scholarly journals The mathematics of the reproduction number R for Covid-19: A primer for demographers

2021 ◽  
Author(s):  
Luis Rosero-Bixby ◽  
Tim Miller
Keyword(s):  
Infection Control ◽  
Time Constant ◽  
Reproduction Number ◽  
Control Strategies ◽  
Weighted Average ◽  
Reproduction Rate ◽  
Economic Costs ◽  
Key Indicator ◽  
Net Reproduction ◽  
Over Time

The reproduction number R is a key indicator used to monitor the dynamics of Covid-19 and to assess the effects of infection control strategies that frequently have high social and economic costs. Despite having an analog in demography’s “net reproduction rate” that has been routinely computed for a century, demographers may not be familiar with the concept and measurement of R in the context of Covid-19. This article is intended to be a primer for understanding and estimating R in demography. We show that R can be estimated as a ratio between the numbers of new cases today divided by the weighted average of cases in previous days. We present two alternative derivations for these weights based on how risks have changed over time: constant vs. exponential decay. We then provide estimates of these weights, and demonstrate their use in calculating R to trace the course of the first pandemic year in 53 countries.

scholarly journals The mathematics of the reproduction number R for Covid-19: A primer for demographers

2020 ◽  
Author(s):  
Luis Rosero-Bixby ◽  
Tim Miller
Keyword(s):  
Reproduction Number ◽  
Control Strategies ◽  
Weighted Average ◽  
Reproductive Number ◽  
Reproduction Rate ◽  
Economic Costs ◽  
Simple Method ◽  
Important Indicator ◽  
Key Indicator ◽  
Net Reproduction

BACKGROUNDThe reproduction number R is a key indicator to characterize the dynamics of the Covid-19 pandemic and to assess the effect of control strategies that frequently have extremely high social and economic costs. Despite having an analog in demography’s net reproduction rate, demographers may not be familiar with the concept and measurement of R in the context of Covid-19. OBJECTIVETo provide a primer for demographers for understanding and estimating R for Covid-19. METHODSIn order to demystify the complexities of estimating this important indicator, we present a simple method for its calculation, following well-known procedures in demography, a discipline in which an analog of R -- the net reproduction rate -- has been routinely computed for a century. RESULTSWe show that R can be estimated as a quotient between the numbers of new cases today divided by the weighted average of cases in previous days. We present two alternative derivations for these weights: based on how risks change over time (constant vs exponential decay). We provide estimates of these weights and demonstrate their use in calculating R to trace the course of the Covid-19 pandemic in several countries. CONTRIBUTIONThis primer for demographers demonstrates a method for estimating the reproductive number R for the Covid-19 pandemic derived using familiar demographic techniques. The strengths of the proposed approach are the transparency of the assumptions and the simplicity of the procedure.

scholarly journals Containment efficiency and control strategies for the corona pandemic costs

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Claudius Gros ◽  
Roser Valenti ◽  
Lukas Schneider ◽  
Kilian Valenti ◽  
Daniel Gros
Keyword(s):  
Control Strategies ◽  
Economic Value ◽  
Economic Cost ◽  
Sir Model ◽  
Medical Care Cost ◽  
Reproduction Rate ◽  
Economic Costs ◽  
Current Case ◽  
Feedback Parameter ◽  
Social Distancing

AbstractThe rapid spread of the Coronavirus (COVID-19) confronts policy makers with the problem of measuring the effectiveness of containment strategies, balancing public health considerations with the economic costs of social distancing measures. We introduce a modified epidemic model that we name the controlled-SIR model, in which the disease reproduction rate evolves dynamically in response to political and societal reactions. An analytic solution is presented. The model reproduces official COVID-19 cases counts of a large number of regions and countries that surpassed the first peak of the outbreak. A single unbiased feedback parameter is extracted from field data and used to formulate an index that measures the efficiency of containment strategies (the CEI index). CEI values for a range of countries are given. For two variants of the controlled-SIR model, detailed estimates of the total medical and socio-economic costs are evaluated over the entire course of the epidemic. Costs comprise medical care cost, the economic cost of social distancing, as well as the economic value of lives saved. Under plausible parameters, strict measures fare better than a hands-off policy. Strategies based on current case numbers lead to substantially higher total costs than strategies based on the overall history of the epidemic.

