scholarly journals COVID-19 PANDEMICS: HOW FAR ARE WE FROM HERD IMMUNITY?

2020 ◽  
Author(s):  
Carlos Hernandez-Suarez ◽  
Efren Murillo-Zamora ◽  
Francisco Espinoza Gómez
Keyword(s):  
Infection Rate ◽  
Study Design ◽  
Removal Rate ◽  
Herd Immunity ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Fatality Risk

ABSTRACTObjectivesto estimate the current number of total infections in a region in order to measure the progress of the epidemic with the purpose of reopening activities and planning the deployment of vaccines.Study designWe recovered estimates of the basic reproductive number (R0) and the Infection Fatality Risk (IFR) as well as the number of confirmed cases and deaths in several countries.Methodsthis works presents an expression to estimate the number of remaining susceptible in a population using the observed number of SARS-CoV-2 related deaths and current estimates of R0 and IFR.Resultsthe epidemic will infect most of the population causing 2.5 deaths per thousand inhabitants on average, and herd immunity will be achieved when the number of deaths per thousand inhabitants is close to two. This work introduces an expression to provide estimates of the number of remaining susceptible in a region using the reported number of deaths.Conclusionsany region with fewer than 2.5 deaths per thousand individuals will continue accumulating deaths until this average is achieved, and the infection rate will exceed the removal rate until the number of deaths is about two deaths per thousand, when herd immunity is reached. Waves may occur in any region where the number of deaths is below the herd immunity level.

scholarly journals Stability and Hopf Bifurcation of a Vector-Borne Disease Model with Saturated Infection Rate and Reinfection

2019 ◽  
Vol 2019 ◽  
pp. 1-17 ◽  
Author(s):  
Zhixing Hu ◽  
Shanshan Yin ◽  
Hui Wang
Keyword(s):  
Hopf Bifurcation ◽  
Infection Rate ◽  
Disease Model ◽  
Endemic Equilibrium ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Cure Rate ◽  
Vector Borne Disease ◽  
Vector Borne ◽  
The Stability

This paper established a delayed vector-borne disease model with saturated infection rate and cure rate. First of all, according to the basic reproductive number R0, we determined the disease-free equilibrium E0 and the endemic equilibrium E1. Through the analysis of the characteristic equation, we consider the stability of two equilibriums. Furthermore, the effect on the stability of the endemic equilibrium E1 by delay was studied, the existence of Hopf bifurcations of this system in E1 was analyzed, and the length of delay to preserve stability was estimated. The direction and stability of the Hopf bifurcation were also been determined. Finally, we performed some numerical simulation to illustrate our main results.

scholarly journals Caveats on COVID-19 herd immunity threshold: the Spain case

2022 ◽  
Vol 12 (1) ◽  
Author(s):  
David García-García ◽  
Enrique Morales ◽  
Eva S. Fonfría ◽  
Isabel Vigo ◽  
Cesar Bordehore
Keyword(s):  
Upper Bound ◽  
Generation Time ◽  
Time Distribution ◽  
Herd Immunity ◽  
Late Summer ◽  
Spanish Population ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Population Estimates ◽  
Parameter Measuring

AbstractAfter a year of living with the COVID-19 pandemic and its associated consequences, hope looms on the horizon thanks to vaccines. The question is what percentage of the population needs to be immune to reach herd immunity, that is to avoid future outbreaks. The answer depends on the basic reproductive number, R0, a key epidemiological parameter measuring the transmission capacity of a disease. In addition to the virus itself, R0 also depends on the characteristics of the population and their environment. Additionally, the estimate of R0 depends on the methodology used, the accuracy of data and the generation time distribution. This study aims to reflect on the difficulties surrounding R0 estimation, and provides Spain with a threshold for herd immunity, for which we considered the different combinations of all the factors that affect the R0 of the Spanish population. Estimates of R0 range from 1.39 to 3.10 for the ancestral SARS-CoV-2 variant, with the largest differences produced by the method chosen to estimate R0. With these values, the herd immunity threshold (HIT) ranges from 28.1 to 67.7%, which would have made 70% a realistic upper bound for Spain. However, the imposition of the delta variant (B.1.617.2 lineage) in late summer 2021 may have expanded the range of R0 to 4.02–8.96 and pushed the upper bound of the HIT to 90%.

