scholarly journals A mathematical model reveals the influence of population heterogeneity on herd immunity to SARS-CoV-2

Science ◽  
2020 ◽  
Vol 369 (6505) ◽  
pp. 846-849 ◽  
Author(s):  
Tom Britton ◽  
Frank Ball ◽  
Pieter Trapman
Keyword(s):  
Mathematical Model ◽  
Severe Acute Respiratory Syndrome ◽  
Preventive Measures ◽  
Social Activity ◽  
Herd Immunity ◽  
Population Heterogeneity ◽  
Contact Rates ◽  
Mixing Rates ◽  
Age Structured ◽  
Induced Immunity

Despite various levels of preventive measures, in 2020, many countries have suffered severely from the coronavirus disease 2019 (COVID-19) pandemic caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) virus. Using a model, we show that population heterogeneity can affect disease-induced immunity considerably because the proportion of infected individuals in groups with the highest contact rates is greater than that in groups with low contact rates. We estimate that if R0 = 2.5 in an age-structured community with mixing rates fitted to social activity, then the disease-induced herd immunity level can be ~43%, which is substantially less than the classical herd immunity level of 60% obtained through homogeneous immunization of the population. Our estimates should be interpreted as an illustration of how population heterogeneity affects herd immunity rather than as an exact value or even a best estimate.

scholarly journals The disease-induced herd immunity level for Covid-19 is substantially lower than the classical herd immunity level

2020 ◽  
Author(s):  
Tom Britton ◽  
Frank Ball ◽  
Pieter Trapman
Keyword(s):  
Preventive Measures ◽  
Reproduction Number ◽  
Social Activity ◽  
Herd Immunity ◽  
Contact Rates ◽  
Mixing Rates ◽  
Disease Spreading ◽  
Age Structured ◽  
Induced Immunity ◽  
The Basic Reproduction Number

AbstractMost countries are suffering severely from the ongoing covid-19 pandemic despite various levels of preventive measures. A common question is if and when a country or region will reach herd immunity h. The classical herd immunity level hC is defined as hC = 1−1/R0, where R0 is the basic reproduction number, for covid-19 estimated to lie somewhere in the range 2.2-3.5 depending on country and region. It is shown here that the disease-induced herd immunity level hD, after an outbreak has taken place in a country/region with a set of preventive measures put in place, is actually substantially smaller than hC. As an illustration we show that if R0 = 2.5 in an age-structured community with mixing rates fitted to social activity studies, and also categorizing individuals into three categories: low active, average active and high active, and where preventive measures affect all mixing rates proportionally, then the disease-induced herd immunity level is hD = 43% rather than hC = 1−1/2.5 = 60%. Consequently, a lower fraction infected is required for herd immunity to appear. The underlying reason is that when immunity is induced by disease spreading, the proportion infected in groups with high contact rates is greater than that in groups with low contact rates. Consequently, disease-induced immunity is stronger than when immunity is uniformly distributed in the community as in the classical herd immunity level.

scholarly journals Age-targeted dose allocation can halve COVID-19 vaccine requirements

2020 ◽  
Author(s):  
Michael T. Meehan ◽  
Daniel G. Cocks ◽  
Jamie M. Caldwell ◽  
James M. Trauer ◽  
Adeshina I. Adekunle ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Severe Disease ◽  
Herd Immunity ◽  
Population Level ◽  
Morbidity And Mortality ◽  
Effective Strategy ◽  
Risk Of Infection ◽  
Middle Aged ◽  
Contact Rates ◽  
Age Structured

ABSTRACTIn anticipation of COVID-19 vaccine deployment, we use an age-structured mathematical model to investigate the benefits of optimizing age-specific dose allocation to suppress the transmission, morbidity and mortality of SARS-CoV-2 and the associated disease, COVID-19. To minimize transmission, we find that the highest priority individuals across 179 countries are typically those between 30 and 59 years of age because of their high contact rates and higher risk of infection and disease. Conversely, morbidity and mortality are initially most effectively reduced by targeting 60+ year olds who are more likely to experience severe disease. However, when population-level coverage is sufficient — such that herd immunity can be achieved through targeted dose allocation — prioritizing middle-aged individuals becomes the most effective strategy to minimize hospitalizations and deaths. For each metric considered, we show that optimizing the allocation of vaccine doses can more than double their effectiveness.

