scholarly journals Heterogeneity and Superspreading Effect on Herd Immunity

2020 ◽  
Author(s):  
Shmuel Safra ◽  
Yaron Oz ◽  
Ittai Rubinstein
Keyword(s):  
Reproduction Number ◽  
Herd Immunity ◽  
Infected Population ◽  
Drastic Effect ◽  
Two Parameters

We model and calculate the fraction of infected population necessary for herd immunity to occur,taking into account the heterogeneity in infectiousness and susceptibility, as well as the correlation between the two parameters. We show that these cause the reproduction number to decrease with progression, and consequently have a drastic effect on the estimate of the necessary percentage of the population that has to contract the disease for herd immunity to be reached. We discuss the implications to COVID-19 and other pandemics.

scholarly journals COVID-19 outbreak in Algeria: A mathematical Model to predict cumulative cases

2020 ◽  
Author(s):  
Mohamed Hamidouche
Keyword(s):  
Reproduction Number ◽  
Herd Immunity ◽  
New Novel ◽  
First Case ◽  
Serial Interval ◽  
Prediction Time ◽  
Sporadic Cases ◽  
Novel Coronavirus ◽  
Two Parameters ◽  
Actual Incidence

AbstractIntroductionSince December 29, 2019 a pandemic of new novel coronavirus-infected pneumonia named COVID-19 has started from Wuhan, China, has led to 254 996 confirmed cases until midday March 20, 2020. Sporadic cases have been imported worldwide, in Algeria, the first case reported on February 25, 2020 was imported from Italy, and then the epidemic has spread to other parts of the country very quickly with 139 confirmed cases until March 21, 2020.MethodsIt is crucial to estimate the cases number growth in the early stages of the outbreak, to this end, we have implemented the Alg-COVID-19 Model which allows to predict the incidence and the reproduction number R0 in the coming months in order to help decision makers.The Alg-COVIS-19 Model initial equation 1, estimates the cumulative cases at t prediction time using two parameters: the reproduction number R0 and the serial interval SI.ResultsWe found R0=2.55 based on actual incidence at the first 25 days, using the serial interval SI= 4,4 and the prediction time t=26. The herd immunity HI estimated is HI=61%. Also, The Covid-19 incidence predicted with the Alg-COVID-19 Model fits closely the actual incidence during the first 26 days of the epidemic in Algeria Fig. 1.A. which allows us to use it.According to Alg-COVID-19 Model, the number of cases will exceed 5000 on the 42th day (April 7th) and it will double to 10000 on 46th day of the epidemic (April 11th), thus, exponential phase will begin (Table 1; Fig.1.B) and increases continuously until reaching à herd immunity of 61% unless serious preventive measures are considered.DiscussionThis model is valid only when the majority of the population is vulnerable to COVID-19 infection, however, it can be updated to fit the new parameters values.

scholarly journals Universal Rule for Covid 19 and Herd Immunity in the US

2021 ◽  
Author(s):  
Jacob G. Kuriyan
Keyword(s):  
South Dakota ◽  
North Dakota ◽  
Herd Immunity ◽  
Sir Model ◽  
Single Line ◽  
Removal Rates ◽  
Infected Population ◽  
The Us ◽  
Data Points ◽  
Universal Rule

AbstractA new Universal rule for Covid 19 data is derived in this paper using the SIR model.It relates infection and removal rates and is validated by the global Covid 19 data. Over 186,000 data points, from 190 countries and the states of the US, for the period April 1 to December 12, 2020 - fall on a single line, as the Universal rule predicts, transcending geography, ethnicity and race.The Universal rule requires that Herd immunity begin when just 25% of the population is vaccinated. With the anticipated 100 million vaccinations in the first 100 days of the Biden administration, Herd immunity may be imminent in the US.The Universal rule promotes a temporary stasis with continuing infections and hospitalizations and becomes a barrier to runaway infections, making it practically impossible to reach Herd immunity, as Sweden discovered. Reduced infected population seems to be a third option to stifle the epidemic - a little known accomplishment, first by North Dakota and subsequently by twelve other U.S. states, including South Dakota.

scholarly journals Covid 19: Need of vaccine induced herd immunity in India

2020 ◽  
Vol 2 (4) ◽  
pp. 82-84
Author(s):  
D. Pragathi ◽  
Dinesh Kumar Kukunuri ◽  
Venkatesh Paturu
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Herd Immunity ◽  
Traditional Concept ◽  
Contagious Diseases ◽  
Research Article ◽  
Past Data ◽  
The Mean ◽  
Novel Coronavirus ◽  
Indirect Protection

