A common narrative among insurance actuaries and business economists is that national or regional pension systems can be finetuned, optimized, and improved simply by tinkering with demographic and financial parameters; all within the context of the “right” mathematical model. Indeed, recent papers in the actuarial literature have offered technical fixes around savings rates, retirement ages, decumulation strategies as well as more refined mortality and interest rate models. But alas, not everything in the world of pensions and retirement can be optimized, in particular as it relates to the history, background culture, or religion of the underlying population.

This paper documents a statistically significant relationship between a region’s pension plan “health status” and the fraction of the region’s population identifying as Protestant Christians (PC). We begin the analysis at the national level using a well-known pension quality index and then obtain similar results for the actuarial funded status of U.S. state pension plans.

Overall, this work is within the sphere of recent literature that indicates historical religious beliefs, values, and culture matter for financial economic outcomes; a factor which obviously can’t be optimized within a mathematical Hamilton–Jacobi–Bellman (HJB) equation. In other words, some things in retirement are truly beyond control.

Sense of agency is the sense that one is causing an action. The increase in machine or system autonomy leads to an increase in the loss of sense of agency for the operation causing the loss of pleasure in the operation or sense of responsibility for the consequences of operations. Designing a sense of agency is necessary, especially in the context of machine autonomy. This calls for the control of the sense of agency, which requires the construction of a model to predict the sense of agency and establishing a design methodology to manipulate the factors of sense of agency. We propose the mathematical model that predicts the sense of agency in a human-machine system based on the comparator model and free-energy principle and what to design to enhance the sense of agency. Proposed model explains the effects of prediction error, prediction uncertainty, and observation uncertainty for body, machine, and environment feedback on the sense of agency. The model generally reveals the interaction effect between prediction error and prediction uncertainty and between prediction error and observation uncertainty. The model prediction can be widely applied as a design guide for enhancing sense of agency of human-machine interfaces.

As a heavy load is applied to the parallel manipulators, it causes inaccuracies while positioning the end-effector or unbalanced dynamic forces in the legs. Various load-balancing techniques overcome this. However, the disadvantage of most load-balancing mechanisms is that they add inertia to the assembly and decrease the speed of motion. This article studies a new load-balancing method (a passive damper mechanism). The passive balancing mechanism is proposed to negate the inertia effects while countering the static inaccuracies in the parallel mechanism. This is verified by the structural analysis of the mechanism. The impact of the damper element on the dynamics of the mechanism is unknown. Hence, a complete mathematical model for the balancing mechanism has been developed to study its impact on the dynamics of the entire structure. Laplace transformations characterize the system response. The inclusion of a passive damper in a 3-prismatic-prismatic-revolute-spherical system was examined and found to be stable and critically damped. Such a passive damper was envisaged to facilitate additional force transmission for the actuators, and the DC gain from the system response validates the torque support for the actuators.

Coronavirus disease 2019 (COVID-19) has been described as having an overdispersed offspring distribution, i.e. high variation in the number of secondary transmissions of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) per single primary COVID-19 case. Accordingly, countermeasures focused on high-risk settings and contact tracing could efficiently reduce secondary transmissions. However, as variants of concern with elevated transmissibility continue to emerge, controlling COVID-19 with such focused approaches has become difficult. It is vital to quantify temporal variations in the offspring distribution dispersibility. Here, we investigated offspring distributions for periods when the ancestral variant was still dominant (summer, 2020; wave 2) and when Alpha variant (B.1.1.7) was prevailing (spring, 2021; wave 4). The dispersion parameter (k) was estimated by analysing contact tracing data and fitting a negative binomial distribution to empirically observed offspring distributions from Nagano, Japan. The offspring distribution was less dispersed in wave 4 (k = 0.32; 95% confidence interval (CI) 0.24–0.43) than in wave 2 (k = 0.21 (95% CI 0.13–0.36)). A high proportion of household transmission was observed in wave 4, although the proportion of secondary transmissions generating more than five secondary cases did not vary over time. With this decreased variation, the effectiveness of risk group-focused interventions may be diminished.