scholarly journals Estimation of the Basic Reproduction Number of Novel Influenza A (H1N1) pdm09 in Elementary Schools Using the SIR Model

2017 ◽  
Vol 11 (1) ◽  
pp. 64-72 ◽  
Author(s):  
Daisuke Furushima ◽  
Shoko Kawano ◽  
Yuko Ohno ◽  
Masayuki Kakehashi
Keyword(s):  
Elementary Schools ◽  
Infection Rate ◽  
School Size ◽  
Influenza A ◽  
Missing Values ◽  
Sir Model ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Influenza A H1n1 ◽  
Novel Influenza A

Background: The novel influenza A (H1N1) pdm09 (A/H1N1pdm) pandemic of 2009-2010 had a great impact on society. Objective: We analyzed data from the absentee survey, conducted in elementary schools of Oita City, to evaluate the A/H1N1pdm pandemic and to estimate the basic reproductive number (R0 ) of this novel strain. Method: We summarized the overall absentee data and calculated the cumulative infection rate. Then, we classified the data into 3 groups according to school size: small (<300 students), medium (300–600 students), and large (>600 students). Last, we estimated the R0 value by using the Susceptible-Infected-Recovered (SIR) mathematical model. Results: Data from 60 schools and 27,403 students were analyzed. The overall cumulative infection rate was 44.4%. There were no significant differences among the grades, but the cumulative infection rate increased as the school size increased, being 37.7%, 44.4%, and 46.6% in the small, medium, and large school groups, respectively. The optimal R0 value was 1.33, comparable with that previously reported. The data from the absentee survey were reliable, with no missing values. Hence, the R0 derived from the SIR model closely reflected the observed R0 . The findings support previous reports that school children are most susceptible to A/H1N1pdm virus infection and suggest that the scale of an outbreak is associated with the size of the school. Conclusion: Our results provide further information about the A/H1N1pdm pandemic. We propose that an absentee survey should be implemented in the early stages of an epidemic, to prevent a pandemic.

scholarly journals Epidemiology of the Zika virus outbreak in the Cabo Verde Islands, West Africa

2017 ◽  
Author(s):  
José Lourenço ◽  
Maria de Lourdes Monteiro ◽  
Tomás Valdez ◽  
Júlio Monteiro Rodrigues ◽  
Oliver G. Pybus ◽  
...  
Keyword(s):  
West Africa ◽  
Zika Virus ◽  
Attack Rate ◽  
Herd Immunity ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Mathematical Framework ◽  
Single Wave ◽  
Cabo Verde ◽  
Small Observation

AbstractIntroductionThe Zika virus (ZIKV) outbreak in the island nation of Cabo Verde was of unprecedented magnitude in Africa and the first to be associated with microcephaly in the continent.MethodsUsing a simple mathematical framework we present a first epidemiological assessment of attack and observation rates from 7,580 ZIKV notified cases and 18 microcephaly reports between July 2015 and May 2016.ResultsIn line with observations from the Americas and elsewhere, the single-wave Cabo Verdean ZIKV epidemic was characterized by a basic reproductive number of 1.85 (95% CI, 1.5 −2.2), with overall the attack rate of 51.1% (range 42.1 - 61.1) and observation rate of 2.7% (range 2.29 - 3.33).ConclusionCurrent herd-immunity may not be sufficient to prevent future small-to-medium epidemics in Cabo Verde. Together with a small observation rate, these results highlight the need for rapid and integrated epidemiological, molecular and genomic surveillance to tackle forthcoming outbreaks of ZIKV and other arboviruses.

scholarly journals A Mathematical Analysis of an In-vivo Ebola Virus Transmission Dynamics Model

