On the Rate of Growth of the Population of the United States since 1790 and Its Mathematical Representation

Misinformation Caused Increased Urban Mobility and the End of Social Confinement Before the Second Wave of COVID-19 in Amazonia

Tendentious projections about COVID-19 in Brazil provided an appealing excuse for individuals and decision-makers to justify poor choices during a critical phase of the pandemic. The erroneous results likely contributed to premature resumption of in-person school classes and easing of restrictions on social contact, favoring the resurgence of COVID-19. In Manaus, the largest city in the Amazon region, the COVID-19 pandemic did not end in 2020 of its own accord, but rather rebounded in a disastrous second wave of the disease.

Global population: from Super-Malthus behavior to Doomsday criticality

The report discusses global population changes from the Holocene beginning to 2023, via two Super Malthus (SM) scaling equations. SM-1 is the empowered exponential dependence: P t = P 0 e x p ± t / τ β , and SM-2 is the Malthus-type relation with the time-dependent growth rate r ( t ) or relaxation time τ ( t ) = 1 / r ( t ) : P t = P 0 e x p r t × t = P 0 e x p τ t / t . Population data from a few sources were numerically filtered to obtain a 'smooth' dataset, allowing the distortions-sensitive and derivative-based analysis. The test recalling SM-1 equation revealed the essential transition near the year 1970 (population: ~ 3 billion): from the compressed exponential behavior ( β > 1 ) to the stretched exponential one ( β < 1 ). For SM-2 dependence, linear changes of τ T during the Industrial Revolutions period, since ~ 1700, led to the constrained critical behavior P t = P 0 e x p b ' t / T C - t , whereT C ≈ 2216 is the extrapolated year of the infinite population. The link to the 'hyperbolic' von Foerster Doomsday equation is shown. Results are discussed in the context of complex systems physics, the Weibull distribution in extreme value theory, and significant historic and prehistoric issues revealed by the distortions-sensitive analysis.

Climate-influenced performance and offspring development of merino sheep in a dry temperate-cold valley

This study aims to explore the effects of climate on the performance and offspring development of aged Merino sheep relocated from an arid, cold environment with harsh grazing conditions to a dry, temperate-cold valley with irrigated pasture production. We utilized time series data from merino sheep in a dry temperate-cold climate in southern Argentina to characterize their growth curves, assess the impact of climate on performance, and compare offspring growth with maternal growth. Our approach involved developing a dynamic model, a non-autonomous differential equation growth curve based on the widely used Brody model. The model considered variables such as local temperature, age, sex, origin, and pregnancy status to determine the optimal combination of parameters for sheep growth in our dataset. The results have shown that moving the old sheep from the steppe to the valley resulted in an increase of an average of 1 kg in weight, but their offspring had an asymptotic weight of 65 kg, 17 kg more than their mothers. The optimum temperature for the growth rate was 15.7+/-0.56 C and 8.7+/-6.3C for the asymptotic weight.

Electromagnetic fields effects on microbial growth in cocoa fermentation: A controlled experimental approach using established growth models

Understanding the effects of electromagnetic fields is crucial in the fermentation of cocoa beans, since through precise control of fermentation conditions the sensory and nutritional properties of cocoa beans could be improved. This study aimed to evaluate the effect of oscillating magnetic fields (OMF) on the kinetic growth of the core microbial communities of the Collections Castro Naranjal (CCN 51) cocoa bean. The data was obtained by three different models: Gompertz, Baranyi, and Logistic. The cocoa beans were subjected to different OMF strengths ranging from 0 mT to 80 mT for 1 h using the Helmholtz coil electromagnetic device. The viable microbial populations of lactic acid bacteria (LAB), acetic acid bacteria (AAB), and yeast (Y) were quantified using the colony-forming unit (CFU) counting method. The logistic model appropriately described the growth of LAB and Y under magnetic field exposure. Whereas the Baranyi model was suitable for describing AAB growth. The microbial populations in cocoa beans exposed to magnetic fields showed lower (maximum specific growth rate (μmax), values than untreated controls, with AAB exhibiting the highest average growth rate value at 5 mT and Y having the lowest average maximum growth rate value at 80 mT. The lower maximum specific growth rates and longer lag phases when exposed to magnetic fields compared to controls demonstrate the influence of magnetic fields on microbial growth kinetics.

A non-singular fractional-order logistic growth model with multi-scaling effects to analyze and forecast population growth in Bangladesh

This paper is primarily concerned with data analysis employing the nonlinear least squares curve fitting method and the mathematical prediction of future population growth in Bangladesh. Available actual and adjusted census data (1974-2022) of the Bangladesh population were applied in the well-known autonomous logistic population growth model and found that all data sets of the logistic (exact), Atangana-Baleanu-Caputo (ABC) fractional-order derivative approach, and logistic multi-scaling approximation fit with good agreement. Again, the existence and uniqueness of the solution for fractional-order and Hyers-Ulam stability have been studied. Generally, the growth rate and maximum environmental support of the population of any country slowly fluctuate with time. Including an approximate closed-form solution in this analysis confers several advantages in assessing population models for single species. Prior studies predominantly employed constant growth rates and carrying capacity, neglecting the investigation of fractional-order methods. Thus, the current study fills a crucial gap in the literature by introducing a more formal approach to analyzing population dynamics. Therefore, we bank on the findings of this article to contribute to accurate population forecasting and planning, national development, and national progress.

