Optimal Choice of Vaccination Scheduling in a Population Composed of Two Groups

2022 ◽  
pp. 188-204
Author(s):  
Oğuz Gürerk ◽  
Mustafa Akan
Keyword(s):  
Simple Model ◽  
Differential Equations ◽  
Herd Immunity ◽  
Economic Cost ◽  
Economic Loss ◽  
Sir Model ◽  
Optimal Choice ◽  
Heterogeneous Groups ◽  
Total Economic Cost

In this chapter, the authors present a simple model to determine the optimal choice of vaccination scheduling for a society composed of two groups of individuals in order to minimize the economic loss only, assuming herd immunity. First, a simple classical SIR model is presented to form the basis of the analysis; second, the model is revised to include the effects of vaccination which in turn will be extended to include two heterogeneous groups of individuals forming a society. The solutions of relevant differential equations will then be used to calculate the total economic cost of each scenario presented.

Spectral Methods

2018 ◽  
Author(s):  
S. G. Rajeev
Keyword(s):  
Simple Model ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Linear Algebra ◽  
Spectral Methods ◽  
Differential Operators ◽  
Higher Dimensions ◽  
Standard Linear ◽  
Sommerfeld Equation ◽  
Spectral Discretization

Thenumerical solution of ordinary differential equations (ODEs)with boundary conditions is studied here. Functions are approximated by polynomials in a Chebychev basis. Sections then cover spectral discretization, sampling, interpolation, differentiation, integration, and the basic ODE. Following Trefethen et al., differential operators are approximated as rectangular matrices. Boundary conditions add additional rows that turn them into square matrices. These can then be diagonalized using standard linear algebra methods. After studying various simple model problems, this method is applied to the Orr–Sommerfeld equation, deriving results originally due to Orszag. The difficulties of pushing spectral methods to higher dimensions are outlined.

scholarly journals The Economic Cost of Diet and Its Association with Adherence to the Mediterranean Diet in a Cohort of Spanish Primary Schoolchildren

2021 ◽  
Vol 18 (3) ◽  
pp. 1282
Author(s):  
Rosario Pastor ◽  
Noemi Pinilla ◽  
Josep A. Tur
Keyword(s):  
Mediterranean Diet ◽  
Fast Food ◽  
Area Under The Curve ◽  
Economic Cost ◽  
Food Prices ◽  
Cross Sectional Survey ◽  
Cross Sectional ◽  
Old Spanish ◽  
Total Economic Cost ◽  
Data Frequency

Background: Adoption of a certain dietary pattern is determined by different factors such as taste, cost, convenience, and nutritional value of food. Objective: To assess the association between the daily cost of a diet and its overall quality in a cohort of 6–12-year-old Spanish schoolchildren. Methods: A cross-sectional survey was conducted on a cohort (n = 130; 47% female) of 6–12-year-old children schooled in primary education in the central region of Spain. Three-day 24 h records were administered, and the nutritional quality of the diet was also determined by means of Mediterranean Adequacy Index (MAI). A questionnaire on sociodemographic data, frequency of eating in fast-food restaurants, and supplement intake were also recorded. The person responsible for the child’s diet and the schooler himself completed the questionnaires, and homemade measures were used to estimate the size of the portions. Food prices were obtained from the Household Consumption Database of the Spanish Ministry of Agriculture, Fisheries and Food. The economic cost of the diet was calculated by multiplying the amount in grams of the food consumed by each child by the corresponding price in grams and adding up the total amount for each participant. The total economic cost of the diet was calculated in €/day and in €/1000 kcal/day. Results: The area under the curve (AUC) for €/day and €/1000 kcal/day represent 62.6% and 65.6%, respectively. According to AUC values, adherence to Mediterranean diet (MD) is a moderate predictor of the monetary cost of the diet. A direct relationship between the cost of the diet and the adherence to MD was observed [OR (€/1000 kcal/day) = 3.012; CI (95%): 1.291; 7.026; p = 0.011]. Conclusions: In a cohort of Spanish schoolchildren with low adherence to the MD, a higher cost of the diet standardized to 1000 kcal was associated with above-average MAI values.

