scholarly journals Defining and Computing Reproduction Numbers to Monitor the Outbreak of Covid-19 or Other Epidemics

2021 ◽  
Author(s):  
Paulo Zingano ◽  
Janaina Zingano ◽  
Alessandra Silva ◽  
Carolina Zingano
Keyword(s):  
Evolution Equations ◽  
Herd Immunity ◽  
Epidemiological Models ◽  
Seir Model ◽  
Full Implementation ◽  
Intervention Measures ◽  
Reproduction Numbers

We present a general approach to define reproduction ratios or numbers to monitor the outbreak of epidemics that are modeled by mathematical evolution equations. This provides a solution to an important topic that has not been completely settled in the literature, especially in the case of complex epidemiological models. We illustrate our procedure with a full implementation of a standard deterministic SEIR model that is applied to examine the Covid-19 outbreaks and the effects of intervention measures in several countries in America (Argentina, Brazil, Mexico, USA) and Europe (France, Italy, Spain and UK) in 2020. Our code is also used to investigate herd immunity levels for Covid-19, indicating values between 85% and 90%.

scholarly journals An evaluation of mathematical models for the outbreak of COVID-19

2020 ◽  
Vol 3 (2) ◽  
pp. 85-93 ◽  
Author(s):  
Ning Wang ◽  
Yuting Fu ◽  
Hu Zhang ◽  
Huipeng Shi
Keyword(s):  
Mathematical Models ◽  
Scientific Evidence ◽  
Herd Immunity ◽  
Intervention Measures ◽  
Reproduction Numbers ◽  
Critical Problems ◽  
Latent Effects ◽  
Health And Economic Development ◽  
Asymptomatic Infections ◽  
Challenging Question

Abstract Mathematical modelling performs a vital part in estimating and controlling the recent outbreak of coronavirus disease 2019 (COVID-19). In this epidemic, most countries impose severe intervention measures to contain the spread of COVID-19. The policymakers are forced to make difficult decisions to leverage between health and economic development. How and when to make clinical and public health decisions in an epidemic situation is a challenging question. The most appropriate solution is based on scientific evidence, which is mainly dependent on data and models. So one of the most critical problems during this crisis is whether we can develop reliable epidemiological models to forecast the evolution of the virus and estimate the effectiveness of various intervention measures and their impacts on the economy. There are numerous types of mathematical model for epidemiological diseases. In this paper, we present some critical reviews on mathematical models for the outbreak of COVID-19. Some elementary models are presented as an initial formulation for an epidemic. We give some basic concepts, notations, and foundation for epidemiological modelling. More related works are also introduced and evaluated by considering epidemiological features such as disease tendency, latent effects, susceptibility, basic reproduction numbers, asymptomatic infections, herd immunity, and impact of the interventions.

scholarly journals Herd immunity thresholds for SARS-CoV-2 estimated from unfolding epidemics

2020 ◽  
Author(s):  
Ricardo Aguas ◽  
Rodrigo M. Corder ◽  
Jessica G. King ◽  
Guilherme Gonçalves ◽  
Marcelo U. Ferreira ◽  
...  
Keyword(s):  
Severe Acute Respiratory Syndrome ◽  
Individual Variation ◽  
Herd Immunity ◽  
Epidemiological Models ◽  
Classical Formula ◽  
Social Distancing ◽  
Individual Susceptibility ◽  
Reproduction Numbers ◽  
Selective Depletion

As severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) spreads, the susceptible subpopulation declines causing the rate at which new infections occur to slow down. Variation in individual susceptibility or exposure to infection exacerbates this effect. Individuals that are more susceptible or more exposed tend to be infected and removed from the susceptible subpopulation earlier. This selective depletion of susceptibles intensifies the deceleration in incidence. Eventually, susceptible numbers become low enough to prevent epidemic growth or, in other words, the herd immunity threshold is reached. Here we fit epidemiological models with inbuilt distributions of susceptibility or exposure to SARS-CoV-2 outbreaks to estimate basic reproduction numbers (R0) alongside coefficients of individual variation (CV) and the effects of containment strategies. Herd immunity thresholds are then calculated as 1 − (1/R0)1/(1+CV2) or 1 − (1/R0)1/(1+2CV2), depending on whether variation is on susceptibility or exposure. Our inferences result in herd immunity thresholds around 10-20%, considerably lower than the minimum coverage needed to interrupt transmission by random vaccination, which for R0 higher than 2.5 is estimated above 60%. We emphasize that the classical formula, 1 − 1/R0, remains applicable to describe herd immunity thresholds for random vaccination, but not for immunity induced by infection which is naturally selective. These findings have profound consequences for the governance of the current pandemic given that some populations may be close to achieving herd immunity despite being under more or less strict social distancing measures.

scholarly journals The effectiveness of Non-pharmaceutical interventions in reducing the COVID-19 contagion in the UK, an observational and modelling study

PLoS ONE ◽  
2021 ◽  
Vol 16 (11) ◽  
pp. e0260364
Author(s):  
Giorgos Galanis ◽  
Corrado Di Guilmi ◽  
David L. Bennett ◽  
Georgios Baskozos
Keyword(s):  
Reproduction Number ◽  
Herd Immunity ◽  
Government Policies ◽  
Epidemiological Models ◽  
Seir Model ◽  
Epidemic Curve ◽  
Behavioural Insights ◽  
Herd Immunity Effect ◽  
The Uk ◽  
Pharmaceutical Interventions

Epidemiological models used to inform government policies aimed to reduce the contagion of COVID-19, assume that the reproduction number is reduced through Non-Pharmaceutical Interventions (NPIs) leading to physical distancing. Available data in the UK show an increase in physical distancing before the NPIs were implemented and a fall soon after implementation. We aimed to estimate the effect of people’s behaviour on the epidemic curve and the effect of NPIs taking into account this behavioural component. We have estimated the effects of confirmed daily cases on physical distancing and we used this insight to design a behavioural SEIR model (BeSEIR), simulated different scenaria regarding NPIs and compared the results to the standard SEIR. Taking into account behavioural insights improves the description of the contagion dynamics of the epidemic significantly. The BeSEIR predictions regarding the number of infections without NPIs were several orders of magnitude less than the SEIR. However, the BeSEIR prediction showed that early measures would still have an important influence in the reduction of infections. The BeSEIR model shows that even with no intervention the percentage of the cumulative infections within a year will not be enough for the epidemic to resolve due to a herd immunity effect. On the other hand, a standard SEIR model significantly overestimates the effectiveness of measures. Without taking into account the behavioural component, the epidemic is predicted to be resolved much sooner than when taking it into account and the effectiveness of measures are significantly overestimated.

scholarly journals Incorporating false negative tests in epidemiological models for SARS-CoV-2 transmission and reconciling with seroprevalence estimates

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Rupam Bhattacharyya ◽  
Ritoban Kundu ◽  
Ritwik Bhaduri ◽  
Debashree Ray ◽  
Lauren J. Beesley ◽  
...  
Keyword(s):  
False Negative ◽  
Population Based ◽  
Training Data ◽  
Epidemiological Models ◽  
Rt Pcr ◽  
Antibody Prevalence ◽  
Igg Antibody ◽  
False Negatives ◽  
Seir Model ◽  
Study Population