Hepatitis E is an increasingly serious worldwide public health problem that has attracted extensive attention. It is necessary to accurately predict the incidence of hepatitis E to better plan ahead for future medical care. In this study, we developed a Bi-LSTM model that incorporated meteorological factors to predict the prevalence of hepatitis E. The hepatitis E data used in this study are collected from January 2005 to March 2017 by Jiangsu Provincial Center for Disease Control and Prevention. ARIMA, GBDT, SVM, LSTM and Bi-LSTM models are adopted in this study. The data from January 2009 to September 2014 are used as the training set to fit models, and data from October 2014 to March 2017 are used as the testing set to evaluate the predicting accuracy of different models. Selecting models and evaluating the effectiveness of the models are based on mean absolute per cent error (MAPE), root mean square error (RMSE) and mean absolute error (MAE). A total of 44 923 cases of hepatitis E are detected in Jiangsu Province from January 2005 to March 2017. The average monthly incidence rate is 0.35 per 100 000 persons in Jiangsu Province. Incorporating meteorological factors of temperature, water vapour pressure, and rainfall as a combination into the Bi-LSTM Model achieved the state-of-the-art performance in predicting the monthly incidence of hepatitis E, in which RMSE is 0.044, MAPE is 11.88%, and MAE is 0.0377. The Bi-LSTM model with the meteorological factors of temperature, water vapour pressure, and rainfall can fully extract the linear and non-linear information in the hepatitis E incidence data, and has significantly improved the interpretability, learning ability, generalisability and prediction accuracy.

The alveolar hydatid disease, also known as alveolar echinococcosis, of humans is certainly one of the most dangerous zoonoses worldwide. The disease is caused by Echinococcus multilocularis – the fox tapeworm. Red foxes (Vulpes vulpes) are currently counted as the most important carriers (reservoirs) of E. multilocularis in the Northern Hemisphere. The possible routes of infection of E. multilocularis to humans are complex and still require research. Until now, it has been unknown whether E. multilocularis eggs can be moved by wind at all. This analysis shows, based on calculations, that E. multilocularis eggs can be transported by wind. Using a mathematical model, flight distances depending on wind speed and take-off heights are calculated for dense and less dense (coniferous) forest areas. The results – differentiated for seasons and as overall average – are based on mean values of wind speeds which were measured over a ten-year period in an experimental forest stand in the Solling (Germany). Due to their rate of descent, wind-related spreading of E. multilocularis eggs is possible. The average flight distance covered by E. multilocularis eggs in forest areas, depending on their starting altitude and wind speed, is between approximately 1.3 m and approximately 17 m. From the mathematical point of view, the wind factor can definitely be seen as one of the multiple vectors associated with environmental contamination by E. multilocularis eggs. Consequently, the possible wind-borne spread of E. multilocularis eggs poses an infection risk to humans that should be considered and requires further research.

Two simple mathematical models of advection and diffusion of hydrogen within the retina are discussed. The work is motivated by the hydrogen clearance technique, which is used to estimate blood flow in the retina. The first model assumes that the retina consists of three, well-mixed layers with different thickness, and the second is a two-dimensional model consisting of three regions that represent the layers in the retina. Diffusion between the layers and leakage through the outer edges are considered. Solutions to the governing equations are obtained by employing Fourier series and finite difference methods for the two models, respectively. The effect of important parameters on the hydrogen concentration is examined and discussed. The results contribute to understanding the dispersal of hydrogen in the retina and in particular the effect of flow in the vascular retina. It is shown that the predominant features of the process are captured by the simpler model.