Occurrence and removal of antibiotics from aquaculture wastewater by solar-driven Fe(VI)/oxone process

In this study, the occurrence and removal of ten selected antibiotics from aquaculture wastewater by the process solar + Fe(VI)+oxone were investigated. The detection levels of the antibiotics in the aquaculture wastewater samples were at ng/L. The degradation of the selected antibiotics under the process solar + Fe(VI)+oxone followed pseudo-first-order kinetics. As the most abundant antibiotic in the studied aquaculture wastewater, norfloxacin (NFX) was used as the model compound to study the reaction mechanism and detoxification ability of the treatment system, as well as the effects of reaction parameters and environmental factors. The active species including O2•-, O21, and Fe(V)/Fe(IV) contributed to NFX degradation in the process solar + Fe(VI)+oxone. Decarboxylation, the piprazine ring opening, defluorination of the benzene ring, oxygen addition and the cleavage of the quinolone/benzene ring were main degradation pathways of NFX. Around 20% mineralization was reached and the inhibition rate of the bacteria (Escherichia Coli) growth was reduced from 95.5% to 47.1% after the NFX degradation for 60 min. Despite the suppression of NFX degradation by NO2-, PO43- and humic acid, the NFX degradation in three aquaculture wastewater samples was faster than that in ultrapure water due to the positive effect of Br-and other factors. The above results demonstrate the treatment process solar-driven Fe(VI)/oxone has a good potential in antibiotics removal from the aquaculture wastewater.

Modeling and evaluating site and provenance variation in height-diameter relationships for Betula alnoides Buch.-Ham. ex D. Don in southern China

Tree height (H) and stem diameter at breast height (DBH) (H-D) relationship is correlated with timber yield and quality as well as stability of forest and is crucial in forest management and genetic breeding. It is influenced by not only environmental factors such as site quality and climate factors but also genetic control that is mostly neglected. A dataset of H and DBH of 25 provenances of Betula alnoides Buch.-Ham. ex D. Don at four sites was used to model the H-D relationship. The dummy variable nonliner mixed-effect equations were applied to evaluate the effects of sites and provenances on variations of the H-D relationship and to select superior provenances of B. alnoides. Weibull equation was selected as the base model for the H-D relationship. The sites affected asymptotes of the H-D curves, and the provenance effect on asymptotes of the H-D curves varied across sites. Taking above-average DBH and lower asymptote of the H-D curves as indicators, five excellent provenances were screened out at each site with a rate of 20%. Their selection gains of individual volume ranged from 1.99% to 29.81%, and their asymptote parameter (kj) and H-D ratio were 7.17%-486.05% and 3.07-4.72% lower than the relevant total means at four sites, respectively. Genetic selection based on the H-D relationship could promote selection efficiency of excellent germplasms and was beneficial for the large-sized timber production of B. alnoides.

Solving the stochastic dynamics of population growth

Population growth is a fundamental process in ecology and evolution. The population size dynamics during growth are often described by deterministic equations derived from kinetic models. Here, we simulate several population growth models and compare the size averaged over many stochastic realizations with the deterministic predictions. We show that these deterministic equations are generically bad predictors of the average stochastic population dynamics. Specifically, deterministic predictions overestimate the simulated population sizes, especially those of populations starting with a small number of individuals. Describing population growth as a stochastic birth process, we prove that the discrepancy between deterministic predictions and simulated data is due to unclosed-moment dynamics. In other words, the deterministic approach does not consider the variability of birth times, which is particularly important with small population sizes. We show that some moment-closure approximations describe the growth dynamics better than the deterministic prediction. However, they do not reduce the error satisfactorily and only apply to some population growth models. We explicitly solve the stochastic growth dynamics, and our solution applies to any population growth model. We show that our solution exactly quantifies the dynamics of a community composed of different strains and correctly predicts the fixation probability of a strain in a serial dilution experiment. Our work sets the foundations for a more faithful modeling of community and population dynamics. It will allow the development of new tools for a more accurate analysis of experimental and empirical results, including the inference of important growth parameters.

A comparative analysis of growth kinetics, image analysis, and biofuel potential of different algal strains

Due to the global population growth and economic development, energy demand has increased worldwide. Countries take steps to improve their alternative and renewable energy sources. Algae is one of the alternative energy sources and can be used to produce renewable biofuel. In this study, nondestructive, practical, and rapid image processing techniques were applied to determine the algal growth kinetics and biomass potential of four algal strains, including C. minutum, Chlorella sorokiniana, C. vulgaris, and S. obliquus. Laboratory experiments were conducted to determine different aspects of biomass and chlorophyll production of those algal strains. Suitable non-linear growth models, including Logistic, modified Logistic, Gompertz, and modified Gompertz models, were employed to determine the growth pattern of algae. Moreover, the methane potential of harvested biomass was calculated. The algal strains were incubated for 18 days, and the growth kinetics were determined. After the incubation, the biomass was harvested and assessed for its chemical oxygen demand content and biomethane potential. Among the tested strains, C. sorokiniana was the best in biomass productivity (111.97 ± 0.9 mg L^-1d^-1). The calculated vegetation indices, namely; colorimetric difference, color index vegetation, vegetative, excess green, excess green minus excess red, combination, and brown index values showed a significant correlation with biomass and chlorophyll content. Among the tested growth models, the modified Gompertz shows the best growth pattern. Further, the estimated theoretical CH₄ yield was highest for C. minutum (0.98 mL g^-1) compared to other tested strains. The present findings suggest that image analysis can be used as an alternative method to study the growth kinetics and biomass production potential of different algae during cultivation in wastewater.

Deep bootstrap for Bayesian inference

For a Bayesian, the task to define the likelihood can be as perplexing as the task to define the prior. We focus on situations when the parameter of interest has been emancipated from the likelihood and is linked to data directly through a loss function. We survey existing work on both Bayesian parametric inference with Gibbs posteriors and Bayesian non-parametric inference. We then highlight recent bootstrap computational approaches to approximating loss-driven posteriors. In particular, we focus on implicit bootstrap distributions defined through an underlying push-forward mapping. We investigate independent, identically distributed (iid) samplers from approximate posteriors that pass random bootstrap weights through a trained generative network. After training the deep-learning mapping, the simulation cost of such iid samplers is negligible. We compare the performance of these deep bootstrap samplers with exact bootstrap as well as MCMC on several examples (including support vector machines or quantile regression). We also provide theoretical insights into bootstrap posteriors by drawing upon connections to model mis-specification. This article is part of the theme issue 'Bayesian inference: challenges, perspectives, and prospects'.

