Reproduction Numbers and Critical Immunity Levels for Epidemics in a Community of Households

1996 ◽  
pp. 267-276 ◽  
Author(s):  
Niels G. Becker ◽  
Klaus Dietz
Keyword(s):  
Reproduction Numbers

COVID-19: Time-Dependent Effective Reproduction Number and Sub-notification Effect Estimation Modeling (Preprint)

2020 ◽  
Author(s):  
Eduardo Atem De Carvalho ◽  
Rogerio Atem De Carvalho
Keyword(s):  
New York ◽  
Reproduction Number ◽  
Moving Average ◽  
Real Data ◽  
Time Dependent ◽  
Initial Value ◽  
Health Authorities ◽  
Reproduction Numbers ◽  
Effect Estimation ◽  
The Impact

BACKGROUND Since the beginning of the COVID-19 pandemic, researchers and health authorities have sought to identify the different parameters that govern their infection and death cycles, in order to be able to make better decisions. In particular, a series of reproduction number estimation models have been presented, with different practical results. OBJECTIVE This article aims to present an effective and efficient model for estimating the Reproduction Number and to discuss the impacts of sub-notification on these calculations. METHODS The concept of Moving Average Method with Initial value (MAMI) is used, as well as a model for Rt, the Reproduction Number, is derived from experimental data. The models are applied to real data and their performance is presented. RESULTS Analyses on Rt and sub-notification effects for Germany, Italy, Sweden, United Kingdom, South Korea, and the State of New York are presented to show the performance of the methods here introduced. CONCLUSIONS We show that, with relatively simple mathematical tools, it is possible to obtain reliable values for time-dependent, incubation period-independent Reproduction Numbers (Rt). We also demonstrate that the impact of sub-notification is relatively low, after the initial phase of the epidemic cycle has passed.

scholarly journals Qualitative properties of mathematical model of English language education

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Atena Ghasemabadi ◽  
Nahid Soltanian
Keyword(s):  
Mathematical Model ◽  
Global Stability ◽  
Equilibrium Point ◽  
English Language ◽  
Language Education ◽  
Qualitative Properties ◽  
English Language Education ◽  
Compound Matrices ◽  
Reproduction Numbers ◽  
Coexistence Equilibrium

AbstractThis paper presents a mathematical model that examines the impacts of traditional and modern educational programs. We calculate two reproduction numbers. By using the Chavez and Song theorem, we show that backward bifurcation occurs. In addition, we investigate the existence and local and global stability of boundary equilibria and coexistence equilibrium point and the global stability of the coexistence equilibrium point using compound matrices.

scholarly journals The Deterministic Evolution Of Illicit Drug Consumption Within a Given Population

2018 ◽  
Vol 62 ◽  
pp. 139-157 ◽  
Author(s):  
Yusra Bibi Ruhomally ◽  
Nabeelah Banon Jahmeerbaccus ◽  
Muhammad Zaid Dauhoo
Keyword(s):  
Drug Users ◽  
Illicit Drug ◽  
Drug Consumption ◽  
Dynamic Evolution ◽  
Evidence Based ◽  
Relative Importance ◽  
Epidemic Threshold ◽  
Drug Usage ◽  
Policy Makers ◽  
Reproduction Numbers

We study the NERA model that describes the dynamic evolution of illicit drug usage in a population. The model consists of nonusers (N) and three categories of drug users: the experimental (E) category, the recreational (R) category and the addict (A) category. Two epidemic threshold term known as the reproduction numbers, R0 and μ are defined and derived. Sensitivity analysis of R0 on the parameters are performed in order to determine their relative importance to illicit drug prevalence. The local and global stability of the equilibrium states are also analysed. We also prove that a transcritical bifurcation occurs at R0 = 1. It is shown that an effective campaign of prevention can help to fight against the prevalence of illicit drug consumption. We demonstrate persistence when R0 > 1 and conditions for the extinction of drug consumption are also established. Numerical simulations are performed to verify our model. Our results show that the NERA model can assist policy makers in targeting prevention for maximum effectiveness and can be used to adopt evidence-based policies to better monitor and quantify drug use trends.

scholarly journals Rapid review of available evidence on the serial interval and generation time of COVID-19

BMJ Open ◽  
2020 ◽  
Vol 10 (11) ◽  
pp. e040263
Author(s):  
John Griffin ◽  
Miriam Casey ◽  
Áine Collins ◽  
Kevin Hunt ◽  
David McEvoy ◽  
...  
Keyword(s):  
Generation Time ◽  
Social Contact ◽  
Careful Consideration ◽  
Rapid Review ◽  
Eligibility Criteria ◽  
Reproduction Numbers ◽  
Serial Interval ◽  
Scientific Papers ◽  
The Mean ◽  
Parameter Values

The serial interval is the time between symptom onsets in an infector–infectee pair. The generation time, also known as the generation interval, is the time between infection events in an infector–infectee pair. The serial interval and the generation time are key parameters for assessing the dynamics of a disease. A number of scientific papers reported information pertaining to the serial interval and/or generation time for COVID-19. Objective Conduct a review of available evidence to advise on appropriate parameter values for serial interval and generation time in national COVID-19 transmission models for Ireland and on methodological issues relating to those parameters. Methods We conducted a rapid review of the literature covering the period 1 January 2020 and 21 August 2020, following predefined eligibility criteria. Forty scientific papers met our inclusion criteria and were included in the review. Results The mean of the serial interval ranged from 3.03 to 7.6 days, based on 38 estimates, and the median from 1.0 to 6.0 days (based on 15 estimates). Only three estimates were provided for the mean of the generation time. These ranged from 3.95 to 5.20 days. One estimate of 5.0 days was provided for the median of the generation time. Discussion Estimates of the serial interval and the generation time are very dependent on the specific factors that apply at the time that the data are collected, including the level of social contact. Consequently, the estimates may not be entirely relevant to other environments. Therefore, local estimates should be obtained as soon as possible. Careful consideration should be given to the methodology that is used. Real-time estimations of the serial interval/generation time, allowing for variations over time, may provide more accurate estimates of reproduction numbers than using conventionally fixed serial interval/generation time distributions.