Trachoma is an infectious disease and it is the leading cause of preventable blindness worldwide. To achieve its elimination, the World Health Organization set a goal of reducing the prevalence in endemic areas to less than $5$ % by 2020, utilizing the SAFE (surgery, antibiotics, facial cleanliness, environmental improvement) strategy. However, in Burundi, trachoma prevalences of greater than $5$ % are still reported in 11 districts and it is hypothesized that this is due to the poor implementation of the environmental improvement factor of the SAFE strategy. In this paper, a model based on an ordinary differential equation, which includes an environmental transmission component, is developed and analysed. The model is calibrated to recent field data and is used to estimate the reductions in trachoma that would have occurred if adequate environmental improvements were implemented in Burundi. Given the assumptions in the model, it is clear that environmental improvement should be considered as a key component of the SAFE strategy and, hence, it is crucial for eliminating trachoma in Burundi.

The article aims to estimate and forecast the transmissibility of shigellosis and explore the association of meteorological factors with shigellosis. The mathematical model named Susceptible–Exposed–Symptomatic/Asymptomatic–Recovered–Water/Food (SEIARW) was used to explore the feature of shigellosis transmission based on the data of Wuhan City, China, from 2005 to 2017. The study applied effective reproduction number (Reff) to estimate the transmissibility. Daily meteorological data from 2008 to 2017 were used to determine Spearman's correlation with reported new cases and Reff. The SEIARW model fit the data well (χ2 = 0.00046, p > 0.999). The simulation results showed that the reservoir-to-person transmission of the shigellosis route has been interrupted. The Reff would be reduced to a transmission threshold of 1.00 (95% confidence interval (CI) 0.82–1.19) in 2035. Reducing the infectious period to 11.25 days would also decrease the value of Reff to 0.99. There was a significant correlation between new cases of shigellosis and atmospheric pressure, temperature, wind speed and sun hours per day. The correlation coefficients, although statistically significant, were very low (<0.3). In Wuhan, China, the main transmission pattern of shigellosis is person-to-person. Meteorological factors, especially daily atmospheric pressure and temperature, may influence the epidemic of shigellosis.

To uncover the chewing mechanism of Cyrtotrachelus buqueti Guer, a mathematical model was created and a kinematic analysis of its rostrum mouthparts was conducted for, to our knowledge, the first time. To reduce noise and improve the quality of scanning electron micrographs of the weevil's mouthparts, nonlocal means and integral nonlocal means algorithms were proposed. Additionally, based on a comparison and analysis of five classical edge detection algorithms, a multiscale edge detection algorithm based on the B-spline wavelet was used to obtain the boundaries of structural features. The least squares method was used to analyze the data of the mouthparts to fit the mathematical model and fitted curves were obtained using Gaussian equations. The results show that curvature and concave–convex variations of the weevil's mouthparts can highlight fluctuations in friction effects when it chews bamboo shoots, which is helpful in preventing debris from bamboo shoots or other debris from sticking to the mouthpart surfaces. Moreover, this paper highlights the utility of micro-computed tomography (microCT) for three-dimensional (3D) reconstruction and a flowchart is suggested. The reconstructed slices were 9.0 μm thick and an accurate 3D rendered model was obtained from a series of microCT slices. Finally, a real model of the rostrum mouthparts was analyzed using finite-element analysis. The results provide a biological template for the design of a novel bionic drilling mechanism.

The total coronavirus disease (COVID-19) cases caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection have reached 139 million worldwide and nearing 3 million deaths on April 16, 2021. The availability of accurate data is crucial as it makes it possible to analyze correctly the infection trends and make better forecasts. The reported recovered cases for many US states are surprisingly low. This could be due to difficulties in keeping track of recoveries, which resulted in higher numbers for the reported active cases than the actual numbers on the ground. In this work, based on the typical range of recovery rate for COVID-19, we estimate the active data from the total cases and death cases and bring out a correction for the data for all the US states reported on Worldometer.