An experimental critique of the population carrying capacity concept

Carrying capacity has multiple definitions, but nowadays, it is mainly referred to as the maximum number of individuals of a particular species sustained by the environment. We examined whether multiple populations of two flour beetle species grown under controlled laboratory conditions reach similar asymptotic population sizes when provided with similar amounts of food resources. We demonstrate that the variation in the asymptotic population sizes was considerably larger than that of the initial food resources and that the latter had no significant effect on the former. Our results experimentally contribute to past literature criticizing the carrying capacity concept, demonstrating that there is no single carrying capacity even under strict laboratory conditions. Therefore, we should not expect to often find "carrying capacities" in nature, where resources fluctuate over time, and interspecific interactions are ubiquitous. We suggest that the classic meaning of carrying capacity should be revisited or saved chiefly for didactic purposes.

Environmental Malthusianism and demography

As anthropogenic climate change threatens human existence on Earth, historians have begun to explore the scientific antecedents of environmental Malthusianism, the idea that human population growth is a major driver of ecosystem degradation and that environmental protection requires a reduction in human numbers. These accounts, however, neglect the antagonistic relationship between environmental Malthusianism and demography, thereby creating an illusion of scientific consensus. This article details the entwined histories of environmental Malthusianism and demography, revealing points of disagreement - initially over methods of analyzing and predicting population growth and later over the role of population growth in ecosystem degradation - and moments of strategic collaboration that benefited both groups of scientists. It contends that the image of scientific consensus in existing histories has lent support to ongoing calls for population control, detracting attention from more proximate causes of environmental devastation, such as polluting modes of production, extractive business practices and government subsidies for fossil fuel development.

A comparative study for predictive monitoring of COVID-19 pandemic

COVID-19 pandemic caused by novel coronavirus (SARS-CoV-2) crippled the world economy and engendered irreparable damages to the lives and health of millions. To control the spread of the disease, it is important to make appropriate policy decisions at the right time. This can be facilitated by a robust mathematical model that can forecast the prevalence and incidence of COVID-19 with greater accuracy. This study presents an optimized ARIMA model to forecast COVID-19 cases. The proposed method first obtains a trend of the COVID-19 data using a low-pass Gaussian filter and then predicts/forecasts data using the ARIMA model. We benchmarked the optimized ARIMA model for 7-days and 14-days forecasting against five forecasting strategies used recently on the COVID-19 data. These include the auto-regressive integrated moving average (ARIMA) model, susceptible-infected-removed (SIR) model, composite Gaussian growth model, composite Logistic growth model, and dictionary learning-based model. We have considered the daily infected cases, cumulative death cases, and cumulative recovered cases of the COVID-19 data of the ten most affected countries in the world, including India, USA, UK, Russia, Brazil, Germany, France, Italy, Turkey, and Colombia. The proposed algorithm outperforms the existing models on the data of most of the countries considered in this study.

Eco-evolutionary feedbacks among pollinators, herbivores, and their plant resources

Eco-evolutionary feedbacks among multiple species occur when one species affects another species' evolution via its effects on the abundance and traits of a shared partner species. What happens if those two species enact opposing effects on their shared partner's population growth? Furthermore, what if those two kinds of interactions involve separate traits? For example, many plants produce distinct suites of traits that attract pollinators (mutualists) and deter herbivores (antagonists). Here, we develop a model to explore how pollinators and herbivores may influence each other's interactions with a shared plant species via evolutionary effects on the plant's nectar and toxin traits. The model results predict that herbivores indirectly select for the evolution of increased nectar production by suppressing plant population growth. The model also predicts that pollinators indirectly select for the evolution of increased toxin production by plants and increased counterdefenses by herbivores via their positive effects on plant population growth. Unless toxins directly affect pollinator foraging, plants always evolve increases in attraction and defense traits when they interact with both kinds of foragers. This work highlights the value of incorporating ecological dynamics to understand the entangled evolution of mutualisms and antagonisms in natural communities.

Fitness effects of plasmids shape the structure of bacteria-plasmid interaction networks

SignificanceAntimicrobial resistance (AMR) poses a great challenge for modern medicine. Plasmids are important vectors of antibiotic resistance genes. Plasmids can have context-dependent effects on their hosts, generally slowing their growth rate but also providing protection from specific antibiotics and heavy metals. Thus, models that predict population densities based on interactions between species are useful for explaining plasmid dynamics. Here, we predict with a simple ecological model the properties of a host (e.g., bacteria) and symbiont (e.g., plasmid) interaction network. Using experimental microbial communities and a conjugative plasmid, we confirm our predictions that beneficial symbionts spread more widely through a microbial community and provide key experimental results for network ecologists seeking to uncover the determinants of ecological network structure.

Production of protease with Bacillus megaterium DSM32: Partial characterisation of the enzyme and modelling of the production

Proteases hold an important position in today's world commercial enzyme market. Among various microbial producer genera, Bacillus is leading the commercial protease production. However, industry is still actively looking for new microbial protease producers with distinctive properties. Therefore, this study was undertaken for the evaluation of protease production by Bacillus megaterium DSM 32 strain in terms of its protease productivity, calculation of various production kinetics, partial characterisation of the enzyme, and modelling the protease production process. As results, the highest protease activity, specific cellular protease production rate, and protease productivity were calculated as 255.42 U mL−1, 36.2514 U g−1, and 16.1313 U mL−1 h−1, respectively, in shake flask fermentations. Partial characterisation studies showed that the enzyme has 45 °C and pH 8 as optimum working conditions, and its activity increased by 24% with the addition of 5 mM Mn+2 to the reaction medium. Additionally, the enzyme showed high stability and kept almost full activity in a cell-free medium for 20 days at 4 °C. Furthermore, modified Gompertz model provided the best fit in describing protease production with the lowest error and high fit values.

