# Understanding Soaring Coronavirus Cases and the Effect of Contagion Policies in the UK

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. Population Dynamics

#### 2.2. Training and Testing the Model

## 3. Results and Discussion

## 4. Conclusions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

`odeint`from

`scipy`[14], a

`Python`wrapper for

`LSODA`from the

`FORTRAN`library

`ODEPACK`[15]. The non-linear square fittings where carried out by using

`curve_fit`from

`scipy`[14].

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Sketch of transitions in the (

**a**) free and (

**b**) controlled SIR network models of disease transmission, and (

**c**) model of the preventive social response, $\mathfrak{A}\left(t\right)$. S, I, R and V stand for susceptible, infected, recovered, and vaccinated, respectively. Additionally, $\beta $, $\alpha $ and $\nu $ are the infection, recovery, and vaccination rates, respectively. In the controlled SIR model, the infection rate is reduced by the factor $(1-\mathfrak{A}(t-\tau \left)\right)$, which depends on the incubation time period, $\tau $, the effectiveness of the social response, $\eta \in [0,1]$, the time when the awareness reaches its peak, ${t}_{0}$, the time extension of the maximum level of alert, T, and the characteristic times for reaching maximum awareness, so-called social inertia, ${\delta}_{i}$, and the relaxation time after lifting restrictions, ${\delta}_{r}$, respectively.

**Figure 2.**SARS-CoV-2 new daily cases (left axis): blue circles for first-wave data used to fit free and controlled SIR models (light-blue lines), red circles for second- and third-wave data used to test the models and their predictions (light-blue dashed lines). (

**a**) Free SIR model captures the essence of the time evolution of new CoVid-19 cases over March–July 2020 (inset plot), but totally fails to predict the second and third waves. (

**b**) The controlled SIR model without vaccination fits better to first-wave data (inset plot) than the free version. The grey area represents the effectiveness of preventive measures, $\mathfrak{A}\left(t\right)$ (right axis). The first wave of social awareness is fit together with $\beta $ and $\alpha $, showing a maximum of effectiveness ${\eta}_{1}\simeq 65\%$, social inertia ${\delta}_{i}\simeq 21\phantom{\rule{0.166667em}{0ex}}\mathrm{d}$, and social relaxation starting at mid June 2020, with prediction of no measures in ${\delta}_{r}\simeq 45\phantom{\rule{0.166667em}{0ex}}\mathrm{d}$ after relaxation begins. The second wave of social awareness begins in September (confirmed by the Prime Minister [10]), reaching ${\eta}_{2}\simeq 60\%$ by mid October 2020 (three-tier system was introduced [11]). The upsurge of CoVid-19 cases in December 2020 is again a consequence of social relaxation. (

**c**–

**e**) Controlled SIR model with vaccination rates: $0.1\%{\mathrm{d}}^{-1},\phantom{\rule{0.166667em}{0ex}}0.2\%{\mathrm{d}}^{-1},$ and $0.4\%{\mathrm{d}}^{-1}$, respectively, along with a third-wave of preventive measures (expected to reach maximum effectiveness, ${\eta}_{3}=70\%$, by the mid January 2021). To avoid a fourth wave, the vaccination campaign would need to deliver $\sim 200\times {10}^{3}$ vaccines per day ($\sim 0.4\%N/\mathrm{d}$) as of the first week of January 2021.

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**MDPI and ACS Style**

Durán-Olivencia, M.A.; Kalliadasis, S.
Understanding Soaring Coronavirus Cases and the Effect of Contagion Policies in the UK. *Vaccines* **2021**, *9*, 735.
https://doi.org/10.3390/vaccines9070735

**AMA Style**

Durán-Olivencia MA, Kalliadasis S.
Understanding Soaring Coronavirus Cases and the Effect of Contagion Policies in the UK. *Vaccines*. 2021; 9(7):735.
https://doi.org/10.3390/vaccines9070735

**Chicago/Turabian Style**

Durán-Olivencia, Miguel A., and Serafim Kalliadasis.
2021. "Understanding Soaring Coronavirus Cases and the Effect of Contagion Policies in the UK" *Vaccines* 9, no. 7: 735.
https://doi.org/10.3390/vaccines9070735