Predictive adaptive responses (PARs) are a form of developmental plasticity in which the developmental response to an environmental cue experienced early in life is delayed and yet, at the same time, the induced phenotype anticipates (i.e., is completely developed before) exposure to the eventual environmental state predicted by the cue, in which the phenotype is adaptive. We model this sequence of events to discover, under various assumptions concerning the cost of development, what lengths of delay, developmental time, and anticipation are optimal. We find that in many scenarios modeled, development of the induced phenotype should be completed at the exact same time that the environmental exposure relevant to the induced phenotype begins: that is, in contrast to our observed cases of PARs, there should be no anticipation. Moreover, unless slow development is costly, development should commence immediately after the cue: there should be no delay. Thus, PARs, which normally have non-zero delays and/or anticipation, are highly unusual. Importantly, the exceptions to these predictions of zero delays and anticipation occurred when developmental time was fixed and delaying development was increasingly costly. We suggest, therefore, that PARs will only evolve under three kinds of circumstances: (i) there are strong timing constraints on the cue and the environmental status, (ii) delaying development is costly, and development time is either fixed or slow development is costly, or (iii) when the period between the cue and the eventual environmental change is variable and the cost of not completing development before the change is high. These predictions are empirically testable.

Plant shoot gravitropism is a complex phenomenon resulting from gravity sensing, curvature sensing (proprioception), the ability to uphold self-weight and growth. Although recent data analysis and modelling have revealed the detailed morphology of shoot bending, the relative contribution of bending force (derived from the gravi-proprioceptive response) and stretching force (derived from shoot axial growth) behind gravitropism remains poorly understood. To address this gap, we combined morphological data with a theoretical model to analyze shoot bending in wild-type and lazy1-like 1 mutant Arabidopsis thaliana. Using data from actual bending events, we searched for model parameters that minimized discrepancies between the data and mathematical model. The resulting model suggests that both the bending force and the stretching force differ significantly between the wild type and mutant. We discuss the implications of the mechanical forces associated with differential cell growth and present a plausible mechanical explanation of shoot gravitropism.

This study aimed at estimating the transmissibility of hepatitis C. The data for hepatitis C cases were collected in six districts in Xiamen City, China from 2004 to 2018. A population-mixed susceptible-infectious-chronic-recovered (SICR) model was used to fit the data and the parameters of the model were calculated. The basic reproduction number (R0) and the number of newly transmitted cases by a primary case per month (MNI) were adopted to quantitatively assess the transmissibility of hepatitis C virus (HCV). Eleven curve estimation models were employed to predict the trends of R0 and MNI in the city. The SICR model fits the reported HCV data well (P < 0.01). The median R0 of each district in Xiamen is 0.4059. R0 follows the cubic model curve, the compound curve and the power function curve. The median MNI of each district in Xiamen is 0.0020. MNI follows the cubic model curve, the compound curve and the power function curve. The transmissibility of HCV follows a decreasing trend, which reveals that under the current policy for prevention and control, there would be a high feasibility to eliminate the transmission of HCV in the city.

In aquatic microbial systems, high-magnitude variations in abundance, such as sudden blooms alternating with comparatively long periods of very low abundance (“apparent disappearance”), are relatively common. We suggest that in order for this to occur, such variations in abundance in microbial systems and, in particular, the apparent disappearance of species do not require seasonal or periodic forcing of any kind or external factors of any other nature. Instead, such variations can be caused by internal factors and, in particular, by bacteria–phage interaction. Specifically, we suggest that the variations in abundance and the apparent disappearance phenomenon can be a result of phage infection and the lysis of infected bacteria. To illustrate this idea, we consider a reasonably simple mathematical model of bacteria–phage interaction based on the model suggested by Beretta and Kuang, which assumes neither periodic forcing nor action of other external factors. The model admits a loss of stability via Andronov–Hopf bifurcation and exhibits dynamics which explains the phenomenon. These properties of the model are especially distinctive for spatially nonhomogeneous biosystems as well as biosystems with some sort of cooperation or community effects.

