Estimating the effective reproduction number of COVID-19 from population-wide wastewater data: An application in Kagawa, Japan

Although epidemiological surveillance of COVID-19 has been gradually downgraded globally, the transmission of COVID-19 continues. It is critical to quantify the transmission dynamics of COVID-19 using multiple datasets including wastewater virus concentration data. Herein, we propose a comprehensive method for estimating the effective reproduction number using wastewater data. The wastewater virus concentration data, which were collected twice a week, were analyzed using daily COVID-19 incidence data obtained from Takamatsu, Japan between January 2022 and September 2022. We estimated the shedding load distribution (SLD) as a function of time since the date of infection, using a model employing the delay distribution, which is assumed to follow a gamma distribution, multiplied by a scaling factor. We also examined models that accounted for the temporal smoothness of viral load measurement data. The model that smoothed temporal patterns of viral load was the best fit model (WAIC = 2795.8), which yielded a mean estimated distribution of SLD of 3.46 days (95% CrI: 3.01-3.95 days). Using this SLD, we reconstructed the daily incidence, which enabled computation of the effective reproduction number. Using the best fit posterior draws of parameters directly, or as a prior distribution for subsequent analyses, we first used a model that assumed temporal smoothness of viral load concentrations in wastewater, as well as infection counts by date of infection. In the subsequent approach, we examined models that also incorporated weekly reported case counts as a proxy for weekly incidence reporting. Both approaches enabled estimations of the epidemic curve as well as the effective reproduction number from twice-weekly wastewater viral load data. Adding weekly case count data reduced the uncertainty of the effective reproduction number. We conclude that wastewater data are still a valuable source of information for inferring the transmission dynamics of COVID-19, and that inferential performance is enhanced when those data are combined with weekly incidence data.

Establishing a Multi-Vial Design Space for the Freeze-Drying Process by Means of Mathematical Modeling of the Primary Drying Stage

Primary drying is the most critical stage of the freeze-drying process. This work aimed to establish a design space for this process by means of mathematical modeling of the primary drying stage, capable of addressing the thermal characteristics of distinct vial suppliers. Modeling of primary drying was implemented on Microsoft Excel using steady-state heat and mass transfer equations at two extreme conditions as assessed by risk analysis, to predict product temperature and primary-drying time. The heat transfer coefficients (Kv) of four different vial suppliers were experimentally determined, both, at the center and edge of the freeze-dryer's shelf. Statistically significant differences (ANOVA p<0.05) were observed between suppliers throughout the assessed pressure range. Overall, the average Kve/Kvc (edge/center) ratio was higher than 1.6 for all suppliers due to the radiation effect. A design space for the drying process was established using mathematical modeling taking into account the Kv of the worst-case supplier, in the shelf edge. A primary drying cycle was carried out at a shelf temperature of -25 °C and a chamber pressure of 45 mTorr for 8 % sucrose and at -10 °C and 75 mTorr for 5 % NaCl. Freeze-dried products with good cosmetic appearance were obtained for the four vial suppliers both, in the shelf center and edge. The results show that it is possible to predict and establish the critical parameters for the primary drying stage, under a design space concept, considering the differences in the Kv of vial suppliers without adverse consequences on the quality of the finished freeze-dried product.

Forecasting of Indian tourism industry using modeling approach

Currently, India has become one of the largest economies of the world in which tourism and hospitality have significantly contributed; however, the growth rate of tourism industry has been greatly affected during the COVID-19 pandemic. In this study, we have used the modeling approach to analyze and understand the growth pattern of Indian tourism industry. To achieve this, we consider the data of international tourist arrivals before and after the lockdown. The Dickey-Fuller test, AIC and BIC methods are used to obtain the best fitted model and further, the accuracy of obtained model is also analyzed. Data and forecasting indicate that the weather and public holidays significantly affect the tourism industry.