Generalized SIR (GSIR) epidemic model: An improved framework for the predictive monitoring of COVID-19 pandemic

Novel coronavirus respiratory disease COVID-19 has caused havoc in many countries across the globe. In order to contain infection of this highly contagious disease, most of the world population is constrained to live in a complete or partial lockdown for months together with a minimal human-to-human interaction having far reaching consequences on countries' economy and mental well-being of their citizens. Hence, there is a need for a good predictive model for the health advisory bodies and decision makers for taking calculated proactive measures to contain the pandemic and maintain a healthy economy. This paper extends the mathematical theory of the classical Susceptible-Infected-Removed (SIR) epidemic model and proposes a Generalized SIR (GSIR) model that is an integrative model encompassing multiple waves of daily reported cases. Existing growth function models of epidemic have been shown as the special cases of the GSIR model. Dynamic modeling of the parameters reflect the impact of policy decisions, social awareness, and the availability of medication during the pandemic. GSIR framework can be utilized to find a good fit or predictive model for any pandemic. The study is performed on the COVID-19 data for various countries with detailed results for India, Brazil, United States of America (USA), and World. The peak infection, total expected number of COVID-19 cases and thereof deaths, time-varying reproduction number, and various other parameters are estimated from the available data using the proposed methodology. The proposed GSIR model advances the existing theory and yields promising results for continuous predictive monitoring of COVID-19 pandemic.

Modified BBO-Based Multivariate Time-Series Prediction System With Feature Subset Selection and Model Parameter Optimization

Multivariate time-series prediction is a challenging research topic in the field of time-series analysis and modeling, and is continually under research. The echo state network (ESN), a type of efficient recurrent neural network, has been widely used in time-series prediction, but when using ESN, two crucial problems have to be confronted: 1) how to select the optimal subset of input features and 2) how to set the suitable parameters of the model. To solve this problem, the modified biogeography-based optimization ESN (MBBO-ESN) system is proposed for system modeling and multivariate time-series prediction, which can simultaneously achieve feature subset selection and model parameter optimization. The proposed MBBO algorithm is an improved evolutionary algorithm based on biogeography-based optimization (BBO), which utilizes an S -type population migration rate model, a covariance matrix migration strategy, and a Lévy distribution mutation strategy to enhance the rotation invariance and exploration ability. Furthermore, the MBBO algorithm cannot only optimize the key parameters of the ESN model but also uses a hybrid-metric feature selection method to remove the redundancies and distinguish the importance of the input features. Compared with the traditional methods, the proposed MBBO-ESN system can discover the relationship between the input features and the model parameters automatically and make the prediction more accurate. The experimental results on the benchmark and real-world datasets demonstrate that MBBO outperforms the other traditional evolutionary algorithms, and the MBBO-ESN system is more competitive in multivariate time-series prediction than other classic machine-learning models.

The effects of Wuhan highway lockdown measures on the spread of COVID-19 in China

To verify the effects of Wuhan highway lockdown measures on the spread of COVID-19 across China cities, we extracted the vehicle outflow from Wuhan to 245 cities from the Chinese highway toll system. A dynamic exponential risk model that considered the vehicle outflow, city gross domestic product, city population, and distance between two cities was established to characterize the spread of pandemics and quantify the blocking effects. Results showed that an early highway lockdown measure could indeed reduce the confirmed cases and vehicles with 1-9 seats played a leading role. The confirmed cases in Guangxi, Henan, and Shanxi could be reduced by more than 50%, as well as Hubei by 20% if the highway was closed 3 days in advance. The blocking effects on Fujian, Jiangxi, Guangdong, Hunan, and Shandong were not obvious, where the number of confirmed cases only decreased by a small proportion (below 10%). The findings could be used to help each provincial government to adjust policies properly and improve the effectiveness of epidemic control and prevention. Moreover, the proposed method could also be applied to various countries or regions affected by COVID-19, as well as other similar pandemics.

A Slow Single-Species Model with Non-Symmetric Variation of the Coefficients

A single-species population model exhibiting a symmetric slow variation for the carrying capacity and intrinsic growth rate is evaluated explicitly. However, it is unrealistic to eliminate the possibility of a clear separation in the evolution of the biotic environmental elements; thus, this paper considers the situation where these elements have a hierarchical variation on the time scales. Accordingly, two particular situations are recognized, which are the carrying capacity varies faster than the growth rate and vice versa. Applying the multi-time scaling technique in such a system provides a small parameter, which leads us to construct analytical approximate expressions for the population behavior, using the perturbation approach. Such approximations display very good agreement with the numerical simulations.

Effects on Cell Growth, Lipid and Biochemical Composition of Thalassiosira weissflogii (Bacillariophyceae) Cultured under Two Nitrogen Sources

The protein and polyunsaturated fatty acid (PUFA) enrichment of microalgae can improve their nutritional value for larvae of various reared organisms. Protein enrichment can be achieved by increasing nitrogen concentration and selecting nitrogen sources that are easy to assimilate during microalga culture. Nitrogen-rich cultures can increase organism growth, biomass, and protein content, but their lipid content tends to stall. Since the diatom Thalassiosira weissflogii is usually provided to feed shrimp larvae, this study evaluated its digestibility and biochemical composition, culturing it with two nitrogen sources (NaNO3 and NH4Cl) at different concentrations (111.25, 222.50, 445 and 890 µM). The cell abundance, dry-weight biomass, Chl a, proteins, carbohydrates, total lipids and essential fatty acids were determined. The cell density and biomass peaked faster (day 12) with treatment < 890 µM than with 890 µM (day 15) in both nitrogen sources. However, the highest cell density, biomass and peak protein yield were not significantly different among treatments, suggesting the need to compare maintenance costs for a given production. After nine days of culture, concentrations ≤ 222.5 µM increased lipid content irrespective of the nitrogen source and decreased by 10–20% afterwards. With higher lipid production, the dominant PUFA were eicosapentaenoic acid (EPA) and docosahexaenoic acid (DHA). One gram of NH4Cl provides ~60% more nitrogen than 1 g of NaNO3. In conclusion, based on time and growth rate, T. weissflogii cultivated with NH4Cl at 222.50 µM produced EPA and DHA at a better yield–cost ratio for biomass and lipid production. Furthermore, its nutritional value as enriched live-food for the reared larvae of marine organisms suggests potential biotechnological applications for aquaculture.