scholarly journals Estimating SARS-CoV-2 infections from deaths, confirmed cases, tests, and random surveys

2021 ◽  
Vol 118 (31) ◽  
pp. e2103272118
Author(s):  
Nicholas J. Irons ◽  
Adrian E. Raftery
Keyword(s):  
Herd Immunity ◽  
The United States ◽  
Sir Model ◽  
Mitigation Strategies ◽  
Time Varying ◽  
Fatality Rate ◽  
Multiple Sources ◽  
Population Prevalence ◽  
Sample Testing ◽  
True Infection

There are multiple sources of data giving information about the number of SARS-CoV-2 infections in the population, but all have major drawbacks, including biases and delayed reporting. For example, the number of confirmed cases largely underestimates the number of infections, and deaths lag infections substantially, while test positivity rates tend to greatly overestimate prevalence. Representative random prevalence surveys, the only putatively unbiased source, are sparse in time and space, and the results can come with big delays. Reliable estimates of population prevalence are necessary for understanding the spread of the virus and the effectiveness of mitigation strategies. We develop a simple Bayesian framework to estimate viral prevalence by combining several of the main available data sources. It is based on a discrete-time Susceptible–Infected–Removed (SIR) model with time-varying reproductive parameter. Our model includes likelihood components that incorporate data on deaths due to the virus, confirmed cases, and the number of tests administered on each day. We anchor our inference with data from random-sample testing surveys in Indiana and Ohio. We use the results from these two states to calibrate the model on positive test counts and proceed to estimate the infection fatality rate and the number of new infections on each day in each state in the United States. We estimate the extent to which reported COVID cases have underestimated true infection counts, which was large, especially in the first months of the pandemic. We explore the implications of our results for progress toward herd immunity.

scholarly journals Impact of COVID-19 Variants on the Second Wave in India and Subsequent Discretion of Possibilities of the Third Wave

2021 ◽  
pp. 115-126
Author(s):  
Sudarshan Ramaswamy ◽  
Meera Dhuria ◽  
Sumedha M. Joshi ◽  
Deepa H Velankar
Keyword(s):  
Herd Immunity ◽  
Sir Model ◽  
The Other ◽  
Third Wave ◽  
Focal Points ◽  
Current Analysis ◽  
The Third ◽  
The Impact ◽  
Second Wave ◽  
Insight Into

Introduction: Epidemiological comprehension of the COVID-19 situation in India can be of great help in early prediction of any such indications in other countries and possibilities of the third wave in India as well. It is essential to understand the impact of variant strains in the perspective of the rise in daily cases during the second wave – Whether the rise in cases witnessed is due to the reinfections or the surge is dominated by emergence of mutants/variants and reasons for the same. Overall objective of this study is to predict early epidemiological indicators which can potentially lead to COVID-19 third wave in India. Methodology: We analyzed both the first and second waves of COVID-19 in India and using the data of India’s SARS-CoV-2 genomic sequencing, we segregated the impact of the Older Variant (OV) and the other major variants (VOI / VOC).  Applying Kermack–McKendrick SIR model to the segregated data progression of the epidemic in India was plotted in the form of proportion of people infected. An equation to explain herd immunity thresholds was generated and further analyzed to predict the possibilities of the third wave. Results: Considerable difference in ate of progression of the first and second wave was seen. The study also ascertains that the rate of infection spread is higher in Delta variant and is expected to have a higher threshold (>2 times) for herd immunity as compared to the OV. Conclusion: Likelihood of the occurrence of the third wave seems unlikely based on the current analysis of the situation, however the possibilities cannot be ruled out. Understanding the epidemiological details of the first and second wave helped in understanding the focal points responsible for the surge in cases during the second wave and has given further insight into the future.

scholarly journals Human Resource Professional Priorities and Challenges in Times of COVID-19 Pandemic