scholarly journals Can medication mitigate the need for a strict lock down?: A mathematical study of control strategies for COVID-19 infection

2020 ◽  
Author(s):  
Mohsin Ali ◽  
Mudassar Imran ◽  
Adnan Khan
Keyword(s):  
Reproduction Number ◽  
Virus Disease ◽  
Control Strategies ◽  
Transmission Dynamics ◽  
Effective Control ◽  
Mathematical Study ◽  
Seir Model ◽  
Epidemic Curve ◽  
Asymptomatic Individuals ◽  
Over Time

AbstractWe formulate a deterministic epidemic model to study the effects of medication on the transmission dynamics of Corona Virus Disease (COVID-19). We are especially interested in how the availability of medication could change the necessary quarantine measures for effective control of the disease. We model the transmission by extending the SEIR model to include asymptomatic, quarantined, isolated and medicated population compartments. We calculate the basic reproduction number R0 and show that for R0 < 1 the disease dies out and for R0 > 1 the disease is endemic. Using sensitivity analysis we establish that R0 is most sensitive to the rates of quarantine and medication. We also study how the effectiveness and the rate of medication along with the quarantine rate affect R0. We devise optimal quarantine, medication and isolation strategies, noting that availability of medication reduces the duration and severity of the lock-down needed for effective disease control. Our study also reinforces the idea that with the availability of medication, while the severity of the lock downs can be eased over time some social distancing protocols need to be observed, at least till a vaccine is found. We also analyze the COVID-109 outbreak data for four different countries, in two of these, India and Pakistan the curve is still rising, and in he other two, Italy and Spain, the epidemic curve is now falling due to effective quarantine measures. We provide estimates of R0 and the proportion of asymptomatic individuals in the population for these countries.

The replacement of generations in Serbia in the period 1950-2000

Stanovnistvo ◽  
2001 ◽  
Vol 39 (1-4) ◽  
pp. 45-71 ◽  
Author(s):  
Goran Penev
Keyword(s):  
Birth Cohort ◽  
20Th Century ◽  
Regional Differences ◽  
Cohort Analysis ◽  
Reproduction Rate ◽  
Demographic Analysis ◽  
Period Analysis ◽  
Net Reproduction

The article deals with the replacement of generations in Serbia, its dynamics in the second half of the 20th century, and the importance of direct determinants. It points to the major regional differences in the domain of the population reproduction among the large areas of Serbia (Central Serbia, Vojvodina, and Kosovo-Metohija). Two approaches of demographic analysis were applied: period and cohort analysis. Basic indicators, definitions, and shortcomings were presented. The results of the period analysis indicate that up until 1988 (with the exceptions of 1957 and 1981), the fertility in Serbia constantly reached a level of fertility necessary to ensure the replacement. Since 1989, the net reproduction rate has constantly been below unity. In Central Serbia and Vojvodina, the population has not been reproducing itself for more than 45 years (since 1956). The situation has been completely different in Kosovo-Metohija, where fertility has been above the level necessary to ensure reproduction during the entire second half of 20th century. The cohort analysis applied to six chosen generations (birth cohort of 1950, 1955, 1960, 1965, 1970, and 1975) indicates that in Serbia, only women born in 1960 ensured the replacement. In Central Serbia and Vojvodina, none of the studied generations succeeded in ensuring the replacement, while in Kosovo-Metohija all generations did.

scholarly journals Evaluation of a home-based 7-day infection control strategy for healthcare workers following high-risk exposure to severe acute respiratory coronavirus virus 2 (SARS-CoV-2): A cohort study

2020 ◽  
pp. 1-4
Author(s):  
Carla Benea ◽  
Laura Rendon ◽  
Jesse Papenburg ◽  
Charles Frenette ◽  
Ahmed Imacoudene ◽  
...  
Keyword(s):  
High Risk ◽  
Infection Control ◽  
Control Strategy ◽  
Healthcare Workers ◽  
Control Strategies ◽  
Risk Exposure ◽  
Nasopharyngeal Swab ◽  
Home Based ◽  
Respiratory Coronavirus ◽  
Second Wave