AbstractSusceptible-Exposed-Infected-Removed (SEIR)-type epidemiologic models, modeling unascertained infections latently, can predict unreported cases and deaths assuming perfect testing. We apply a method we developed to account for the high false negative rates of diagnostic RT-PCR tests for detecting an active SARS-CoV-2 infection in a classic SEIR model. The number of unascertained cases and false negatives being unobservable in a real study, population-based serosurveys can help validate model projections. Applying our method to training data from Delhi, India, during March 15–June 30, 2020, we estimate the underreporting factor for cases at 34–53 (deaths: 8–13) on July 10, 2020, largely consistent with the findings of the first round of serosurveys for Delhi (done during June 27–July 10, 2020) with an estimated 22.86% IgG antibody prevalence, yielding estimated underreporting factors of 30–42 for cases. Together, these imply approximately 96–98% cases in Delhi remained unreported (July 10, 2020). Updated calculations using training data during March 15-December 31, 2020 yield estimated underreporting factor for cases at 13–22 (deaths: 3–7) on January 23, 2021, which are again consistent with the latest (fifth) round of serosurveys for Delhi (done during January 15–23, 2021) with an estimated 56.13% IgG antibody prevalence, yielding an estimated range for the underreporting factor for cases at 17–21. Together, these updated estimates imply approximately 92–96% cases in Delhi remained unreported (January 23, 2021). Such model-based estimates, updated with latest data, provide a viable alternative to repeated resource-intensive serosurveys for tracking unreported cases and deaths and gauging the true extent of the pandemic.

scholarly journals Will the Large-scale Vaccination Succeed in Containing the COVID-19 Epidemic and How Soon?

2021 ◽  
Author(s):  
Shilei Zhao ◽  
Tong Sha ◽  
Yongbiao Xue ◽  
Chung-I Wu ◽  
Hua Chen
Keyword(s):  
United States Of America ◽  
Vaccine Efficacy ◽  
Large Scale ◽  
Herd Immunity ◽  
Vaccination Rate ◽  
Epidemic Dynamics ◽  
Intervention Measures ◽  
Vaccination Scheme ◽  
Mutant Strains ◽  
Promising Solution

The availability of vaccines provides a promising solution to containing the COVID-19 pandemic. Here, we develop an epidemiological model to quantitatively analyze and predict the epidemic dynamics of COVID-19 under vaccination. The model is applied to the daily released numbers of confirmed cases of Israel and United States of America to explore and predict the trend under vaccination based on their current epidemic status and intervention measures. For Israel, of which 53.83% of the population was fully vaccinated, under the current intensity of NPIs and vaccination scheme, the pandemic is predicted to end between May 14, 2021 to May 16, 2021 depending on an immunity duration between 180 days and 365 days; Assuming no NPIs after March 24, 2021, the pandemic will ends later, between July 4, 2021 to August 26, 2021. For USA, if we assume the current vaccination rate (0.268% per day) and intensity of NPIs, the pandemic will end between February 3, 2022 and August 17, 2029 depending on an immunity duration between 180 days and 365 days. However, assuming an immunity duration of 180 days and with no NPIs, the pandemic will not end, and instead reach an equilibrium state with a proportion of the population remaining actively infected. Overall the daily vaccination rate should be chosen according to the vaccine efficacy and the immunity duration to achieve herd immunity. In some situations, vaccination alone cannot stop the pandemic, and NPIs are necessary both to supplement vaccination and accelerate the end of the pandemic. Considering that vaccine efficacy and duration of immunity may be reduced for new mutant strains, it is necessary to remain cautiously optimistic about the prospect of the pandemic under vaccination.

scholarly journals Are the Objectives Proposed by the WHO for Routine Measles Vaccination Coverage and Population Measles Immunity Sufficient to Achieve Measles Elimination from Europe?

Vaccines ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 218
Author(s):  
Pedro Plans-Rubió
Keyword(s):  
World Health Organization ◽  
Vaccination Coverage ◽  
Herd Immunity ◽  
World Health ◽  
Measles Elimination ◽  
Reproduction Numbers ◽  
The World ◽  
Measles Vaccination ◽  
Health Organization ◽  
Measles Vaccination Coverage