scholarly journals The risk for a new COVID-19 wave and how it depends on R 0 , the current immunity level and current restrictions

2021 ◽  
Vol 8 (7) ◽  
pp. 210386
Author(s):  
Tom Britton ◽  
Pieter Trapman ◽  
Frank Ball
Keyword(s):  
Preventive Measures ◽  
Social Activity ◽  
Herd Immunity ◽  
Data Fitting ◽  
Time Varying ◽  
Two Factors ◽  
Simplistic Model ◽  
Induced Immunity ◽  
Epidemic Wave ◽  
Future Outbreak

The COVID-19 pandemic has hit different regions differently. The current disease-induced immunity level î in a region approximately equals the cumulative fraction infected, which primarily depends on two factors: (i) the initial potential for COVID-19 in the region ( R 0 ), and (ii) the preventive measures put in place. Using a mathematical model including heterogeneities owing to age, social activity and susceptibility, and allowing for time-varying preventive measures, the risk for a new epidemic wave and its doubling time are investigated. Focus lies on quantifying the minimal overall effect of preventive measures p Min needed to prevent a future outbreak. It is shown that î plays a more influential roll than when immunity is obtained from vaccination. Secondly, by comparing regions with different R 0 and î it is shown that regions with lower R 0 and low î may need higher preventive measures ( p Min ) compared with regions having higher R 0 but also higher î , even when such immunity levels are far from herd immunity. Our results are illustrated on different regions but these comparisons contain lots of uncertainty due to simplistic model assumptions and insufficient data fitting, and should accordingly be interpreted with caution.

scholarly journals Effect of Vaccination to COVID-19 Disease Progression and Herd Immunity

2021 ◽  
Vol 9 (1) ◽  
pp. 262-272
Author(s):  
Randy L. Caga-anan ◽  
Michelle N. Raza ◽  
Grace Shelda G. Labrador ◽  
Ephrime B. Metillo ◽  
Pierre del Castillo ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Disease Progression ◽  
Herd Immunity ◽  
Vaccination Rate ◽  
The Philippines ◽  
Model Parameters ◽  
Delay Term ◽  
Induced Immunity ◽  
Determining Factor ◽  
Disease Free

Abstract A mathematical model of COVID-19 with a delay-term for the vaccinated compartment is developed. It has parameters accounting for vaccine-induced immunity delay, vaccine effectiveness, vaccination rate, and vaccine-induced immunity duration. The model parameters before vaccination are calibrated with the Philippines’ confirmed cases. Simulations show that vaccination has a significant effect in reducing future infections, with the vaccination rate being the dominant determining factor of the level of reduction. Moreover, depending on the vaccination rate and the vaccine-induced immunity duration, the system could reach a disease-free state but could not attain herd immunity. Simulations are also done to compare the effects of the various available vaccines. Results show that Pfizer-BioNTech has the most promising effect while Sinovac has the worst result relative to the others.

scholarly journals The risk for a new COVID-19 wave – and how it depends on R0, the current immunity level and current restrictions

2020 ◽  
Author(s):  
Tom Britton ◽  
Pieter Trapman ◽  
Frank Ball
Keyword(s):  
Preventive Measures ◽  
Reproduction Number ◽  
Social Activity ◽  
Herd Immunity ◽  
Time Varying ◽  
The World ◽  
Two Factors ◽  
Second Wave ◽  
Different Parts ◽  
Future Outbreak

AbstractThe COVID-19 pandemic has hit different parts of the world differently: some regions are still in the rise of the first wave, other regions are now facing a decline after a first wave, and yet other regions have started to see a second wave. The current immunity level î in a region is closely related to the cumulative fraction infected, which primarily depends on two factors: a) the initial potential for COVID-19 in the region (often quantified by the basic reproduction number R0), and b) the timing, amount and effectiveness of preventive measures put in place. By means of a mathematical model including heterogeneities owing to age, social activity and susceptibility, and allowing for time-varying preventive measures, the risk for a new epidemic wave and its doubling time, and how they depend on R0, î and the overall effect of the current preventive measures, are investigated. Focus lies on quantifying the minimal overall effect of preventive measures pMin needed to prevent a future outbreak. The first result shows that the current immunity level î plays a more influential roll than when immunity is obtained from vaccination. Secondly, by comparing regions with different R0 and î it is shown that regions with lower R0 and low î may now need higher preventive measures (pMin) compared with other regions having higher R0 but also higher î, even when such immunity levels are far from herd immunity.

scholarly journals Will SARS-CoV-2 Become Just Another Seasonal Coronavirus?