2021 ◽  
Vol 47 (4) ◽  
pp. 1464-1477
Author(s):  
Seleman Ismail ◽  
Adeline Peter Mtunya
Keyword(s):  
Mathematical Model ◽  
Infection Rate ◽  
Ebola Virus ◽  
Virus Transmission ◽  
Transmission Dynamics ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Model Parameters ◽  
Sensitivity Index

Ebola virus (EBOV) infection is a hemorrhagic and hazardous disease, which is among the most shocking threats to human health causing a large number of deaths. Currently, there are no approved curative therapies for the disease. In this study, a mathematical model for in-vivo Ebola virus transmission dynamics was analyzed. The analysis of the model mainly focused on the sensitivity of basic reproductive number,  pertaining to the model parameters. Particularly, the sensitivity indices of all parameters of  were computed by using the forward normalized sensitivity index method. The results showed that a slight change in the infection rate immensely influences  while the same change in the production rate of the virus has the least impact on . Thus, , being a determining factor  of the disease progression, deliberate control measures targeting the infection rate, the most positively sensitive parameter, are required. This implies that reducing infection rate will redirect the disease to extinction. Keywords: Ebola virus infection, immune response, sensitivity index, mathematical model.

scholarly journals Implications of Test Characteristics and Population Seroprevalence on “Immune Passport” Strategies

2020 ◽  
Author(s):  
Daniel B Larremore ◽  
Kate M Bubar ◽  
Yonatan H Grad
Keyword(s):  
False Positive ◽  
Herd Immunity ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Serological Tests ◽  
Test Characteristics ◽  
Simple Question ◽  
Minimum Requirements ◽  
Test Specificity ◽  
Repeat Infection

Abstract Various forms of “immune passports” or “antibody certificates” are being considered in conversations around reopening economies after periods of social distancing. A critique of such programs focuses on the uncertainty around whether seropositivity means immunity from repeat infection. However, an additional important consideration is that the low positive predictive value of serological tests in the setting of low population seroprevalence and imperfect test specificity will lead to many false-positive passport holders. Here, we pose a simple question: how many false-positive passports could be issued while maintaining herd immunity in the workforce? Answering this question leads to a simple mathematical formula for the minimum requirements of serological tests for a passport program, which depend on the population prevalence and the value of the basic reproductive number, R0. Our work replaces speculation in the press with rigorous analysis, and will need to be considered in policy decisions that are based on individual and population serology results.

scholarly journals Modelling the Transmission Dynamics of Tuberculosis in the Ashanti Region of Ghana

2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Felix Okoe Mettle ◽  
Prince Osei Affi ◽  
Clement Twumasi
Keyword(s):  
Deterministic Model ◽  
Equilibrium Points ◽  
Herd Immunity ◽  
Transmission Dynamics ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Seir Model ◽  
High Burden ◽  
Ashanti Region ◽  
Over Time

Mathematical models can aid in elucidating the spread of infectious disease dynamics within a given population over time. In an attempt to model tuberculosis (TB) dynamics among high-burden districts in the Ashanti Region of Ghana, the SEIR epidemic model with demography was employed within both deterministic and stochastic settings for comparison purposes. The deterministic model showed success in modelling TB infection in the region to the transmission dynamics of the stochastic SEIR model over time. It predicted tuberculosis dying out in ten of twelve high-burden districts in the Ashanti Region, but an outbreak in Obuasi municipal and Amansie West district. The effect of introducing treatment at the incubation stage of TB transmission was also investigated, and it was discovered that treatment introduced at the exposed stage decreased the spread of TB. Branching process approximation was used to derive explicit forms of relevant epidemiological quantities of the deterministic SEIR model for stability analysis of equilibrium points. Numerical simulations were performed to validate the overall infection rate, basic reproductive number, herd immunity threshold, and Malthusian parameter based on bootstrapping, jackknife, and Latin Hypercube sampling schemes. It was recommended that the Ghana Health Service should find a good mechanism to detect TB in the early stages of infection in the region. Public health attention must also be given to districts with a potentially higher risk of experiencing endemic TB even though the estimates of the overall epidemic thresholds from our SEIR model suggested that the Ashanti Region as a whole had herd immunity against TB infection.