Introduction: Herd immunity is a traditional concept nothing but a form of indirect protection from contagious diseases. In a mass community, there is no need to be everyone immune. If a high proportion of members in the community are immune, spreading of the disease is reduced even to non-immunized patients. This study offers an overview of vaccine-induced herd immunity importance in this pandemic and how it will be achieved. Methodology: The data of basic reproduction number Ro values for COVID 19 of 10 weeks in India which were estimated by Ro package in R software are extracted from a research article (reference no.4) and taken the mean Ro value due to fluctuations as well as to avoid great errors by using MS Excel. Herd immunity is calculated by using a standard equation stated as R=(1-Pc )(1-P1)Ro   Results:  The mean basic reproduction number Ro for COVID 19 in India was calculated as 1.671 by using MS excel and the herd 3 determines that only 40.16% proportion of individuals need to immunized through a vaccine to achieve herd immunity towards COVID 19 in India. Conclusion: This study estimates mean base reproduction Ro as 1.671 and Herd Immunity Threshold (HIT) as 40.16% by using past data. This study concludes that vaccine-induced herd immunity helps us by playing a key role to eliminate novel coronavirus.

scholarly journals Mathematics Modeling of Diabetes Mellitus Type SEIIT By Considering Treatment And Genetic Factors

2018 ◽  
Vol 3 (1) ◽  
pp. 29
Author(s):  
Asmaidi Asmaidi ◽  
Eka Dodi Suryanto
Keyword(s):  
Diabetes Mellitus ◽  
Mathematical Models ◽  
Fixed Points ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Initial Point ◽  
Diabetes Mellitus Type ◽  
Infected Population ◽  
Group I ◽  
Starting Point

SEIIT stands for Susceptible (S), Exposed (E), Infected population untreated (I) and Infected population treated (IT). Infected groups consisted in two categories, untreated (I) and with treatment (IT) by presented to insulin. Susceptible shifted to exposed by gene. Prefered outcomes are mathematical models for diabetes mellitus type SEIIT, conventional type, determining breakpoint and basic reproduction number, breakpoint analysis, breakpoint stability simulation. The results were mathematical models or diabetes mellitus compartment charts/diagrams. These diagram were both analysed analitically and numerically. The analyses presented two fixed points, with desease and without desease. Each point was analysed by its basic reproduction number, analitically and numerically, at fixed points without desease Ro < 1, while the other Ro > 1. Human population at condition Ro < 1 tent to move from susceptibel from the initial standpoint and becomes stabilized at . Proportion of exposed (e) is diminishing from the starting point and stabilized at e = 0. Infected untreated dimished from the initial stage and stabilized at i = 0 . Infected with treatment (iT) was increased from initial point, diminished and stabilized at iT = 0. Human behavior when R0 > 1, susceptible (s) increased at the beginning then fluctuated, stabilized finally at . Exposed (e) lower at first then stabilized at . Untreated infected group (i) lower from initial then stabilized when .00393. Treatment group initiate an increasing value, then fluctuated and stabilized at .

scholarly journals Pandemic spread in communities via random graphs

2021 ◽  
Vol 2021 (11) ◽  
pp. 113501
Author(s):  
Dor Minzer ◽  
Yaron Oz ◽  
Muli Safra ◽  
Lior Wainstain
Keyword(s):  
Branching Process ◽  
Reproduction Number ◽  
Herd Immunity ◽  
Connected Component ◽  
Natural Evolution ◽  
Contact Graph ◽  
Process Framework ◽  
The Difference ◽  
Number Of Individuals ◽  
The Basic Reproduction Number

Abstract Working in the multi-type Galton–Watson branching-process framework we analyse the spread of a pandemic via a general multi-type random contact graph. Our model consists of several communities, and takes, as input, parameters that outline the contacts between individuals in distinct communities. Given these parameters, we determine whether there will be an outbreak and if yes, we calculate the size of the giant-connected-component of the graph, thereby, determining the fraction of the population of each type that would be infected before it ends. We show that the pandemic spread has a natural evolution direction given by the Perron–Frobenius eigenvector of a matrix whose entries encode the average number of individuals of one type expected to be infected by an individual of another type. The corresponding eigenvalue is the basic reproduction number of the pandemic. We perform numerical simulations that compare homogeneous and heterogeneous spread graphs and quantify the difference between them. We elaborate on the difference between herd immunity and the end of the pandemic and the effect of countermeasures on the fraction of infected population.

scholarly journals Herd Immunity in India: A Review

2021 ◽  
Vol 3 (1) ◽  
pp. 18-21
Author(s):  
Sheema Fatima Khan
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Natural Infection ◽  
Herd Immunity ◽  
Herd Effect ◽  
Susceptible Population ◽  
Herd Protection ◽  
Cdc Guidelines ◽  
And Control

Herd Immunity is a brilliant solution to tackle and control global pandemics, if taken proper route for immunization such as through vaccination. It is defined as the number of immune individuals against a transmissible virus in a completely susceptible population. The term herd protection or herd effect is the protection to the whole population due to herd immunity. Herd immunity threshold is the minimum proportion of immune population required for herd effect or herd protection. To calculate the threshold, we use basic reproduction number (R0) to measure the rate of transmission of pathogen, in this case SARS-CoV-2. However, a better measure is effective reproduction number (Re). India is major example of herd immunity. Despite strict lockdown and other Covid measure, due to already crowded area the virus could spread fast and to vast majority of people if one of them were to catch it. This explains the steady decline in the number of coronavirus cases in India. At the end, until an approved effective vaccination available, public will still need to follow all the CDC guidelines in order to avoid the large deaths along with natural infection.

