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

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.

Biology and life tables of Telenomus remus (Hymenoptera: Scelionidae) as parasitoid of Spodoptera frugiperda (J. E. Smith) (Lepidoptera: Noctuidae)

Telenomus remus (Hymenoptera: Scelionidae), is an endoparasitoid on eggs of Spodoptera frugiperda (J. E. Smith). S. frugiperda. The information of T. remus as a natural enemy of S. frugiperda is very limited. The research objective is to determine some biological aspects of T. remus, i.e. longevity, fecundity, and life table variables. The demographic statistics using the jackknife method. T. remus is collected from the field identified as T. remus. The immature stage of T. remus reached 8.13 days, the longevity of the male was 10.07 days, while a female was 10.29 days with a fecundity of 75 eggs, and a sex ratio of male and female was 1:2.16. T. remus life table, i.e. gross reproduction rate (GRR) was 74.67 individuals/generation, net reproduction rate (R0) was 45260.60 females/females/generation, with generation period (T) was 8.62 days, and intrinsic rate of increase (r) was 1.24 females/female/day. The success parasitization of T. remus reaches 91%.

Biology and life table of Trichogramma chilotraeae, Egg parasitoids of Spodoptera frugiperda (J. E. Smith) (Lepidoptera: Noctuidae)

Spodoptera frugiperda is a species of armyworm that attacks maize crops globally and is a dangerous new invasive pest in Indonesia. Biological control, which employs natural enemies, is one method of controlling this pest. One of the natural enemies found in the field is the egg parasitoid of the Trichogrammatidae family. This study aimed to determine the reproductive capacity of the parasitoid on S. frugiperda eggs. The tested parasitoids were collected from S. frugiperda eggs on corn cultivations in Tenjolaya Village, Bogor Regency, West Java Province. The identification results showed that the parasitoid species used in this study was Trichogramma chilotraeae. The development periods of eggs, first instar larvae, second instar larvae, and pupae in the laboratory were 1.16 days, 1.18 days, 1.39 days, and 3.28 days, respectively. The reproductive capacity of T. chilotraeae on S. frugiperda eggs, referred to as the net reproduction rate (Ro), was 28.13, gross reproduction rate (GRR) was 30.43. the average time for one generation (T) was 9.07. The intrinsic rate of increase (r) was 5.54, and Doubling time (DT) was 1.88. Thus, the egg parasitoid of T. chilotraeae was not very effective as a potential biological agent for S. frugiperda.

The Influence of Kin Proximity on the Reproductive Success of American Couples, 1900–1910

Children require a large amount of time, effort, and resources to raise. Physical help, financial contributions, medical care, and other types of assistance from kin and social network members allow couples to space births closer together while maintaining or increasing child survival. We examine the impact of kin availability on couples' reproductive success in the early twentieth-century United States with a panel data set of over 3.1 million couples linked between the 1900 and 1910 U.S. censuses. Our results indicate that kin proximity outside the household was positively associated with fertility, child survival, and net reproduction, and suggest that declining kin availability was an important contributing factor to the fertility transition in the United States. We also find important differences between maternal and paternal kin inside the household—including higher fertility among women residing with their mother-in-law than among those residing with their mother—that support hypotheses related to the contrasting motivations and concerns of parents and parents-in-law.

Differential impact of physical distancing strategies on social contacts relevant for the spread of SARS-CoV-2: evidence from a cross-national online survey, March–April 2020

ObjectivesWe investigate changes in social contact patterns following the gradual introduction of non-pharmaceutical interventions and their implications for infection transmission in the early phase of the pandemic.Design, setting and participantsWe conducted an online survey based on targeted Facebook advertising campaigns across eight countries (Belgium, France, Germany, Italy, the Netherlands, Spain, UK and USA), achieving a sample of 51 233 questionnaires in the period 13 March–12 April 2020. Poststratification weights based on census information were produced to correct for selection bias.Outcome measuresParticipants provided data on social contact numbers, adoption of protective behaviours and perceived level of threat. These data were combined to derive a weekly index of infection transmission, the net reproduction number Rt .ResultsEvidence from the USA and UK showed that the number of daily contacts mainly decreased after governments issued the first physical distancing guidelines. In mid-April, daily social contact numbers had decreased between 61% in Germany and 87% in Italy with respect to pre-COVID-19 levels, mostly due to a contraction in contacts outside the home. Such reductions, which were uniform across age groups, were compatible with an Rt equal or smaller than one in all countries, except Germany. This indicates lower levels of infection transmission, especially in a period of gradual increase in the adoption rate of the face mask outside the home.ConclusionsWe provided a comparable set of statistics on social contact patterns during the COVID-19 pandemic for eight high-income countries, disaggregated by week and other demographic factors, which could be leveraged by the scientific community for developing more realistic epidemic models of COVID-19.