Feathers play a critical role in thermoregulation and directly influence poultry production. Poor feathering adversely affects living appearance and carcass quality, thus reducing profits. However, producers tend to ignore the importance of feather development and do not know the laws of feather growth and development. The objective of this study was to fit growth curves to describe the growth and development of feathers in yellow-feathered broilers during the embryonic and posthatching periods using different nonlinear functions (Gompertz, logistic and Bertalanffy). Feather mass and length were determined during the embryonic development and posthatching stages to identify which growth model most accurately described the feather growth pattern. The results showed that chick embryos began to grow feathers at approximately embryonic (E) day 10, and the feathers grew rapidly from E13 to E17. There was little change from E17 to the day of hatching (DOH). During the embryonic period, the Gompertz function (Y = 798.48e−203 431exp(−0.87t), Akaike’s information criterion (AIC) = −0.950 × 103, Bayesian information criterion (BIC) = −0.711 × 103 and mean square error (MSE) = 559.308) provided the best fit for the feather growth curve compared with the other two functions. After hatching, feather mass and length changed little from the DOH to day (D) 14, increased rapidly from D21 to D91 and then grew slowly after D91. The first stage of feather molting occurred from 2 to 3 weeks of age when the down feathers were mostly shed and replaced with juvenile feathers, and the second stage occurred at approximately 13 to 15 weeks of age. The three nonlinear functions could overall fit the feather growth curve well, but the Bertalanffy model (Y = 116.88 × (1−0.86e−0.02t)3, AIC = 1.065 × 105, BIC = 1.077 × 105 and MSE = 11.308) showed the highest degree of fit among the models. Therefore, the Gompertz model exhibited the best goodness of fit for the feather growth curve during the embryonic development, while the Bertalanffy model was the most suitable model due to its accurate ability to predict the growth and development of feathers during the growth period, which is an important commercial characteristic of yellow-feathered chickens.

Hand, foot and mouth disease (HFMD) has spread widely and leads to high disease burden in many countries. However, relative transmissibility from male to female individuals remains unclear. HFMD surveillance database was built in Shenzhen City from 2013 to 2017. An intersex transmission susceptible–infectious–recovered model was developed to calculate the transmission relative rate among male individuals, among female individuals, from male to female and from female to male. Two indicators, ratio of transmission relative rate (Rβ) and relative transmissibility index (RTI), were developed to assess the relative transmissibility of male vs. female. During the study period, 270 347 HFMD cases were reported in the city, among which 16 were death cases with a fatality of 0.0059%. Reported incidence of total cases, male cases and female cases was 0.0057 (range: 0.0036–0.0058), 0.0052 (range: 0.0032–0.0053) and 0.0044 (range: 0.0026–0.0047), respectively. The difference was statistically significant between male and female (t = 3.046, P = 0.002). Rβ of male vs. female, female vs. female, from female to male vs. female and from male to female vs. female was 7.69, 1.00, 1.74 and 7.13, respectively. RTI of male vs. female, female vs. female, from female to male vs. female and from male to female vs. female was 3.08, 1.00, 1.88 and 1.43, respectively. Transmissibility of HFMD is different between male and female individuals. Male cases seem to be more transmissible than female.

Chickenpox is a common acute and highly contagious disease in childhood; moreover, there is currently no targeted treatment. Carrying out an early warning on chickenpox plays an important role in taking targeted measures in advance as well as preventing the outbreak of the disease. In recent years, the infectious disease dynamic model has been widely used in the research of various infectious diseases. The logistic differential equation model can well demonstrate the epidemic characteristics of epidemic outbreaks, gives the point at which the early epidemic rate changes from slow to fast. Therefore, our study aims to use the logistic differential equation model to explore the epidemic characteristics and early-warning time of varicella. Meanwhile, the data of varicella cases were collected from first week of 2008 to 52nd week of 2017 in Changsha. Finally, our study found that the logistic model can be well fitted with varicella data, besides the model illustrated that there are two peaks of varicella at each year in Changsha City. One is the peak in summer–autumn corresponding to the 8th–38th week; the other is in winter–spring corresponding to the time from the 38th to the seventh week next year. The ‘epidemic acceleration week’ average value of summer–autumn and winter–spring are about the 16th week (ranging from the 15th to 17th week) and 45th week (ranging from the 44th to 47th week), respectively. What is more, taking warning measures during the acceleration week, the preventive effect will be delayed; thus, we recommend intervene during recommended warning weeks which are the 15th and 44th weeks instead.