Background: The World Health Organization (WHO) proposed two-dose measles vaccination coverage of at least 95% of the population and percentages of measles immunity in the population of 85%−95% in order to achieve measles elimination in Europe. The objectives of this study were: (1) to determine the measles vaccination coverage required to establish herd immunity against measles viruses with basic reproduction numbers (Ro) ranging from 6 to 60, and (2) to assess whether the objectives proposed by the WHO are sufficient to establish herd immunity against measles viruses. Methods: The herd immunity effects of the recommended objectives were assessed by considering the prevalence of protected individuals required to establish herd immunity against measles viruses with Ro values ranging from 6 to 60. Results: The study found that percentages of two-dose measles vaccination coverage from 88% to 100% could establish herd immunity against measles viruses with Ro from 6 to 19, assuming 95% measles vaccination effectiveness. The study found that the objective of 95% for two-dose measles vaccination coverage proposed by the WHO would not be sufficient to establish herd immunity against measles viruses with Ro ≥ 10, assuming 95% measles vaccination effectiveness. By contrast, a 97% measles vaccination coverage objective was sufficient to establish herd immunity against measles viruses, with Ro values from 6 to 13. Measles immunity levels recommended in individuals aged 1−4 years (≥85%) and 5−9 years (≥90%) might not be sufficient to establish herd immunity against most measles viruses, while those recommended in individuals aged 10 or more years (≥95%) could be sufficient to establish herd immunity against measles viruses with Ro values from 6 to 20. Conclusion: To meet the goal of measles elimination in Europe, it is necessary to achieve percentages of two-dose measles vaccination coverage of at least 97%, and measles immunity levels in children aged 1−9 years of at least 95%.

scholarly journals Modelling the Effectiveness of Epidemic Control Measures in Preventing the Transmission of COVID-19 in Malaysia

2020 ◽  
Vol 17 (15) ◽  
pp. 5509 ◽  
Author(s):  
Balvinder Singh Gill ◽  
Vivek Jason Jayaraj ◽  
Sarbhan Singh ◽  
Sumarni Mohd Ghazali ◽  
Yoon Ling Cheong ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Model Calibration ◽  
Reproduction Number ◽  
Close Contact ◽  
Movement Control ◽  
Control Measures ◽  
Seir Model ◽  
Epidemic Curve ◽  
Reproduction Numbers ◽  
Control Order

Malaysia is currently facing an outbreak of COVID-19. We aim to present the first study in Malaysia to report the reproduction numbers and develop a mathematical model forecasting COVID-19 transmission by including isolation, quarantine, and movement control measures. We utilized a susceptible, exposed, infectious, and recovered (SEIR) model by incorporating isolation, quarantine, and movement control order (MCO) taken in Malaysia. The simulations were fitted into the Malaysian COVID-19 active case numbers, allowing approximation of parameters consisting of probability of transmission per contact (β), average number of contacts per day per case (ζ), and proportion of close-contact traced per day (q). The effective reproduction number (Rt) was also determined through this model. Our model calibration estimated that (β), (ζ), and (q) were 0.052, 25 persons, and 0.23, respectively. The (Rt) was estimated to be 1.68. MCO measures reduce the peak number of active COVID-19 cases by 99.1% and reduce (ζ) from 25 (pre-MCO) to 7 (during MCO). The flattening of the epidemic curve was also observed with the implementation of these control measures. We conclude that isolation, quarantine, and MCO measures are essential to break the transmission of COVID-19 in Malaysia.

scholarly journals Bayesian Inference of State-Level COVID-19 Basic Reproduction Numbers across the United States

2021 ◽  
Author(s):  
Abhishek Mallela ◽  
Jacob Neumann ◽  
Ely F Miller ◽  
Ye Chen ◽  
Richard G Posner ◽  
...  
Keyword(s):  
United States ◽  
Bayesian Inference ◽  
Disease Transmission ◽  
Case Reports ◽  
Herd Immunity ◽  
State Level ◽  
The United States ◽  
Expected Number ◽  
Reproduction Numbers ◽  
A Posteriori Estimates