Species Mixing Proportion and Aridity Influence in the Height–Diameter Relationship for Different Species Mixtures in Mediterranean Forests

Estimating tree height is essential for modelling and managing both pure and mixed forest stands. Although height–diameter (H–D) relationships have been traditionally fitted for pure stands, attention must be paid when analyzing this relationship behavior in stands composed of more than one species. The present context of global change makes also necessary to analyze how this relationship is influenced by climate conditions. This study tends to cope these gaps, by fitting new H–D models for 13 different Mediterranean species in mixed forest stands under different mixing proportions along an aridity gradient in Spain. Using Spanish National Forest Inventory data, a total of 14 height–diameter equations were initially fitted in order to select the best base models for each pair species-mixture. Then, the best models were expanded including species proportion by area (mi) and the De Martonne Aridity Index (M). A general trend was found for coniferous species, with taller trees for the same diameter size in pure than in mixed stands, being this trend inverse for broadleaved species. Regarding aridity influence on H–D relationships, humid conditions seem to beneficiate tree height for almost all the analyzed species and species mixtures. These results may have a relevant importance for Mediterranean coppice stands, suggesting that introducing conifers in broadleaves forests could enhance height for coppice species. However, this practice only should be carried out in places with a low probability of drought. Models presented in our study can be used to predict height both in different pure and mixed forests at different spatio-temporal scales to take better sustainable management decisions under future climate change scenarios.

Accuracy of predicting epidemic outbreaks

During the outbreak of a virus, perhaps the greatest concern is the future evolution of the epidemic: How many people will be infected and which regions will be affected the most? The accurate prediction of an epidemic enables targeted disease countermeasures (e.g., allocating medical staff and quarantining). But when can we trust the prediction of an epidemic to be accurate? In this work we consider susceptible-infected-susceptible (SIS) and susceptible-infected-removed (SIR) epidemics on networks with time-invariant spreading parameters. (For time-varying spreading parameters, our results correspond to an optimistic scenario for the predictability of epidemics.) Our contribution is twofold. First, accurate long-term predictions of epidemics are possible only after the peak rate of new infections. Hence, before the peak, only short-term predictions are reliable. Second, we define an exponential growth metric, which quantifies the predictability of an epidemic. In particular, even without knowing the future evolution of the epidemic, the growth metric allows us to compare the predictability of an epidemic at different points in time. Our results are an important step towards understanding when and why epidemics can be predicted reliably.

Distribution Patterns of Benthic Foraminifera in Fish Farming Areas (Corsica, France): Implications for the Implementation of Biotic Indices in Biomonitoring Studies

Corsican marine aquaculture is one of the highest contributors of fish production in France, which may result in environmental perturbations caused by organic matter (OM) accumulation under fish farms and impacting natural communities. This study aimed to (1) characterise the environmental conditions at two different fish farms, (2) monitor the response of benthic foraminiferal species to this activity, and (3) assess the accuracy of existing foraminiferal biotic indices. In 2017, sea floor sediment was sampled in transects from two Corsican fish farms for living foraminiferal and sedimentary analyses. Four indices were calculated and compared: exp(H′bc), Foram-AMBI, Foram Stress Index and TSI-Med. A significant increase in total organic carbon (TOC) has been shown, mainly below the fish cages. Communities were characterized by a shift from high density, opportunistic and tolerant species under the cages to lower densities and more sensitive species further away. According to their distribution patterns along the TOC gradient, we propose to update the ecological group classification of seven species to improve Foram-AMBI’s accuracy and sensitivity: Triloculina oblonga and Quinqueloculina lamarckiana to Ecological Group (EG) I; Rosalina bradyi to EGIII; and Bolivina dilatata, Bulimina aculeata and Quinqueloculina stalkeri to EGIV. We recommend prioritising the use of TSI-Med and Foram-AMBI with the updated list to assess ecological quality in coastal waters of the Mediterranean Sea.

System dynamics kinetic model for predicting biogas production in anaerobic condition: Preliminary assessment

INTRODUCTION

This preliminary assessment of a grey-box model, was predicated on system dynamics principles and developed using Vensim® DSS software. The purpose is to predict biogas production under anaerobic conditions for energy utilization at the design stage.

OBJECTIVE

To describe the process of a developed system dynamics model to predict biogas production under anaerobic conditions.

METHODS

This method involves two-stage kinetics of the biogas production process in anaerobic conditions using the first-order and Gompertz functions. The model is depicted in two parts: causal loop diagram and stock-flow diagram. The causal loop diagram describes the anaerobic digestion process a substrate undergoes for the production of biogas, while stock-flow diagram depicts basic building blocks of the dynamic behavior of an anaerobic digestion process. Primary data is from a laboratory-scale experiment of biogas production using vegetal wastes, while the secondary one is from the literature on studies using similar substrates.

RESULTS

Primary and secondary data are used to validate and stimulate the developed model. The kinetic model shows the substrate being reduced exponentially with increasing time; consumption of substrate and production of methane and carbon dioxide follows exponential growth and decay pattern, with carbon dioxide production starting early compared to methane, and was produced at a rate faster due to the strong and resilient characteristics of fermentative microorganisms.

DISCUSSION

Comparing data from empirical and model simulation shows some close relationship, though not too perfectly. Both results reflect signs of inhibitions occurring within the substrates in the digester under anaerobic conditions explaining the low methane yield or instability.

The Evolution of Resource Provisioning in Pollination Mutualisms

AbstractResource dynamics influence the contemporary ecology of consumer-resource mutualisms. Suites of resource traits, such as floral nectar components, also evolve in response to different selective pressures, changing the ecological dynamics of the interacting species at the evolutionary equilibrium. Here we explore the evolution of resource-provisioning traits in a biotically pollinated plant that produces nectar as a resource for beneficial consumers. We develop a mathematical model describing natural selection on two quantitative nectar traits: maximum nectar production rate and maximum nectar reservoir volume. We use this model to examine how nectar production dynamics evolve under different ecological conditions that impose varying cost-benefit regimes on resource provisioning. The model results predict that natural selection favors higher nectar production when ecological factors limit the plant or pollinator's abundance (e.g., a lower productivity environment or a higher pollinator conversion efficiency). We also find that nectar traits evolve as a suite in which higher costs of producing one trait select for a compensatory increase in investment in the other trait. This empirically explicit approach to studying the evolution of consumer-resource mutualisms illustrates how natural selection acting via direct and indirect pathways of species interactions generates patterns of resource provisioning seen in natural systems.