The effect of control measures on COVID-19 transmission in South Korea

Countries around the world have taken control measures to mitigate the spread of COVID-19, including Korea. Social distancing is considered an essential strategy to reduce transmission in the absence of vaccination or treatment. While interventions have been successful in controlling COVID-19 in Korea, maintaining the current restrictions incurs great social costs. Thus, it is important to analyze the impact of different polices on the spread of the epidemic. To model the COVID-19 outbreak, we use an extended age-structured SEIR model with quarantine and isolation compartments. The model is calibrated to age-specific cumulative confirmed cases provided by the Korea Disease Control and Prevention Agency (KDCA). Four control measures—school closure, social distancing, quarantine, and isolation—are investigated. Because the infectiousness of the exposed has been controversial, we study two major scenarios, considering contributions to infection of the exposed, the quarantined, and the isolated. Assuming the transmission rate would increase more than 1.7 times after the end of social distancing, a second outbreak is expected in the first scenario. The epidemic threshold for increase of contacts between teenagers after school reopening is 3.3 times, which brings the net reproduction number to 1. The threshold values are higher in the second scenario. If the average time taken until isolation and quarantine reduces from three days to two, cumulative cases are reduced by 60% and 47% in the first scenario, respectively. Meanwhile, the reduction is 33% and 41%, respectively, for rapid isolation and quarantine in the second scenario. Without social distancing, a second wave is possible, irrespective of whether we assume risk of infection by the exposed. In the non-infectivity of the exposed scenario, early detection and isolation are significantly more effective than quarantine. Furthermore, quarantining the exposed is as important as isolating the infectious when we assume that the exposed also contribute to infection.

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

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.

Biological aspects of the two-spotted spider mite on strawberry plants under silicon application

ABSTRACT Silicon is an inducer of plant resistance to arthropod pests, being a promising strategy for integrated management. The aim of this study was to evaluate the effect of silicon on biological, reproductive and population aspects of parental and F1 generations of the two-spotted spider mite on strawberry plants. Potassium silicate, nanosilica and water were applied to the plants. Two-spotted spider mite females were confined to strawberry leaf disks for oviposition and, after hatching, larvae were observed until the emergence of adults. Once adults had been obtained, couples were formed in order to evaluate pre-oviposition, oviposition, longevity and fertility, with an estimated net reproduction rate, intrinsic rate of increase, finite rate of increase and the necessary time for doubling the generation. Silicon prolonged the duration of some immature stages of the mites in parental and F1 generations, did not affect the duration of the whole biological cycle, though. The periods of pre-oviposition, oviposition and longevity of the parental generation and the longevity and oviposition of F1 generation of the two-spotted spider mite were negatively affected by potassium silicate and nanosilica. The population parameters of the parental generation of the mites indicated that nanosilica is able to lead to a long-run decrease of this pest population.

State, population characteristics of Tulipa biebersteiniana Schult & Schult Fil. on the territory of the left bank of Transnistria and features of its reproduction in vivo and in vitro

The ontogenetic states of T. biebersteiniana in the broad interpretation which grows in Transdnistria was refined. In the tract of Kalagur-Stroentsy four age states were defined, on limestone faults along the valley of the Dniester - five. A comparative study of the main demographic indicators of mesophilic and xerophilous ecological groups of T. biebersteiniana has been conducted. The morphometric indicators of the populations of both ecogroups have been identified and analyzed: total population density, ontogenetic spectrum, projective cover, and age and efficathy indices. The method of propagation of mesophilic and xerophilous ecogroups representatives has been clarified. Mesophilic plants propagated vegetatively, the forming bulbs have a sporophyte origin, and the mature mesophilic populations are renewed homophasically. Xerophilous plants reproduce mainly sexually; the reproduction of developing populations is mainly heterophasic. Both ecogroups were rejuvenated, so their resistance as the survival in phytocenosis was unified by the comparable reproduction and replacement indices. The surveyed mesophilic and xerophilous populations were classified as young, left-handed, normal, and incomplete. Populations of both ecogroups, being young, with high reproduction and replacement indices, were not affected by the tulip breaking virus, and were relatively resistant and adapted to their biotope. Prospects for their continued existence now are quite favorable in the absence of sudden and sharp effects on them of possible biotic and abiotic stressors. There is a low net reproduction in the plants of the mesophilic group in natural populations. The inducing of additional micro bulbs in the culture of in vitro based on indirect somatic embryogenesis is promising to increase T. biebersteiniana propagation rate.