Bioelectrochemical reactor to manage anthropogenic sulfate pollution for freshwater ecosystems: Mathematical modeling and experimental validation

Anthropogenic sulfate loading into otherwise low-sulfate freshwater systems can cause significant ecological consequences as a biogeochemical stressor. To address this challenge, in situ bioremediation technologies have been developed to leverage naturally occurring microorganisms that transform sulfate into sulfide rather than implementing resource-intensive physio-chemical processes. However, bioremediation technologies often require the supply of electron donors to facilitate biological sulfate reduction. Bioelectrochemical systems (BES) can be an alternative approach for supplying molecular hydrogen as an electron donor for sulfate-reducing bacteria through water electrolysis. Although the fundamental mechanisms behind BESs have been studied, limited research has evaluated the design and operational parameters of treatment systems when developing BESs on a scale relevant to environmental systems. This study aimed to develop an application-based mathematical model to evaluate the performance of BESs across a range of reactor configurations and operational modes. The model was based on sulfate transformation by hydrogenotrophic sulfate-reducing bacteria coupled with the recovery of solid iron sulfide species formed by the oxidative dissolution of dissolved ferrous iron from a stainless steel anode. Sulfate removal closely corresponded to the rate of electrolytic hydrogen production and hydraulic residence time but was less sensitive to specific microbial rate constants. The mathematical model results were compared to experimental data from a pilot-scale BES tested with nonacidic mine drainage as a case study. The close agreement between the mathematical model and the pilot-scale BES experiment highlights the efficacy of using a mathematical model as a tool to develop a conceptual design of a scaled-up treatment system.

A mathematical model for investigation of dry band location on 22 kV bushing with and without RTV coating: Experimental study

As different pollutants are deposited on the high voltage bushings, a dry band forms, which causes a flashover. The bushing's contaminated layer will weaken its insulation and have an impact on its electrical characteristics. The performance of bushings in dry band conditions of various lengths was investigated in this proposed piece of work, and a dynamic arc model is presented for the arc process in polluted bushings. It shows satisfactory performance in modelling the arc variables for various dry band positions. The developed dynamic open model for contaminated bushings with and without RTV coating predicted the flashover voltage and dry band positions. Any type of contamination, such as sea salt, road salt, and industrial pollutants prevalent in several sites, can be studied using the established model. Ultimately, it was discovered that there was good agreement between the model's results and the outcomes of the experiments. •Mathematical modeling of 22 kV bushing is conceded out for diverse polluted dry band location at lead-in, lead-out and middle region of bushing surface.•Dynamic arc modeling involved in bushing flashover process for different dry band location is done and flashover voltage is predicted•Experimental work is carried out to find FOV for the bushing with different dry location and compared with predicted FOV.

Modelling of tuberculosis dynamics incorporating indirect transmission of contaminated environment and infectivity of smear-negative individuals: A case study for Xinjiang, China

Xinjiang has been one of the high incidence areas of pulmonary tuberculosis (PTB) in China. Besides being infected by direct contacting with active PTB individuals (direct infection), the susceptible would be infected because of the exposure to the environment contaminated by Mycobacterium tuberculosis (indirect infection). Active PTB individuals include not only the smear-positive PTB (PTB+) but also the smear-negative PTB (PTB-) who are infectious due to their ability to release tiny Mycobacterium tuberculosis particles even in the absence of visible Mycobacterium tuberculosis in sputum. By taking account of direct/indirect infection and the difference between PTB+ and PTB- individuals in transmission capability, a periodic dynamical PTB transmission model is proposed. The model is fitted to the newly monthly PTB+ and PTB- cases in Xinjiang from 2008 to 2017 by Markov Chain Monte Carlo algorithm. Moreover, global sensitivity analysis is constructed to address the uncertainty of some key parameters by using Latin hypercube sampling and partial rank correlation coefficient methods. Basic reproduction number R0 for PTB transmission in Xinjiang is estimated to be 2.447 (95% CrI:(1.203, 3.844)), indicating that PTB has been prevalent in Xinjiang over the study period. Our results suggest that reducing the direct/indirect transmission rates, early screening, isolating and treating the latent, PTB+ and PTB- individuals, and enhancing the clearance of Mycobacterium tuberculosis in the environment could more effectively control PTB transmission in Xinjiang. The model fits the reported PTB data well and achieves acceptable prediction accuracy. We believe that our model can provide heuristic support for controlling PTB transmission in Xinjiang.