Abstract Objective: Evidence-based infection control strategies are needed for healthcare workers (HCWs) following high-risk exposure to severe acute respiratory coronavirus virus 2 (SARS-CoV-2). In this study, we evaluated the negative predictive value (NPV) of a home-based 7-day infection control strategy. Methods: HCWs advised by their infection control or occupational health officer to self-isolate due to a high-risk SARS-CoV-2 exposure were enrolled between May and October 2020. The strategy consisted of symptom-triggered nasopharyngeal SARS-CoV-2 RNA testing from day 0 to day 7 after exposure and standardized home-based nasopharyngeal swab and saliva testing on day 7. The NPV of this strategy was calculated for (1) clinical coronavirus disease 2019 (COVID-19) diagnosis from day 8–14 after exposure, and for (2) asymptomatic SARS-CoV-2 detected by standardized nasopharyngeal swab and saliva specimens collected at days 9, 10, and 14 after exposure. Interim results are reported in the context of a second wave threatening this essential workforce. Results: Among 30 HCWs enrolled, the mean age was 31 years (SD, ±9), and 24 (80%) were female. Moreover, 3 were diagnosed with COVID-19 by day 14 after exposure (secondary attack rate, 10.0%), and all cases were detected using the 7-day infection control strategy: the NPV for subsequent clinical COVID-19 or asymptomatic SARS-CoV-2 detection by day 14 was 100.0% (95% CI, 93.1%–100.0%). Conclusions: Among HCWs with high-risk exposure to SARS-CoV-2, a home-based 7-day infection control strategy may have a high NPV for subsequent COVID-19 and asymptomatic SARS-CoV-2 detection. Ongoing data collection and data sharing are needed to improve the precision of the estimated NPV, and here we report interim results to inform infection control strategies in light of a second wave threatening this essential workforce.

scholarly journals Sex-specific deaths in Norway and Sweden during the COVID-19 pandemic: Did mandates make a difference?

2021 ◽  
pp. 140349482110100
Author(s):  
Ralph Catalano
Keyword(s):  
Sex Ratio ◽  
Infection Control ◽  
Temporal Variation ◽  
Risky Behavior ◽  
Control Strategies ◽  
Sex Ratios ◽  
Female Mortality ◽  
All Cause Mortality ◽  
Societal Expectations ◽  
Male To Female

Aims: To determine whether differences between Norway’s and Sweden’s attempts to contain SARS-CoV-2 infection coincided with detectably different changes in their all-cause mortality sex ratios. Measuring temporal variation in the all-cause mortality sex ratio before and during the pandemic in populations exposed to different constraints on risky behavior would allow us to better anticipate changes in the ratio and to better understand its association with infection control strategies. Methods: I apply time Box–Jenkins modeling to 262 months of pre-pandemic mortality sex ratios to arrive at counterfactual values of 10 intra-pandemic ratios. I compare counterfactual to observed values to determine if intra-pandemic ratios differed detectably from those expected as well as whether the Norwegian and Swedish differences varied from each other. Results: The male to female mortality sex ratio in both Norway and Sweden increased during the pandemic. I, however, find no evidence that the increase differed between the two countries despite their different COVID-19 containment strategies. Conclusion: Societal expectations of who will die during the COVID-19 pandemic will likely be wrong if they assume pre-pandemic mortality sex ratios because the intra-pandemic ratios appear, at least in Norway and Sweden, detectably higher. The contribution of differences in policies to reduce risky behavior to those higher ratios appears, however, small.

scholarly journals Salmonella Bacterin Vaccination Decreases Shedding and Colonization of Salmonella Typhimurium in Pigs

2021 ◽  
Vol 9 (6) ◽  
pp. 1163
Author(s):  
Eduarda Alexandra Gonçalves de Oliveira Moura ◽  
Daniela Gomes da Silva ◽  
Caio Henrique Turco ◽  
Thainara Vitoria Carnevalli Sanches ◽  
Gabriel Yuri Storino ◽  
...  
Keyword(s):  
Salmonella Typhimurium ◽  
Blood Count ◽  
Control Strategies ◽  
Control Group ◽  
Blood Samples ◽  
Commercial Vaccine ◽  
Serum Igg ◽  
And Control ◽  
Experimental Group ◽  
Over Time