scholarly journals Balancing costs and benefits of pandemic control in an outbreak phase

2021 ◽  
Author(s):  
Tsuyoshi Hondou
Keyword(s):  
Infection Control ◽  
Cost Benefit Analysis ◽  
Herd Immunity ◽  
Cost Benefit ◽  
Economic Effects ◽  
Control Measures ◽  
Infected Population ◽  
Infection Control Measures ◽  
Previous State ◽  
Applicable Knowledge

Abstract After the first lockdowns in response to the COVID-19 outbreak, many countries faced difficulties in balancing infection control with economics. Due to limited prior knowledge, economists began researching this issue using cost-benefit analysis and found that infection control processes significantly affect economic efficiency. Rowthorn and Maciejowski [R. Rowthorn and J.A. Maciejowski, Oxford Rev. Econ. Policy 36, S38 (2020)] used economic parameters in the United Kingdom to numerically demonstrate that an optimal balance was found in the process, including keeping the infected population stationary. However, universally applicable knowledge, which is indispensable for the guiding principles of infection control, has not yet been developed because these analyses assume regional parameters and a specific disease. Here, we prove the universal result of economic irreversibility by applying the idea of thermodynamics to pandemic control. It means that delaying infection control measures is more expensive than implementing infection control measures early while keeping infected populations stationary. This implies that once the infected population increases, society cannot return to its previous state without extra expenditures. This universal result is analytically obtained by focusing on the infection-spreading phase of pandemics, which is applicable not only to COVID-19, and whether or not “herd immunity” exists. It also confirms the numerical observation of stationary infected populations in its optimally efficient process. Our findings suggest that economic irreversibility is a guiding principle for balancing infection control with economic effects.

scholarly journals Flattening the curve is not enough, we need to squash it: An explainer using a simple model

2020 ◽  
Author(s):  
ES McBryde ◽  
MT Meehan ◽  
JM Trauer
Keyword(s):  
Deterministic Model ◽  
Reproduction Number ◽  
Herd Immunity ◽  
International Travel ◽  
Effective Control ◽  
Curve Versus ◽  
Successful Control ◽  
The Difference ◽  
The Uk ◽  
Local Transmission

AbstractBackgroundAround the world there are examples of both effective control (e.g., South Korea, Japan) and less successful control (e.g., Italy, Spain, United States) of COVID-19 with dramatic differences in the consequent epidemic curves. Models agree that flattening the curve without controlling the epidemic completely is insufficient and will lead to an overwhelmed health service. A recent model, calibrated for the UK and US, demonstrated this starkly.MethodsWe used a simple compartmental deterministic model of COVID-19 transmission in Australia, to illustrate the dynamics resulting from shifting or flattening the curve versus completely squashing it.ResultsWe find that when the reproduction number is close to one, a small decrease in transmission leads to a large reduction in burden (i.e., cases, deaths and hospitalisations), but achieving this early in the epidemic through social distancing interventions also implies that the community will not reach herd immunity.ConclusionsAustralia needs not just to shift and flatten the curve, but to squash it by getting the reproduction number below one. This will require Australia to achieve transmission rates at least two thirds lower than those seen in the most severely affected countries.The knownCOVID-19 has been diagnosed in over 4,000 Australians. Up until mid-March, most were from international travel, but now we are seeing a rise in locally acquired cases.The newThis study uses a simple transmission dynamic model to demonstrate the difference between moderate changes to the reproduction number and forcing the reproduction number below one.The implicationsLowering local transmission is becoming important in reducing the transmission of COVID-19. To maintain control of the epidemic, the focus should be on those in the community who do not regard themselves as at risk.

scholarly journals Hierarchical modeling of the effect of pre-exposure prophylaxis on HIV in the US

2018 ◽  
Author(s):  
Renee Dale ◽  
Ying Chen ◽  
Hongyu He
Keyword(s):  
High Risk ◽  
Rural Areas ◽  
Hierarchical Modeling ◽  
Herd Immunity ◽  
Infected Group ◽  
Model Parameters ◽  
Behavioral Risk ◽  
Sexually Active ◽  
Susceptible Population ◽  
Infected Population

1.AbstractIn this paper we present a differential equation model stratified by behavioral risk and sexual activity. Some susceptible individuals have higher rates of risky behavior that increase their chance of contracting the disease. Infected individuals can be considered to be generally sexually active or inactive. The sexually active infected population is at higher risk of transmitting the disease to a susceptible individual. We further divide the sexually active population into diagnosed or undiagnosed infected individuals. We define model parameters for both the national and the urban case. These parameter sets are used to study the predicted population dynamics over the next 5 years. Our results indicate that the undiagnosed high risk infected group is the largest contributor to the epidemic. Finally, we apply a preventative medication protocol to the susceptible population and observe the effective reduction in the infected population. The simulations suggest that preventative medication effectiveness extends outside of the group that is taking the drug (herd immunity). Our models suggest that a strategy targeting the high risk undiagnosed infected group would have the largest impact in the next 5 years. We also find that such a protocol has similar effects for the national as the urban case, despite the smaller sexual network found in rural areas.

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.

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