Data-driven tools for assessing and combating COVID-19 outbreaks in Brazil based on analytics and statistical methods

2021 ◽  
Keyword(s):  
Data Analytics ◽  
Exploratory Data Analysis ◽  
Reproduction Number ◽  
Healthcare Systems ◽  
Regional Level ◽  
Data Driven ◽  
Effective Response ◽  
Reproduction Numbers ◽  
Exploratory Data ◽  
Using Data

The COVID-19 pandemic is one of the worst public health crises in Brazil and the world that has ever been faced. One of the main challenges that the healthcare systems have when decision-making is that the protocols tested in other epidemics do not guarantee success in controlling the spread of COVID-19, given its complexity. In this context, an effective response to guide the competent authorities in adopting public policies to fight COVID-19 depends on thoughtful analysis and effective data visualization, ideally based on different data sources. In this paper, we discuss and provide tools that can be helpful using data analytics to respond to the COVID-19 outbreak in Recife, Brazil. We use exploratory data analysis and inferential study to determine the trend changes in COVID-19 cases and their effective or instantaneous reproduction numbers. According to the data obtained of confirmed COVID-19 cases disaggregated at a regional level in this zone, we note a heterogeneous spread in most megaregions in Recife, Brazil. When incorporating quarantines decreed, effectiveness is detected in the regions. Our results indicate that the measures have effectively curbed the spread of the disease in Recife, Brazil. However, other factors can cause the effective reproduction number to not be within the expected ranges, which must be further studied.

scholarly journals COVID-19 Time-varying Reproduction Numbers Worldwide: An Empirical Analysis of Mandatory and Voluntary Social Distancing

2021 ◽  
Vol 2021 (407) ◽  
Author(s):  
Alexander Chudik ◽  
◽  
M. Hashem Pesaran ◽  
Alessandro Rebucci ◽  
◽  
...  
Keyword(s):  
Empirical Analysis ◽  
Time Varying ◽  
Social Distancing ◽  
Reproduction Numbers

scholarly journals Estimation of age-stratified contact rates during the COVID-19 pandemic using a novel inference algorithm

2022 ◽  
Author(s):  
Christopher M Pooley ◽  
Andrea B Doeschl-Wilson ◽  
Glenn Marion
Keyword(s):  
Hospital Admissions ◽  
Epidemiological Data ◽  
Joint Analysis ◽  
Model Parameters ◽  
Inference Algorithm ◽  
Public Response ◽  
Contact Rates ◽  
Reproduction Numbers ◽  
Public Data ◽  
Approximate Bayesian

Well parameterised epidemiological models including accurate representation of contacts, are fundamental to controlling epidemics. However, age-stratified contacts are typically estimated from pre-pandemic/peace-time surveys, even though interventions and public response likely alter contacts. Here we fit age-stratified models, including re-estimation of relative contact rates between age-classes, to public data describing the 2020-21 COVID-19 outbreak in England. This data includes age-stratified population size, cases, deaths, hospital admissions, and results from the Coronavirus Infection Survey (almost 9000 observations in all). Fitting stochastic compartmental models to such detailed data is extremely challenging, especially considering the large number of model parameters being estimated (over 150). An efficient new inference algorithm ABC-MBP combining existing Approximate Bayesian Computation (ABC) methodology with model-based proposals (MBP) is applied. Modified contact rates are inferred alongside time-varying reproduction numbers that quantify changes in overall transmission due to pandemic response, and age-stratified proportions of asymptomatic cases, hospitalisation rates and deaths. These inferences are robust to a range of assumptions including the values of parameters that cannot be estimated from available data. ABC-MBP is shown to enable reliable joint analysis of complex epidemiological data yielding consistent parametrisation of dynamic transmission models that can inform data-driven public health policy and interventions.

scholarly journals Differences in how interventions coupled with effective reproduction numbers account for marked variations in COVID-19 epidemic outcomes

2020 ◽  
Vol 17 (5) ◽  
pp. 5085-5098
Author(s):  
Fan Xia ◽  
◽  
Yanni Xiao ◽  
Peiyu Liu ◽  
Robert A. Cheke ◽  
...  
Keyword(s):  
Reproduction Numbers

scholarly journals Gaussian Doubling Times and Reproduction Factors of the COVID-19 Pandemic Disease

2020 ◽  
Author(s):  
Martin Kröger ◽  
Reinhard Schlickeiser
Keyword(s):  
Time Evolution ◽  
Transient Behavior ◽  
Peak Time ◽  
Reproduction Numbers ◽  
Doubling Times ◽  
Pandemic Wave

The Gauss model for the time evolution of the first corona pandemic wave rendered useful in the estimation of peak times, amount of required equipment, and the forecasting of fade out times. At the same time it is probably the simplest analytically tractable model that allows to quantitatively forecast the time evolution of infections and fatalities during a pandemic wave. In light of the various descriptors such as doubling times and reproduction factors currently in use to judge about lock-downs and other measures that aim to prevent spreading of the virus, we hereby provide both exact, and simple approximate relationships between the two relevant parameters of the Gauss model (peak time and width), and the transient behavior of two versions of doubling times, and three variants of reproduction factors including basic reproduction numbers.

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