A box, a trough and marbles: How the Reed-Frost epidemic theory shaped epidemiological reasoning in the 20th century

The article takes the renewed popularity and interest in epidemiological modelling for Covid-19 as a point of departure to ask how modelling has historically shaped epidemiological reasoning. The focus lies on a particular model, developed in the late 1920s through a collaboration of the former field-epidemiologists and medical officer, Wade Hampton Frost, and the biostatistician and population ecologist Lowell Reed. Other than former approaches to epidemic theory in mathematical formula, the Reed-Frost epidemic theory was materialised in a simple mechanical analogue: a box with coloured marbles and a wooden trough. The article reconstructs how the introduction of this mechanical model has reshaped epidemiological reasoning by shifting the field from purely descriptive to analytical practices. It was not incidental that the history of this model coincided with the foundation of epidemiology as an academic discipline, as it valorised and institutionalised new theoretical contributions to the field. Through its versatility, the model shifted the field's focus from mono-causal explanations informed by bacteriology, eugenics or sanitary perspectives towards the systematic consideration of epidemics as a set of interdependent and dynamic variables.

An alternating active-dormitive strategy enables disadvantaged prey to outcompete the perennially active prey through Parrondo's paradox

BACKGROUND

Dormancy is widespread in nature, but while it can be an effective adaptive strategy in fluctuating environments, the dormant forms are costly due to the inability to breed and the relatively high energy consumption. We explore mathematical models of predator-prey systems, in order to assess whether dormancy can be an effective adaptive strategy to outcompete perennially active (PA) prey, even when both forms of the dormitive prey (active and dormant) are individually disadvantaged.

RESULTS

We develop a dynamic population model by introducing an additional dormitive prey population to the existing predator-prey model which can be active (active form) and enter dormancy (dormant form). In this model, both forms of the dormitive prey are individually at a disadvantage compared to the PA prey and thus would go extinct due to their low growth rate, energy waste on the production of dormant prey, and the inability of the latter to grow autonomously. However, the dormitive prey can paradoxically outcompete the PA prey with superior traits and even cause its extinction by alternating between the two losing strategies. We observed higher fitness of the dormitive prey in rich environments because a large predator population in a rich environment cannot be supported by the prey without adopting an evasive strategy, that is, dormancy. In such environments, populations experience large-scale fluctuations, which can be survived by dormitive but not by PA prey.

CONCLUSION

We show that dormancy can be an effective adaptive strategy to outcompete superior prey, recapitulating the game-theoretic Parrondo's paradox, where two losing strategies combine to achieve a winning outcome. We suggest that the species with the ability to switch between the active and dormant forms can dominate communities via competitive exclusion.

A metapopulation model of social group dynamics and disease applied to Yellowstone wolves

The population structure of social species has important consequences for both their demography and transmission of their pathogens. We develop a metapopulation model that tracks two key components of a species' social system: average group size and number of groups within a population. While the model is general, we parameterize it to mimic the dynamics of the Yellowstone wolf population and two associated pathogens: sarcoptic mange and canine distemper. In the initial absence of disease, we show that group size is mainly determined by the birth and death rates and the rates at which groups fission to form new groups. The total number of groups is determined by rates of fission and fusion, as well as environmental resources and rates of intergroup aggression. Incorporating pathogens into the models reduces the size of the host population, predominantly by reducing the number of social groups. Average group size responds in more subtle ways: infected groups decrease in size, but uninfected groups may increase when disease reduces the number of groups and thereby reduces intraspecific aggression. Our modeling approach allows for easy calculation of prevalence at multiple scales (within group, across groups, and population level), illustrating that aggregate population-level prevalence can be misleading for group-living species. The model structure is general, can be applied to other social species, and allows for a dynamic assessment of how pathogens can affect social structure and vice versa.

Methods for Small Area Population Forecasts: State-of-the-Art and Research Needs

Small area population forecasts are widely used by government and business for a variety of planning, research and policy purposes, and often influence major investment decisions. Yet, the toolbox of small area population forecasting methods and techniques is modest relative to that for national and large subnational regional forecasting. In this paper, we assess the current state of small area population forecasting, and suggest areas for further research. The paper provides a review of the literature on small area population forecasting methods published over the period 2001–2020. The key themes covered by the review are extrapolative and comparative methods, simplified cohort-component methods, model averaging and combining, incorporating socioeconomic variables and spatial relationships, ‘downscaling’ and disaggregation approaches, linking population with housing, estimating and projecting small area component input data, microsimulation, machine learning, and forecast uncertainty. Several avenues for further research are then suggested, including more work on model averaging and combining, developing new forecasting methods for situations which current models cannot handle, quantifying uncertainty, exploring methodologies such as machine learning and spatial statistics, creating user-friendly tools for practitioners, and understanding more about how forecasts are used.

Beyond the limit: carrying capacity (K) and the holism/reductionism debate

As the debate about holism and reductionism in ecology has ebbed in the last twenty years, this article aims to reassess the traditional opposition between holistic and reductionist epistemologies during the development of population biology. The history of the notion of carrying capacity, the upper demographic limit of a viable population, will be analyzed as a paradigmatic case of the progressive imposition of reductionist strategies, from both an epistemological and a semantic point of view, since the middle of the twentieth century. Then, Richard Looijen's reduction of the carrying capacity concept to the niche partitioning theory will be assessed and rebuked for both empirical and logical reasons. Eventually, some recent "weak" and "hard" emergent conceptualizations of the notion of carrying capacity, in logistic map models or in coupled niche-population systems, will be presented in order to show how they call into question the nature and the use of the notion of carrying capacity as a predefined ecological limit.