Modelling the preventive treatment under media impact on tuberculosis: A comparison in four regions of China

Preventive treatment for people with latent Tuberculosis infection (LTBI) has aroused our great interest. In this paper, we propose and analyze a novel mathematical model of TB considering preventive treatment with media impact. The basic reproduction number R 0 is defined by the next generation matrix method. In the case without media impact, we prove that the disease-free equilibrium is globally asymptotically stable (unstable) if R 0 < 1 ( R 0 > 1 ) . Furthermore, we obtain that a unique endemic equilibrium exists when R 0 > 1 , which is globally asymptotically stable in the case of permanent immunity and no media impact. We fit the model to the newly reported TB cases data from 2009 to 2019 of four regions in China and estimate the parameters. And we estimated R 0 = 0.5013 < 1 in Hubei indicating that TB in Hubei will be eliminated in the future. However, the estimated R 0 = 1.015 > 1 in Henan, R 0 = 1.282 > 1 in Jiangxi and R 0 = 1.930 > 1 in Xinjiang imply that TB will continue to persist in these three regions without further prevention and control measures. Besides, sensitivity analysis is carried out to illustrate the role of model parameters for TB control. Our finding reveals that appropriately improving the rate of timely treatment for actively infected people and increasing the rate of individuals with LTBI seeking preventive treatment could achieve the goal of TB elimination. In addition, another interesting finding shows that media impact can only reduce the number of active infections to a limited extent, but cannot change the prevalence of TB.

Mathematical model of rabies vaccination in the United States

Rabies is one of the oldest viral diseases and it has been present on every continent except Antarctica. Within the U.S. human rabies cases are quite rare. In the eastern USA, raccoons are the main reservoir hosts and pet vaccination serves as an important barrier against human rabies exposure. In this paper, we develop a compartmental model for rabies transmission amongst raccoons and domestic pets. We find the disease-free equilibria, reproduction numbers for the raccoons and domestic pets. We also determine the vaccination coverage/rates, both for raccoons and pets, needed to achieve the elimination of rabies.

A clock and wavefront self-organizing model recreates the dynamics of mouse somitogenesis in-vivo and in-vitro

During mouse development, presomitic mesoderm cells synchronize Wnt and Notch oscillations, creating sequential phase waves that pattern somites. Traditional somitogenesis models attribute phase waves to a global modulation of the oscillation frequency. However, increasing evidence suggests that they could arise in a self-organizing manner. Here, we introduce the Sevilletor, a novel reaction-diffusion system that serves as a framework to compare different somitogenesis patterning hypotheses. Using this framework, we propose the Clock and Wavefront Self-Organizing model that considers an excitable self-organizing region where phase waves form independent of global frequency gradients. The model recapitulates the change in relative phase of Wnt and Notch observed during mouse somitogenesis and provides a theoretical basis for understanding the excitability of mouse presomitic mesoderm cells in-vitro.

Modeling Zinc Absorption in the Adult Population of Colombia: Insights for Nutritional Evaluation and Intervention Strategies

Zinc is a vital trace element, yet its deficiency is common in various populations. This study addresses the gap in understanding zinc intake and its relationship with key nutritional parameters in a Colombian population. We analyzed data from 12,987 individuals, focusing on the daily intake of zinc, phytate, protein, and calcium, and used the phytate/zinc molar ratio as an input parameter in the Miller et al. (2013) model. This model was employed to estimate the total absorbed zinc (TAZ) and the fractional absorption of zinc (FAZ). Our findings highlight a general trend towards insufficient intake compared to the standards of the Institute of Medicine (IOM) and Colombia, with a significant percentage of the population falling below the estimated average requirement (EAR) and recommended daily allowance (RDA) for zinc, underscoring the need for targeted nutritional strategies. Our study contributes to a broader understanding of zinc nutrition and public health implications in Colombia, providing a basis for future dietary guidelines and health interventions.

