scholarly journals The net reproduction rate and the type-reproduction number in multiregional demography

2010 ◽  
Vol 2009 ◽  
pp. 197-215 ◽  
Author(s):  
Hisashi Inaba
Keyword(s):  
Reproduction Number ◽  
Reproduction Rate ◽  
Net Reproduction ◽  
Type Reproduction Number

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.

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.

Ambient Humidity Affects Development, Survival, and Reproduction of the Invasive Fall Armyworm, Spodoptera frugiperda (Lepidoptera: Noctuidae), in China

2021 ◽  
Author(s):  
Limei He ◽  
Shengyuan Zhao ◽  
Abid Ali ◽  
Shishuai Ge ◽  
Kongming Wu
Keyword(s):  
Spodoptera Frugiperda ◽  
Fall Armyworm ◽  
Intrinsic Rate ◽  
Intrinsic Rate Of Increase ◽  
Reproduction Rate ◽  
Ambient Humidity ◽  
Rate Of Increase ◽  
Population Forecasting ◽  
Survival And Reproduction ◽  
Net Reproduction

Abstract Ambient humidity can directly affect the water balance in insects. The migratory fall armyworm, Spodoptera frugiperda Smith, has spread to more than 60 countries and regions in Africa, Asia, and Oceania that have a great difference in average ambient humidity. Understanding the effects of ambient humidity changes on its development, survival, and reproduction can help to predict its population dynamics in different habitats. Therefore, we evaluated the effects of atmospheric relative humidity (RH) on the development, survival, and reproduction and soil moisture on the pupation and emergence of fall armyworm. As a result, survival and pupal mass increased significantly with increasing RH. Among the five RHs tested, 80% RH was the most suitable for fall armyworm with the highest intrinsic rate of increase (r), finite rate of increase (λ), and net reproduction rate (R0). The population growth at the different RHs in decreasing order was 80 > 100 > 60 > 40 > 20%. A relative moisture (RM) of soil from 6.80 to 47.59% was suitable for fall armyworm pupation, survival, and eclosion, but fall armyworm could not pupate normally in soil with 88.39 and 95.19% RM. The survival and emergence rate of fall armyworm pupae were reduced by irrigation that increased the RM after the mature larvae entered the soil. These findings may be helpful for refining laboratory rearing protocols, population forecasting, and management of fall armyworm.

scholarly journals Time Course of COVID-19 Cases in Austria

2020 ◽  
Vol 17 (9) ◽  
pp. 3270 ◽  
Author(s):  
Hanns Moshammer ◽  
Michael Poteser ◽  
Kathrin Lemmerer ◽  
Peter Wallner ◽  
Hans-Peter Hutter
Keyword(s):  
Public Health ◽  
Infectious Disease ◽  
Time Course ◽  
Reproduction Number ◽  
Average Duration ◽  
Northern Italy ◽  
Reproduction Rate ◽  
Health Measures ◽  
Major Outbreak ◽  
Novel Coronavirus

COVID-19 is an infectious disease caused by a novel coronavirus, which first appeared in China in late 2019, and reached pandemic distribution in early 2020. The first major outbreak in Europe occurred in Northern Italy where it spread to neighboring countries, notably to Austria, where skiing resorts served as a main transmission hub. Soon, the Austrian government introduced strict measures to curb the spread of the virus. Using publicly available data, we assessed the efficiency of the governmental measures. We assumed an average incubation period of one week and an average duration of infectivity of 10 days. One week after the introduction of strict measures, the increase in daily new cases was reversed, and the reproduction number dropped. The crude estimates tended to overestimate the reproduction rate in the early phase. Publicly available data provide a first estimate about the effectiveness of public health measures. However, more data are needed for an unbiased assessment.

Temperature-dependent life history of Eutetranychus africanus (Acari: Tetranychidae) on papaya

2020 ◽  
Vol 25 (3) ◽  
pp. 479-490
Author(s):  
Ming-ying Lin ◽  
Chin-hsing Lin ◽  
Yen-po Lin ◽  
Ching-tzu Tseng
Keyword(s):  
Life History ◽  
Immature Stage ◽  
Invasive Pest ◽  
Intrinsic Rate Of Increase ◽  
Reproduction Rate ◽  
Developmental Duration ◽  
Developmental Threshold ◽  
Rate Of Increase ◽  
History Of ◽  
Net Reproduction

This study was conducted to further understand the biology of Eutetranychus africanus Tucker, a newly invasive pest mite in Taiwan that can cause serious damage to papaya. We report the life history of E. africanus on papaya in laboratory conditions at 12, 17, 22, 27 and 32 ± 0.5 °C, with 70 ± 5 % relative humidity and a photoperiod of L12: D12. Eggs did not hatch at 12 °C. Both developmental duration and longevity were significantly shortened with the increase of temperature. The longest and shortest developmental durations of the immature stage were 37.28 days at 17 °C and 8.70 days at 32 °C, respectively. The longevity of both sexes varied similarly with the change in temperature, with shorter lifespan in males: Females survived for 3.64 days (shortest) at 32 °C to 17.50 days (longest) at 17 °C, whereas males survived for 11.00 days (longest) at 17 °C to 2.57 days (shortest) at 32 °C. The differences in fecundity were significant among all tested temperatures, with 17.61 eggs/female at 27 °C being the highest. The low developmental threshold and thermal summation of the full immature stage were 11.48 °C and 163.93 degree-days, respectively. In two-sex life table analysis, population parameters were significantly affected by temperature except the net reproduction rate. The highest intrinsic rate of increase was 0.1221 day−1 at 27 °C; the average generation time was the shortest (12.61 days) at 32 °C and the longest (48.70 days) at 17 °C. The highest net reproduction rate was 5.06 eggs/female at 27 °C. This report contributes background knowledge to the management of the damage caused by E. africanuson papaya.This study was conducted to further understand the biology of Eutetranychus africanus Tucker, a newly invasive pest mite in Taiwan that can cause serious damage to papaya. We report the life history of E. africanus on papaya in laboratory conditions at 12, 17, 22, 27 and 32 ± 0.5 °C, with 70 ± 5 % relative humidity and a photoperiod of L12: D12. Eggs did not hatch at 12 °C. Both developmental duration and longevity were significantly shortened with the increase of temperature. The longest and shortest developmental durations of the immature stage were 37.28 days at 17 °C and 8.70 days at 32 °C, respectively. The longevity of both sexes varied similarly with the change in temperature, with shorter lifespan in males: Females survived for 3.64 days (shortest) at 32 °C to 17.50 days (longest) at 17 °C, whereas males survived for 11.00 days (longest) at 17 °C to 2.57 days (shortest) at 32 °C. The differences in fecundity were significant among all tested temperatures, with 17.61 eggs/female at 27 °C being the highest. The low developmental threshold and thermal summation of the full immature stage were 11.48 °C and 163.93 degree-days, respectively. In two-sex life table analysis, population parameters were significantly affected by temperature except the net reproduction rate. The highest intrinsic rate of increase was 0.1221 day−1 at 27 °C; the average generation time was the shortest (12.61 days) at 32 °C and the longest (48.70 days) at 17 °C. The highest net reproduction rate was 5.06 eggs/female at 27 °C. This report contributes background knowledge to the management of the damage caused by E. africanus on papaya.

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