Dependence of bacterial growth rate on dynamic temperature changes

Temperature is an important determinant of bacterial growth. While the dependence of bacterial growth on different temperatures has been well studied for many bacterial species, prediction of bacterial growth rate for dynamic temperature changes is relatively unclear. Here, the authors address this issue using a combination of experimental measurements of the growth, at the resolution of 5 min, of Escherichia coli and mathematical models. They measure growth curves at different temperatures and estimate model parameters to predict bacterial growth profiles subject to dynamic temperature changes. They compared these predicted growth profiles for various step‐like temperature changes with experimental measurements using the coefficient of determination and mean square error and based on this comparison, ranked the different growth models, finding that the generalised logistic growth model gave the smallest error. They note that as the maximum specific growth increases the duration of this growth predominantly decreases. These results provide a basis to compute the dependence of the growth rate parameter in biomolecular circuits on dynamic temperatures and may be useful for designing biomolecular circuits that are robust to temperature.

Gesture commands for controlling high-level UAV behavior

Abstract

Directing groups of unmanned air vehicles (UAVs) is a task that typically requires the full attention of several operators. This can be prohibitive in situations where an operator must pay attention to their surroundings. In this paper we present a gesture device that assists operators in commanding UAVs in focus-constrained environments. The operator influences the UAVs’ behavior by using intuitive hand gesture movements. Gestures are captured using an accelerometer and gyroscope and then classified using a logistic regression model. Ten gestures were chosen to provide behaviors for a group of fixed-wing UAVs. These behaviors specified various searching, following, and tracking patterns that could be used in a dynamic environment. A novel variant of the Monte Carlo Tree Search algorithm was developed to autonomously plan the paths of the cooperating UAVs. These autonomy algorithms were executed when their corresponding gesture was recognized by the gesture device. The gesture device was trained to classify the ten gestures and accurately identified them 95% of the time. Each of the behaviors associated with the gestures was tested in hardware-in-the-loop simulations and the ability to dynamically switch between them was demonstrated. The results show that the system can be used as a natural interface to assist an operator in directing a fleet of UAVs.

Article highlights

Bertalanffy-Pütter models for avian growth

This paper explores the ratio of the mass in the inflection point over asymptotic mass for 81 nestlings of blue tits and great tits from an urban parkland in Warsaw, Poland (growth data from literature). We computed the ratios using the Bertalanffy-Pütter model, because this model was more flexible with respect to the ratios than the traditional models. For them, there were a-priori restrictions on the possible range of the ratios. (Further, as the Bertalanffy-Pütter model generalizes the traditional models, its fit to the data was necessarily better.) For six birds there was no inflection point (we set the ratio to 0), for 19 birds the ratio was between 0 and 0.368 (lowest ratio attainable for the Richards model), for 48 birds it was above 0.5 (fixed ratio of logistic growth), and for the remaining eight birds it was in between; the maximal observed ratio was 0.835. With these ratios we were able to detect small variations in avian growth due to slight differences in the environment: Our results indicate that blue tits grew more slowly (had a lower ratio) in the presence of light pollution and modified impervious substrate, a finding that would not have been possible had we used traditional growth curve analysis.

The performance of phenomenological models in providing near-term Canadian case projections in the midst of the COVID-19 pandemic: March - April, 2020

BACKGROUND

The COVID-19 pandemic has had an unprecedented impact on citizens and health care systems globally. Valid near-term projections of cases are required to inform the escalation, maintenance and de-escalation of public health measures, and for short-term health care resource planning.

METHODS

Near-term case and epidemic growth rate projections for Canada were estimated using three phenomenological models: the logistic model, Generalized Richard's model (GRM) and a modified Incidence Decay and Exponential Adjustment (m-IDEA) model. Throughout the COVID-19 epidemic in Canada, these models have been validated against official national epidemiological data on an ongoing basis.

RESULTS

The best-fit models estimated that the number of COVID-19 cases predicted to be reported in Canada as of April 1, 2020 and May 1, 2020 would be 11,156 (90 % prediction interval: 9,156-13,905) and 54,745 (90 % prediction interval: 54,252-55,239). The three models varied in their projections and their performance over the first seven weeks of their implementation. Both the logistic model and GRM under-predicted cases reported a week following the projection date in nearly all instances. The logistic model performed best at the early stages, the m-IDEA model performed best at the later stages, and the GRM performed most consistently during the full period assessed.

CONCLUSIONS

All three models have yielded qualitatively comparable near-term forecasts of cases and epidemic growth for Canada. Under or over-estimation of projected cases and epidemic growth by these models could be associated with changes in testing policies and/or public health measures. Simple forecasting models can be invaluable in projecting the changes in trajectory of subsequent waves of cases to provide timely information to support the pandemic response.

Spatiotemporal Analysis of COVID-19 Incidence Data

(1) Background: A better understanding of COVID-19 dynamics in terms of interactions among individuals would be of paramount importance to increase the effectiveness of containment measures. Despite this, the research lacks spatiotemporal statistical and mathematical analysis based on large datasets. We describe a novel methodology to extract useful spatiotemporal information from COVID-19 pandemic data. (2) Methods: We perform specific analyses based on mathematical and statistical tools, like mathematical morphology, hierarchical clustering, parametric data modeling and non-parametric statistics. These analyses are here applied to the large dataset consisting of about 19,000 COVID-19 patients in the Veneto region (Italy) during the entire Italian national lockdown. (3) Results: We estimate the COVID-19 cumulative incidence spatial distribution, significantly reducing image noise. We identify four clusters of connected provinces based on the temporal evolution of the incidence. Surprisingly, while one cluster consists of three neighboring provinces, another one contains two provinces more than 210 km apart by highway. The survival function of the local spatial incidence values is modeled here by a tapered Pareto model, also used in other applied fields like seismology and economy in connection to networks. Model's parameters could be relevant to describe quantitatively the epidemic. (4) Conclusion: The proposed methodology can be applied to a general situation, potentially helping to adopt strategic decisions such as the restriction of mobility and gatherings.