Simple mathematical model for predicting COVID-19 outbreaks in Japan based on epidemic waves with a cyclical trend

BACKGROUND

Several models have been used to predict outbreaks during the COVID-19 pandemic, with limited success. We developed a simple mathematical model to accurately predict future epidemic waves.

METHODS

We used data from the Ministry of Health, Labour and Welfare of Japan for newly confirmed COVID-19 cases. COVID-19 case data were summarized as weekly data, and epidemic waves were visualized and identified. The periodicity of COVID-19 in each prefecture of Japan was confirmed using time-series analysis and the autocorrelation coefficient, which was used to investigate the longer-term pattern of COVID-19 cases. Outcomes using the autocorrelation coefficient were visualized via a correlogram to capture the periodicity of the data. An algorithm for a simple prediction model of the seventh COVID-19 wave in Japan comprised three steps. Step 1: machine learning techniques were used to depict the regression lines for each epidemic wave, denoting the "rising trend line"; Step 2: an exponential function with good fit was identified from data of rising straight lines up to the sixth wave, and the timing of the rise of the seventh wave and speed of its spread were calculated; Step 3: a logistic function was created using the values calculated in Step 2 as coefficients to predict the seventh wave. The accuracy of the model in predicting the seventh wave was confirmed using data up to the sixth wave.

RESULTS

Up to March 31, 2023, the correlation coefficient value was approximately 0.5, indicating significant periodicity. The spread of COVID-19 in Japan was repeated in a cycle of approximately 140 days. Although there was a slight lag in the starting and peak times in our predicted seventh wave compared with the actual epidemic, our developed prediction model had a fairly high degree of accuracy.

CONCLUSION

Our newly developed prediction model based on the rising trend line could predict COVID-19 outbreaks up to a few months in advance with high accuracy. The findings of the present study warrant further investigation regarding application to emerging infectious diseases other than COVID-19 in which the epidemic wave has high periodicity.

Modeling of liquid-liquid hollow fiber supported membrane equilibrium including the non-ideality of the aqueous and organic phases in the recovery systems of radionuclides in sulphate-halide/aliquat-336 in O-xylene

Study of modeling of L/LHFSLM equilibrium based on the Non-ideality of the Aqueous and Organic Phases in the Recovery of 152+154Eu in H2SO4-Halides/Aliquat-336 in 20% kerosene as feeding phase at pH 3.78-4.55, by the ratio 89.7%,while separation of 90Sr and 134Cs there was a problem between them by using hollow HFSLM only, the reason for that the organic solvents affect the rate of reaction in the Diamino-1,2-cyclohexane/tetraacetic acid (DCTA) as stripping phase concentration from 0.15 to 0.55 mol/L. The system has been developed; this led to the extraction of elements in the same time. The Matlab software program was introduced to obtain some mathematical parameters like, standard deviation (SD), equilibrium constant Kex and standard deviation coefficient (SDC).