PULSE VACCINATION IN THE PERIODIC INFECTION RATE SIR EPIDEMIC MODEL

2008 ◽  
Vol 01 (04) ◽  
pp. 409-432 ◽  
Author(s):  
ZHEN JIN ◽  
MAINUL HAQUE ◽  
QUANXING LIU
Keyword(s):  
Periodic Solution ◽  
Infection Rate ◽  
Dynamical Behavior ◽  
Positive Periodic Solution ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Uniform Persistence ◽  
Sir Epidemic Model ◽  
Pulse Vaccination ◽  
Globally Stable

In this paper a pulse vaccination SIR model with periodic infection rate β(t) is studied. The basic reproductive number R0 is defined. The dynamical behavior of the model is analyzed. It is proved that the infection-free periodic solution is globally stable if R0 < 1. The infection-free periodic solution is unstable and the disease will uniform persistence when R0 > 1. We use standard bifurcation theory to show the existence of the positive periodic solution when R0 → 1+. Numerical simulation can give suggestion, the system has a unique positive periodic, and it is globally stable when R0 > 1.

scholarly journals Estimating the reproductive number R0 of SARS-CoV-2 in the United States and eight European countries and implications for vaccination

2020 ◽  
Author(s):  
Ruian Ke ◽  
Ethan Obie Romero-Severson ◽  
Steven Sanche ◽  
Nick Hengartner
Keyword(s):  
United States ◽  
Herd Immunity ◽  
The United States ◽  
Control Measures ◽  
European Countries ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Individual Level ◽  
Epidemic Period ◽  
Induced Immunity

SARS-CoV-2 rapidly spread from a regional outbreak to a global pandemic in just a few months. Global research efforts have focused on developing effective vaccines against SARS-CoV-2 and the disease it causes, COVID-19. However, some of the basic epidemiological parameters, such as the exponential epidemic growth rate and the basic reproductive number, R0, across geographic areas are still not well quantified. Here, we developed and fit a mathematical model to case and death count data collected from the United States and eight European countries during the early epidemic period before broad control measures were implemented. Results show that the early epidemic grew exponentially at rates between 0.19-0.29/day (epidemic doubling times between 2.4-3.6 days). We discuss the current estimates of the mean serial interval, and argue that existing evidence suggests that the interval is between 6-8 days in the absence of active isolation efforts. Using parameters consistent with this range, we estimated the median R0 value to be 5.8 (confidence interval: 4.7-7.3) in the United States and between 3.6 and 6.1 in the eight European countries. This translates to herd immunity thresholds needed to stop transmission to be between 73% and 84%. We further analyze how vaccination schedules depends on R0, the duration of vaccine-induced immunity to SARS-CoV-2, and show that individual-level heterogeneity in vaccine induced immunity can significantly affect vaccination schedules.

scholarly journals Two new compartmental epidemiological models and their equilibria

2021 ◽  
Author(s):  
Jonas Balisacan ◽  
Monique Chyba ◽  
Corey Shanbrom
Keyword(s):  
Compartmental Model ◽  
Herd Immunity ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Mathematical Epidemiology ◽  
Epidemiological Models ◽  
Classical Models ◽  
Asymptomatic Individuals ◽  
The Stability ◽  
Disease Free

Compartmental models have long served as important tools in mathematical epidemiology, with their usefulness highlighted by the recent COVID-19 pandemic. However, most of the classical models fail to account for certain features of this disease and others like it, such as the ability of exposed individuals to recover without becoming infectious, or the possibility that asymptomatic individuals can indeed transmit the disease but at a lesser rate than the symptomatic. Furthermore, the rise of new disease variants and the imperfection of vaccines suggest that concept of endemic equilibrium is perhaps more pertinent than that of herd immunity. Here we propose a new compartmental epidemiological model and study its equilibria, characterizing the stability of both the endemic and disease-free equilibria in terms of the basic reproductive number. Moreover, we introduce a second compartmental model, generalizing our first, which accounts for vaccinated individuals, and begin an analysis of its equilibria.

Sign in / Sign up

Export Citation Format

Share Document