Viruses ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 854
Author(s):  
Alexander B. Beams ◽  
Rebecca Bateman ◽  
Frederick R. Adler
Keyword(s):  
Mathematical Model ◽  
Herd Immunity ◽  
Population Heterogeneity ◽  
Emerging Pathogens ◽  
Wide Range ◽  
The Future ◽  
General Mathematical Model ◽  
The Right ◽  
Over Time ◽  
Partial Immunity

The future prevalence and virulence of SARS-CoV-2 is uncertain. Some emerging pathogens become avirulent as populations approach herd immunity. Although not all viruses follow this path, the fact that the seasonal coronaviruses are benign gives some hope. We develop a general mathematical model to predict when the interplay among three factors, correlation of severity in consecutive infections, population heterogeneity in susceptibility due to age, and reduced severity due to partial immunity, will promote avirulence as SARS-CoV-2 becomes endemic. Each of these components has the potential to limit severe, high-shedding cases over time under the right circumstances, but in combination they can rapidly reduce the frequency of more severe and infectious manifestation of disease over a wide range of conditions. As more reinfections are captured in data over the next several years, these models will help to test if COVID-19 severity is beginning to attenuate in the ways our model predicts, and to predict the disease.

scholarly journals Data-driven estimate of SARS-CoV-2 herd immunity threshold in populations with individual contact pattern variations

2021 ◽  
Author(s):  
Dan Lu ◽  
Alberto Aleta ◽  
Marco Ajelli ◽  
Romualdo Pastor-Satorras ◽  
Alessandro Vespignani ◽  
...  
Keyword(s):  
Herd Immunity ◽  
Vaccination Strategy ◽  
Mass Vaccination ◽  
Data Driven ◽  
Vaccination Programs ◽  
Contact Patterns ◽  
Social Mixing ◽  
Age Structured ◽  
Individual Contact ◽  
Induced Immunity

The development of efficacious vaccines has made it possible to envision mass vaccination programs aimed at suppressing SARS-CoV-2 transmission around the world. Here we use a data-driven age-structured multilayer representation of the population of 34 countries to estimate the disease induced immunity threshold, accounting for the contact variability across individuals. We show that the herd immunization threshold of random (un-prioritized) mass vaccination programs is generally larger than the disease induced immunity threshold. We use the model to test two additional vaccine prioritization strategies, transmission-focused and age-based, in which individuals are inoculated either according to their behavior (number of contacts) or infection fatality risk, respectively. Our results show that in the case of a sterilizing vaccine the behavioral strategy achieves herd-immunity at a coverage comparable to the disease-induced immunity threshold, but it appears to have inferior performance in averting deaths than the risk vaccination strategy. The presented results have potential use in defining the effects that the heterogeneity of social mixing and contact patterns has on herd immunity levels and the deployment of vaccine prioritization strategies.

Forecast of COVID-19 Trend Following Countrywide Movement Control Order in Malaysia: SEIR Model Approach (Preprint)

2020 ◽  
Author(s):  
Aidalina Mahmud ◽  
Poh Ying Lim ◽  
Hayati Kadir Shahar
Keyword(s):  
Mathematical Model ◽  
Incidence Rate ◽  
Movement Control ◽  
Seir Model ◽  
Infection Incidence ◽  
Contact Rates ◽  
Exposed Population ◽  
Control Order ◽  
Future Work ◽  
Model Approach