Although many persons in the United States have acquired immunity to COVID-19, either through vaccination or infection with SARS-CoV-2, COVID-19 will pose an ongoing threat to non-immune persons so long as disease transmission continues. We can estimate when sustained disease transmission will end in a population by calculating the population-specific basic reproduction number R_0, the expected number of secondary cases generated by an infected person in the absence of any interventions. The value of R_0 relates to a herd immunity threshold (HIT), which is given by 1-1/R_0. When the immune fraction of a population exceeds this threshold, sustained disease transmission becomes exponentially unlikely (barring mutations allowing SARS-CoV-2 to escape immunity). Here, we report state-level R_0 estimates obtained using Bayesian inference. Maximum a posteriori estimates range from 7.1 for New Jersey to 2.3 for Wyoming, indicating that disease transmission varies considerably across states and that reaching herd immunity will be more difficult in some states than others. R_0 estimates were obtained from compartmental models via the next-generation matrix approach after each model was parameterized using regional daily confirmed case reports of COVID-19 from 21-January-2020 to 21-June-2020. Our R_0 estimates characterize infectiousness of ancestral strains, but they can be used to determine HITs for a distinct, currently dominant circulating strain, such as SARS-CoV-2 variant Delta (lineage B.1.617.2), if the relative infectiousness of the strain can be ascertained. On the basis of Delta-adjusted HITs, vaccination data, and seroprevalence survey data, we find that no state has achieved herd immunity as of 20-September-2021.

scholarly journals Calibrating an SIR model for South Korea COVID-19 infections and predicting vaccination impact

2021 ◽  
Author(s):  
Brandon Pae
Keyword(s):  
South Korea ◽  
Vaccination Coverage ◽  
Herd Immunity ◽  
Sir Model ◽  
Transmission Dynamics ◽  
Effective Vaccine ◽  
Epidemiological Models ◽  
Policy Decisions

In the span of 1.5 years, COVID-19 has caused more than 4 million deaths worldwide. To prevent such a catastrophe from reoccurring, it is necessary to test and refine current epidemiological models that impact policy decisions. Thus, we developed a deterministic SIR model to examine the long-term transmission dynamics of COVID-19 in South Korea. Using this model, we analyzed how vaccines would affect the number of cases. We found that a 70% vaccination coverage with a 100% effective vaccine would effectively eliminate the number of cases and herd immunity would have been obtained approximately 85 days after February 15 had there not been a reintroduction of cases.

scholarly journals Estimating the impact of interventions against COVID-19: from lockdown to vaccination

2021 ◽  
Author(s):  
James Thompson ◽  
Stephen Wattam
Keyword(s):  
Spatial Clustering ◽  
Herd Immunity ◽  
Contact Tracing ◽  
Agent Based Model ◽  
Seir Model ◽  
Agent Based ◽  
Resident Population ◽  
First Case ◽  
Equivalent Equation ◽  
The Impact

AbstractCoronavirus disease 2019 (COVID-19) is an infectious disease of humans caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Since the first case was identified in China in December 2019 the disease has spread worldwide, leading to an ongoing pandemic. In this article, we present a detailed agent-based model of COVID-19 in Luxembourg, and use it to estimate the impact, on cases and deaths, of interventions including testing, contact tracing, lockdown, curfew and vaccination.Our model is based on collation, with agents performing activities and moving between locations accordingly. The model is highly heterogeneous, featuring spatial clustering, over 2000 behavioural types and a 10 minute time resolution. The model is validated against COVID-19 clinical monitoring data collected in Luxembourg in 2020.Our model predicts far fewer cases and deaths than the equivalent equation-based SEIR model. In particular, with R0 = 2.45, the SEIR model infects 87% of the resident population while our agent-based model results, on average, in only around 23% of the resident population infected. Our simulations suggest that testing and contract tracing reduce cases substantially, but are much less effective at reducing deaths. Lockdowns appear very effective although costly, while the impact of an 11pm-6am curfew is relatively small. When vaccinating against a future outbreak, our results suggest that herd immunity can be achieved at relatively low levels, with substantial levels of protection achieved with only 30% of the population immune. When vaccinating in midst of an outbreak, the challenge is more difficult. In this context, we investigate the impact of vaccine efficacy, capacity, hesitancy and strategy.We conclude that, short of a permanent lockdown, vaccination is by far the most effective way to suppress and ultimately control the spread of COVID-19.

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