2021 ◽  
pp. 23-33
Author(s):  
Shammy Shiri ◽  
Laveena D'Mello
Keyword(s):  
Human Resource ◽  
Economic Cost ◽  
Economic Loss ◽  
Work Culture ◽  
Business World ◽  
Human Resource Professional ◽  
Culture Shift ◽  
Drastic Increase ◽  
Human Cost ◽  
New Challenges

There has been a world alarming and warming situation due to global outbreak of COVID-19 pandemic taking along most important the human cost, mentally, physically with economic cost too. All of a sudden organization across have been alerted themselves to adapt toward this unforeseen unprecedented event and thereby find new solutions. Organizations around the world are taking measures as it’s important to stay at home for social distancing, this leading to drastic increase in economic loss, poor job satisfaction, reduced motivation and workplace depression crisis among organization’s employees with far reaching impacts. The sudden work culture shift has created new challenges for Human Resource (HR) professionals and in this time of global critical condition, the companies and organizations need their HR professionals to help the employees out of this badly driven health and economic crisis. The HR Professionals has been actively partnering with Business to solve some of the trickiest questions the business world faces today. This article discusses some of the priorities and challenges faced by HR professionals in helping the employees to adjust and cope with their changed work environment during COVID-19 pandemic.

scholarly journals The attainment of herd immunity with a reducing risk of contact infection in modelling 

2021 ◽  
Author(s):  
Kian Boon Law ◽  
Kalaiarasu M Peariasamy ◽  
Hishamshah Ibrahim ◽  
Noor Hisham Abdullah
Keyword(s):  
Infectious Disease ◽  
Disease Transmission ◽  
Herd Immunity ◽  
Sir Model ◽  
Mixed Population ◽  
Transmission Model ◽  
Force Of Infection ◽  
Initial Stage ◽  
And Control ◽  
Model Features

Abstract The risk of contact infection among susceptible individuals in a randomly mixed population can be reduced by the presence of immune individuals and this principle forms the fundamental of herd immunity. The conventional susceptible-infectious-recovered (SIR) model features an infection-induced herd immunity model, but does not include the reducing risk of contact infection among susceptible individuals in the transmission model, therefore tends to overestimate the transmission dynamics of infectious diseases. Here we show that the reducing risk of contact infection among susceptible individuals can be achieved by incorporating the proportion of susceptible individuals (model A) or the inverse of proportion of recovered individuals (model B) in the force of infection of the SIR model. We numerically simulated the conventional SIR model and both new SIR models A and B under the exact condition with a basic reproduction number of 3·0. Prior to the numerical simulation, the threshold for the eradication of infectious disease through herd immunity was expected to be 0·667 (66·7%) for all three models. All three models performed likewise at the initial stage of disease transmission. In the conventional SIR model, the infectious disease subsided when 94·0 % of the population had been infected and recovered, way above the expected threshold for eradication and control of the infectious disease. Both models A and B simulated the infectious disease to diminish when 66·7% and 75·6% of the population had been infected, showing herd immunity might protect more susceptible individuals from the infectious disease as compared to the projection generated by the conventional SIR. Our study shows that model A provides a better framework for modelling herd immunity through vaccination, while model B provides a better framework for modelling herd immunity through infection. Both models overcome the insufficiency of the conventional SIR model in attaining the effect of herd immunity in modelling outputs, which is important and relevant for modelling infectious disease, such as the COVID-19 in a randomly mixed population.

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.

Estimation of the number of affected people due to the Covid-19 pandemic using susceptible, infected and recover model

2020 ◽  
Vol 31 (08) ◽  
pp. 2050111
Author(s):  
Md. Enamul Hoque
Keyword(s):  
Simple Model ◽  
Basic Reproduction Number ◽  
Numerical Solutions ◽  
Reproduction Number ◽  
Sir Model

The Susceptible, Infected and Recover (SIR) model is a very simple model to estimate the dynamics of an epidemic. In the current pandemic due to Covid-19, the SIR model has been used to estimate the dynamics of infection for various infected countries. Numerical solutions are used to obtain the value of parameters for the SIR model. The maximum and minimum basic reproduction number (14.5 and 2.3) are predicted to be in Turkey and China, respectively.

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