BACKGROUND On March 18, 2020, the Malaysian government implemented Movement Control Order (MCO) to limit the contact rates among the population and infected individuals. OBJECTIVE The objective of this study was to forecast the trend of the COVID-19 epidemic in Malaysia in terms of its magnitude and duration. METHODS Data for this analysis was obtained from publicly available databases, from March 17 until March 27, 2020. By applying the Susceptible, Exposed, Infectious and Removed (SEIR) mathematical model and several predetermined assumptions, two analyses were carried out: without and with MCO implementation. RESULTS Without MCO, it is forecasted that it would take 18 days to reach the peak of infection incidence. The incidence rate would plateau at day 80 and end by day 94, with 43% of the exposed population infected. With the implementation of the MCO, it is forecasted that new cases of infection would peak at day 25, plateau at day 90 and end by day 100. At its peak, the infection could affect up to about 40% of the exposed population. CONCLUSIONS It is forecasted that the COVID-19 epidemic in Malaysia will subside soon after the mid-year of 2020. Although the implementation of MCO can flatten the epidemiological curve, it also prolongs the duration of the epidemic. The MCO can result in several unfavorable consequences in economic and psychosocial aspects. A future work of an exit plan for the MCO should also be devised and implemented gradually. The exit plan raises several timely issues of re-infection resurgence after MCO are lifted.

scholarly journals COVID-19: a review of current knowledge regarding exposure, quarantine, isolation and other preventive measures

2021 ◽  
Vol 8 ◽  
pp. 204993612110320
Author(s):  
Robert Rosolanka ◽  
Andres F. Henao-Martinez ◽  
Larissa Pisney ◽  
Carlos Franco-Paredes ◽  
Martin Krsak
Keyword(s):  
Immune Response ◽  
Severe Acute Respiratory Syndrome ◽  
Clinical Response ◽  
Preventive Measures ◽  
Current Knowledge ◽  
Therapeutic Options ◽  
Exposure Control ◽  
Knowledge Gaps ◽  
Vaccination Strategies ◽  
Speed Up

Deeper understanding of the spread, morbidity, fatality, and development of immune response associated with coronavirus disease 2019 (COVID-19), caused by severe acute respiratory syndrome coronavirus 2, is necessary in order to establish an appropriate epidemiological and clinical response. Exposure control represents a key part of the combat against COVID-19, as the effectiveness of current therapeutic options remains partial. Since the preventive measures have not been sufficiently able to slow down this pandemic, in this article we explore some of the pertinent knowledge gaps, while overall looking to effective vaccination strategies as a way out. Early on, such strategies may need to rely on counting the convalescents as protected in order to speed up the immunization of the whole population.

COVID-19: Are Experimental Drugs Cure or Ill?

2021 ◽  
Vol 16 ◽  
Author(s):  
Bensu Karahalil ◽  
Aylin Elkama
Keyword(s):  
Clinical Trials ◽  
Severe Acute Respiratory Syndrome ◽  
Adverse Effects ◽  
Antiviral Treatment ◽  
Herd Immunity ◽  
Mortality Rates ◽  
Death Rates ◽  
Experimental Drugs ◽  
Combined Use ◽  
The World

Background: Coronavirus disease 2019 (COVID-19) is a new strain of coronavirus. It is characterized by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). It has quickly influenced all over the world since it spreads easily. Common symptoms are fever, cough, difficulty in breathing and muscle aches. Despite the urgent need to find an effective antiviral treatment, already available agents are being used alone or in combination all over the world. At the beginning of the pandemic, death rates of infection caused by COVID-19 are high but "is COVID-19 responsible for all deaths?", or “are there any contributions of the frequently used drugs in this period to these deaths?” Surely herd immunity plays a major role and has the contribution in the decline in mortality rates. Meanwhile, it is kept in mind that due to safety concerns, changes have also been made to the dosage and combined use of frequently used drugs. Objective: In this review, answers to two questions above and the safety of treatments, toxicities of agents involving chloroquine, hydroxychloroquine, remdesivir, favipiravir, lopiravir/ritonavir, sarilumab, tocilizumab, siltuximab, corticosteroids and bromhexine which are the most frequently used in both Turkey and all over the world will be summarized. Conclusion: Among these drugs favipiravir seems the most promising drug due to more tolerable adverse effects. More clinical trials with large sample sizes are needed to find the most effective and safe drug for COVID-19 treatment.

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