Solid phase microextraction device coupled with miniature mass spectrometry and mathematical model of its ion chronogram

Modern solid phase microextraction (SPME) device linked with mass spectrometry (SPME-MS) has evolved from producing ion chronogram as flat noisy signal to as unimodal-like signal. We designed a SPME device, which is closer in morphology to LC column, linked it with a miniature mass spectrometer (SPME-Mini MS), and proposed a mathematical model that elution of compound from the SPME device is equivalent to overlay of elution of the compound from the infinite LC columns with the lengths between 0 and the length of the device and it can generate an ion chronogram as right-skew unimodal signal. Rhodamine B as analyte was used for experimental verification and its unimodal signal was used to fit the parameters of a computer simulation program based on the model. The experimental results and simulations empirically cross-confirmed that SPME-Mini MS can generate ion chronogram as clean right-skew unimodal signal. Furthermore, the SPME-Mini MS system was used for quantitative analysis of psychotropic drugs (i.e. risperidone and aripiprazole) in artificial urine. The results preliminarily demonstrated that the system can utilize area under unimodal signal for quantitative analysis and has potential to be applied for on-site, fast and accurate quantification of drugs and other compounds.

Quantifiable identification of flow-limited ventilator dyssynchrony with the deformed lung ventilator model

BACKGROUND

Ventilator dyssynchrony (VD) can worsen lung injury and is challenging to detect and quantify due to the complex variability in the dyssynchronous breaths. While machine learning (ML) approaches are useful for automating VD detection from the ventilator waveform data, scalable severity quantification and its association with pathogenesis and ventilator mechanics remain challenging.

OBJECTIVE

We develop a systematic framework to quantify pathophysiological features observed in ventilator waveform signals such that they can be used to create feature-based severity stratification of VD breaths.

METHODS

A mathematical model was developed to represent the pressure and volume waveforms of individual breaths in a feature-based parametric form. Model estimates of respiratory effort strength were used to assess the severity of flow-limited (FL)-VD breaths compared to normal breaths. A total of 93,007 breath waveforms from 13 patients were analyzed.

RESULTS

A novel model-defined continuous severity marker was developed and used to estimate breath phenotypes of FL-VD breaths. The phenotypes had a predictive accuracy of over 97% with respect to the previously developed ML-VD identification algorithm. To understand the incidence of FL-VD breaths and their association with the patient state, these phenotypes were further successfully correlated with ventilator-measured parameters and electronic health records.

CONCLUSION

This work provides a computational pipeline to identify and quantify the severity of FL-VD breaths and paves the way for a large-scale study of VD causes and effects. This approach has direct application to clinical practice and in meaningful knowledge extraction from the ventilator waveform data.

Study on heat transfer law of moving temperature variable gas in thermoacoustic plate stack

Taking gas and the heat transfer process between gas and plate as the research object, the mathematical model of heat transfer in one working cycle by moving variable temperature air mass under the action of sound field is established, which provides a new idea for understanding thermoacoustic effect. The influence factors in the model are analyzed and it is found that the amplitude of the air mass has a significant influence on the heat transfer, and the heat transfer of the air mass in one working cycle is proportional to the square of the amplitude. In a certain working environment, the thermoacoustic refrigerator has a critical operating frequency, and only when the operating frequency is greater than the critical frequency can refrigeration be realized. The critical operating frequency is independent of the amplitude and increases with the increase of the stack temperature gradient. With the pressure belly point as the reference position, the greater the distance from the reference position, the greater the critical operating frequency. On this basis, the idea of short plate overlapping is put forward and the formation mechanism of temperature difference between two ends of plate overlapping is explained.

An analysis of the effects of chronic low dose-rate radiation exposure on cancer focusing on the differences among cancer types

PURPOSE

The effect of chronic low dose-rate radiation exposure on cancers was investigated by analyzing the data of mice experiments conducted at the Institute for Environmental Sciences (IES). This analysis focuses on the differences between malignant lymphomas and solid cancers.

MATERIALS AND METHODS

The analysis is conducted based on the mathematical model introduced in our previous work. The model is expanded to analyze malignant lymphomas and solid cancers separately. Using the expanded model, the effect of chronic low dose-rate radiation on malignant lymphomas and solid cancers are discussed based on their occurrences, progressions, and mortalities.