Self-Adaptation of Pseudomonas fluorescens Biofilms to Hydrodynamic Stress

In some conditions, bacteria self-organize into biofilms, supracellular structures made of a self-produced embedding matrix, mainly composed of polysaccharides, DNA, proteins, and lipids. It is known that bacteria change their colony/matrix ratio in the presence of external stimuli such as hydrodynamic stress. However, little is still known about the molecular mechanisms driving this self-adaptation. In this work, we monitor structural features of Pseudomonas fluorescens biofilms grown with and without hydrodynamic stress. Our measurements show that the hydrodynamic stress concomitantly increases the cell density population and the matrix production. At short growth timescales, the matrix mediates a weak cell-cell attractive interaction due to the depletion forces originated by the polymer constituents. Using a population dynamics model, we conclude that hydrodynamic stress causes a faster diffusion of nutrients and a higher incorporation of planktonic bacteria to the already formed microcolonies. This results in the formation of more mechanically stable biofilms due to an increase of the number of crosslinks, as shown by computer simulations. The mechanical stability also relies on a change in the chemical compositions of the matrix, which becomes enriched in carbohydrates, known to display adhering properties. Overall, we demonstrate that bacteria are capable of self-adapting to hostile hydrodynamic stress by tailoring the biofilm chemical composition, thus affecting both the mesoscale structure of the matrix and its viscoelastic properties that ultimately regulate the bacteria-polymer interactions.

Modeling and forecasting the spread of COVID-19 pandemic in India and significance of lockdown: A mathematical outlook

A very special type of pneumonic disease that generated the COVID-19 was first identified in Wuhan, China in December 2019 and is spreading all over the world. The ongoing outbreak presents a challenge for data scientists to model COVID-19, when the epidemiological characteristics of the COVID-19 are yet to be fully explained. The uncertainty around the COVID-19 with no vaccine and effective medicine available till today create additional pressure on the epidemiologists and policy makers. In such a crucial situation, it is very important to predict infected cases to support prevention of the disease and aid in the preparation of healthcare service. India is fighting efficiently against COVID-19 and facing greater challenges because of its large population and high population density. Though the government of India is taking all needful steps to prevent its spread but it is not enough to control and stop spread of the disease so far, perhaps due to defiant nature of people living in India. Effective measure to control this disease, medical professionals needs to know the estimated size of this pandemic and pace. In this study, an attempt has been made to understand the spreading capability of COVID-19 in India through some simple models. Findings suggest that the lockdown strategies implemented in India are not successfully reducing the pace of the pandemic significantly after first lockdown.

Optimization of the Effects of Different Temperatures and Compositions of Filmogenic Solution on Lactobacillus Salivarius Using Predictive Mathematical Models

It is well known that intake of probiotic brings health benefits. Lactic bacteria with probiotic potential have aroused the interest of the industry in developing food products that incorporate such benefits. However, incorporating probiotic bacteria into food is a challenge for the industry, given the sensitivity of probiotic cultures to process conditions. Therefore, the objective of this study is to evaluate gelatin- and inulin-based filmogenic solutions as a potential vehicle for incorporating probiotics into food products and to model the fermentation kinetics. L. salivarius (Lactobacillus salivarius) growth in filmogenic solutions was analyzed under the influence of a variety gelatin concentrations (1.0–3.0%) and inulin concentrations (4.0–6.0%) and fermented under the effect of different temperatures (25–45 °C). A full 2³ factorial plan with three replicates at the central point was used to optimize the process. The impacts of process conditions on cell development are fundamental to optimize the process and make it applicable by the industry. The present study showed that the optimal conditions for the development of probiotic cells in filmogenic solutions are a combination of 1.0% gelatin with 4.0% inulin and fermentation temperature of 45 °C. It was observed that the maximum cell growth occurred in an estimated time of about 4 h of fermentation. L. salivarius cell production and substrate consumption during the fermentation of the filmogenic solution were well simulated by a model proposed in this article, with coefficients of determination of 0.981 (cell growth) and 0.991 (substrate consumption).

Vaccination Criteria Based on Factors Influencing COVID-19 Diffusion and Mortality

SARS-CoV-2 is highly contagious, rapidly turned into a pandemic, and is causing a relevant number of critical to severe life-threatening COVID-19 patients. However, robust statistical studies of a large cohort of patients, potentially useful to implement a vaccination campaign, are rare. We analyzed public data of about 19,000 patients for the period 28 February to 15 May 2020 by several mathematical methods. Precisely, we describe the COVID-19 evolution of a number of variables that include age, gender, patient’s care location, and comorbidities. It prompts consideration of special preventive and therapeutic measures for subjects more prone to developing life-threatening conditions while affording quantitative parameters for predicting the effects of an outburst of the pandemic on public health structures and facilities adopted in response. We propose a mathematical way to use these results as a powerful tool to face the pandemic and implement a mass vaccination campaign. This is done by means of priority criteria based on the influence of the considered variables on the probability of both death and infection.

COVID-19 cumulative incidence, intensive care, and mortality in Italian regions compared to selected European countries

Background

The high contagiousness and rapid spreading of the coronavirus disease 2019 (COVID-19) has caused a high number of critical to severe life-threatening cases, which required urgent hospital admission and treatment in intensive care units (ICUs). The pandemic has been a tough test for all European national health systems and their capability to provide an adequate reaction.

Methods

The present work aims to reveal correlations between parameters such as COVID-19 incidence, ICU bed occupancy, ICU excess area, and mortality in Italian regions. Public data for the period of March 1 to July 16, 2020, were analyzed using several mathematical and statistical methods.

Results

The analysis defined two separate groups of Italian regions. The examined variables considered within these groups were interlinked and dependent on each other. The regions of the two groups shared the same kind of fitted model (linear) explaining mortality as a function of cumulative incidence, but with higher value of the constant in one group, so characterized by a high intrinsic “strength” of the pandemic, certainly playing a major role in the generation of a large number of severe and life-threatening cases. These results are confirmed at European level. Other factors may condition mortality and be linked to incidence, such as ICU saturation and excess.

Conclusions

These quantitative results could be a very helpful tool to set up preventive measures and optimize biomedical interventions before the pandemic, in its recurrent waves, could overcome the reaction capacity of any public health system.