemic of COVID-19, the epidemic will obviously re-erupt by . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. Secondly, in terms of the different increase intensities of the phase intervention strategies, we can find from Table 2 that when the monthly increase intensity is greater than 3 (the intensity is 4 or 5), it will cause the fluctuation to rise (the overall trend of the peak is upward)

, and there is a higher peak of infection, which makes it impossible to achieve the end of the epidemic in the first half of this year. In addition, 

It is expected that on 8 th March 2021, the third British lockdown which has lasted for two months will be lifted. The UK started vaccination in December 2020. Part of the population can be immune to the COVID virus until the third lockdown is lifted. In this situation, aiming at a balance infections, deaths and economic losses, we simulated and evaluated what interventions should be taken to control the UK's COVID-19 outbreak after vaccination and the release of feasible methods for the third lockdown.

We have found that between high-intensity suppression and mitigation intervention strategies, choosing a phased and progressive lifting intervention strategy may be an effective and efficient choice to limit the total deaths but maintain essential mobility for avoiding huge economic losses and society anxiety in a long period. The implementation of a progressive lifting strategy can restore necessary production and commercial activities primarily, realize a slow economic recovery and ease the economic burden caused by the country's long-term lockdown. According to the simulation of the model, with the increasing number of people immune to the COVID virus, the epidemic will not rebound of the epidemic, and normalize people's lives as quickly as possible under the control of the lifting intensity.

Under the above circumstances, our model finds that the total number of infections in the United Kingdom is limited to 4.2 million; the total number of deaths in the United Kingdom is 135 thousand, and people can return to their normal lives after four months, and the epidemic will end in early June. In addition, according to our prediction, under this kind of intervention, the UK will not experience a shortage of medical resources as it did in the first half of 2020.

. CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted March 12, 2021. ;  Our findings indicate that the implementation of repressive interventions requires consideration of other conditions in the region, such as cultural differences and industrial structure. The success of China's immediate suppression depends on strict restrictions on the movement of people and sufficient resources from other provinces and cities in China that have no cases of infection. Without sufficient external support, repression of the entire country will have a huge economic impact. Therefore, we have concluded that it is more suitable for the UK to adopt a phased lifting intervention.

Especially, total number of infections estimated in our model is measured by exposed population (asymptomatic, infectious), which may be much larger than other work that only estimates infectious population (symptomatic, infectious).We found that in the COVID-19 outbreak in Wuhan, a high proportion of exposed or infectious people (approximately 42%-60% of the total infected population) are selfhealing. These people may think they are healthy at home because they did not go to the hospital for a COVID-19 test. An important issue is that some SEIR models predict that the number of infections in Wuhan is more than 10 times the number of confirmed cases. 30 Table 1 , but these assumed values may vary by population or country. For example, assuming that the average time from mild cases to severe cases is 7 days, the average time from severe cases to death of hospitalized elderly is 14 days, and so on.

Changes in these variables may affect our estimates of infection and deaths in the UK. Third, our model simulates the mixed infection of the original virus and the mutant virus, assuming a mixed infection rate parameter, which is determined by the population of the main area infected by the mutant virus and the proportion of infection in the area. As the infection spreads, this parameter will also change. In the end, our model's estimate of the population's daily vaccination number is averagely estimated based on the data from the official website of the UK. In the future, with the improvement of vaccine production capacity, the parameters would be further adjusted based on real data in real time to achieve the best prediction results.

. CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The copyright holder for this preprint this version posted March 12, 2021. ; https://doi.org/10.1101/2021.03.10.21252748 doi: medRxiv preprint This paper conducts a feasibility study by defining a mathematical model called SEMCVRD, which analyzes and compares the intervention strategies to control the COVID-19 outbreak in the UK after vaccination and lifting the third lockdown. The model can not only be fitted and evaluated through the public data set of the UK, but also can be fine-tuned based on the real data of other countries using the trained model to achieve prediction and analysis of other countries. The experimental results show that, in the case of continuous increase in the number of people immune to the virus, the implementation of phased and progressive lifting interventions will achieve the best balance of infection, death and economic loss. In the future, we can extend our model to achieve mixed immunization of multiple vaccines and immunization strategies for people of different age groups.

Coronavirus disease 2019. World Heal

Transmission of SARS-CoV-2 Lineage B.1.1.7 in England : Insights from linking epidemiological and genetic data

Safety and Efficacy of the BNT162b2 mRNA Covid-19 Vaccine

BNT162b2 mRNA Covid-19 Vaccine in a Nationwide Mass Vaccination Setting

Israel Is First To

COVID-19 in New Zealand and the impact of the national response: a descriptive epidemiological study

Modelling the COVID-19 epidemic and implementation of population-wide interventions in Italy

The effect of multiple interventions to balance healthcare demand for controlling COVID-19 outbreaks: a modelling study

How will country-based mitigation measures influence the course of the COVID-19 epidemic?

Rolling Interventions for Controlling COVID-19 Outbreaks in the UK to Reduce Healthcare Demand

Feasibility study of mitigation and suppression strategies for controlling COVID-19 outbreaks in London and Wuhan

Feasibility of Controlling COVID-19 Outbreaks in the UK by Rolling Interventions

Impact of non-pharmaceutical interventions (NPIs) to reduce COVID-19 mortality and healthcare demand

Effects of non-pharmaceutical interventions on COVID-19 cases, deaths, and demand for hospital services in the UK: a modelling study

Case characteristics, resource use, and outcomes of 10021 patients with COVID-19 admitted to 920 German hospitals: an observational study

Investigation of three clusters of COVID-19 in Singapore: implications for surveillance and response measures

Feasibility of controlling COVID-19 outbreaks by isolation of cases and contacts

Transmissibility of 2019-nCoV

Incubation period of 2019 novel coronavirus (2019-nCoV) infections among travellers from Wuhan, China

Nowcasting and forecasting the potential domestic and international spread of the 2019-nCoV outbreak originating in Wuhan, China: a modelling study

Early estimation of the case fatality rate of COVID-19 in mainland China: a data-driven analysis

Report of the WHO-China Joint Mission on Coronavirus Disease 2019 (COVID-19). WHO-China Jt. Mission Coronavirus Dis

Modified SEIR and AI prediction of the epidemics trend of COVID-19 in China under public health interventions

The transmissibility of novel Coronavirus in the early stages of the 2019-20 outbreak in Wuhan: Exploring initial point-source exposure sizes and durations using scenario analysis

Overview of the Population

Report/ Annual number of hospital beds in the UK from

Living longer -how our population is changing and why it matters

The Global Impact of COVID-19 and Strategies for Mitigation and Suppression

Early dynamics of transmission and control of COVID-19: a mathematical modelling study