Since the occurrence of swine salmonellosis has increased over time and control strategies other than biosecurity are highly recommended, the present study aimed to evaluate the efficacy of vaccination with Salmonella Choleraesuis and Salmonella Typhimurium bacterins in pigs. Two experimental groups were formed: G1, animals immunized with two doses of a commercial vaccine (n = 20); G2, control group (n = 20). After vaccination, all pigs were orally challenged (D0) with 108 CFU of Salmonella Typhimurium and evaluated for 40 days. Every 10 days after D0, five piglets from each experimental group were euthanized and submitted to the necroscopic examination, when organ samples were collected. Blood samples and rectal swabs were collected before the first dose of the vaccine (D−42), before the second dose (D−21), before the challenge (D0), and thereafter, every three days until D39. Blood count, serum IgG measurement by ELISA, and the excretion of Salmonella Typhimurium in feces were evaluated. While the results from blood count and serum IgG concentration did not differ, the detection and excretion of Salmonella between G1 and G2 differed (p < 0.05). Therefore, it was observed that this vaccine partially protected the animals against experimental infection with Salmonella Typhimurium, reducing the excretion of bacteria in feces.

scholarly journals Implementation of an Antimicrobial Stewardship Program in Five Colombian Hospitals in 2018

2020 ◽  
Vol 41 (S1) ◽  
pp. s273-s273
Author(s):  
Christian Pallares ◽  
María Virginia Villegas Botero
Keyword(s):  
Infection Control ◽  
Antimicrobial Stewardship ◽  
Control Strategies ◽  
Education And Training ◽  
Public Hospitals ◽  
International Standards ◽  
International Consensus ◽  
Stewardship Program ◽  
And Training

Background: More than 50% of antibiotics used in hospitals are unnecessary or inappropriate. The antimicrobial stewardship programs (ASPs) are coordinated efforts to promote the rational and effective use of antibiotics including appropriate selection, dosage, administration, and duration of therapy. When an ASP integrates infection control strategies, it is possible to decrease the transmission of multidrug-resistant pathogens. Methods: In 2018, 5 Colombian hospitals were selected to implement an ASP. Private and public hospitals from different cities were included in the study, ranging from 200 to 700 beds. Our team, consisting of an infectious disease and hospital epidemiologist, visited each hospital to establish the baseline of their ASP program, to define the ASP outcomes according to each hospital’s needs, and to set goals for ASP outcomes in the following 6–12 months. Follow-up was scheduled every 2 months through Skype video conference. The baseline diagnosis or preintervention evaluation was done using a tool adapted from previous reports (ie, international consensus and The Joint Commission international standards). Documentation related to ASPs, such as microbiological profiles, antimicrobial guidelines (AMG) and indicators for the adherence to them as well as antimicrobial resistance (AMR) prevention through protocols, were written and/or updated. Prevention and infection control requirements and protocols were also updated, and cleaning and antiseptic policies were created. Training in rational use of antibiotic, infection control and prevention, and cleaning and disinfection were carried out with the healthcare workers in each institution. Results: Before the intervention, the development of the ASP according to the tool was 27% (range, 5%–47%). The lowest institutional scores were the item related to ASP feedback and reports (11% on average), followed by education and training (14%), defined ASP responsibilities (23%), ASP function according to priorities (26%), and AMR surveillance (27%). After the intervention, the ASP development increased to 57% (range, 39%–81%) in the hospitals. The highest scores achieved were for education and training (90%), surveillance (75%), and the activities of the infection control committee (70%). The items that made the greatest contribution to ASP development were the individual antibiogram, including the bacteria resistance profile, and the development of the AMG based on the local epidemiology in each hospital. Conclusions: The implementation of an ASP should include training and education as well as defining outcomes according to the hospital’s needs. Once the strategy is implemented, follow-up is key to achieving the goals.Funding: NoneDisclosures: None

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