RESULTS

Non-irradiated control group and 20 mGy/day × 400 days irradiated groups are analyzed. The analysis showed that radiation exposure shortened mean life expectancy for both malignant lymphomas and solid cancers (shorter by 89.6 days for malignant lymphomas and 149.3 days for solid cancers). For malignant lymphomas, both the occurrence and the progression are affected by radiation exposure. The mean age at which malignant lymphoma developed in mice was shortened by 32.7 days and the mean progression period was shortened by 57.3 days. The occurrence of solid cancer is also affected by radiation exposure, wherein the mean age at which solid cancer develops was shortened by 147.9 days. However, no significant change in progression period of solid cancers was seen in the analysis.

CONCLUSIONS

The analysis showed that the occurrence and mean lifespan are affected in both malignant lymphomas and solid cancers. The shortening of the progression period is only seen in malignant lymphoma, no significant change was observed in solid cancers.

Investigating the synergistic effects of immunotherapy and normalization treatment in modulating tumor microenvironment and enhancing treatment efficacy

We developed a comprehensive mathematical model of cancer immunotherapy that takes into account: i) Immune checkpoint blockers (ICBs) and the interactions between cancer cells and the immune system, ii) characteristics of the tumor microenvironment, such as the tumor hydraulic conductivity, interstitial fluid pressure, and vascular permeability, iii) spatial and temporal variations of the modeled components within the tumor and the surrounding host tissue, iv) the transport of modeled components through the vasculature and between the tumor-host tissue with convection and diffusion, and v) modeling of the tumor draining lymph nodes were the antigen presentation and the development of cytotoxic immune cells take place. Our model successfully reproduced experimental data from various murine tumor types and predicted immune system profiling, which is challenging to achieve experimentally. It showed that combination of ICB therapy and normalization treatments, that aim to improve tumor perfusion, decreases interstitial fluid pressure and increases the concentration of both innate and adaptive immune cells at the tumor center rather than the periphery. Furthermore, using the model, we investigated the impact of modeled components on treatment outcomes. The analysis found that the number of functional vessels inside the tumor region and the ICB dose administered have the largest impact on treatment outcomes.

A methodology for estimating SARS-CoV-2 importation risk by air travel into Canada between July and November 2021

BACKGROUND

Estimating rates of disease importation by travellers is a key activity to assess both the risk to a country from an infectious disease emerging elsewhere in the world and the effectiveness of border measures. We describe a model used to estimate the number of travellers infected with SARS-CoV-2 into Canadian airports in 2021, and assess the impact of pre-departure testing requirements on importation risk.

METHODS

A mathematical model estimated the number of essential and non-essential air travellers infected with SARS-CoV-2, with the latter requiring a negative pre-departure test result. The number of travellers arriving infected (i.e. imported cases) depended on air travel volumes, SARS-CoV-2 exposure risk in the departure country, prior infection or vaccine acquired immunity, and, for non-essential travellers, screening from pre-departure molecular testing. Importation risk was estimated weekly from July to November 2021 as the number of imported cases and percent positivity (PP; i.e. imported cases normalised by travel volume). The impact of pre-departure testing was assessed by comparing three scenarios: baseline (pre-departure testing of all non-essential travellers; most probable importation risk given the pre-departure testing requirements), counterfactual scenario 1 (no pre-departure testing of fully vaccinated non-essential travellers), and counterfactual scenario 2 (no pre-departure testing of non-essential travellers).

RESULTS

In the baseline scenario, weekly imported cases and PP varied over time, ranging from 145 to 539 cases and 0.15 to 0.28%, respectively. Most cases arrived from the USA, Mexico, the United Kingdom, and France. While modelling suggested that essential travellers had a higher weekly PP (0.37 - 0.65%) than non-essential travellers (0.12 - 0.24%), they contributed fewer weekly cases (62 - 154) than non-essential travellers (84 - 398 per week) given their lower travel volume. Pre-departure testing was estimated to reduce imported cases by one third (counterfactual scenario 1) to one half (counterfactual scenario 2).

CONCLUSIONS

The model results highlighted the weekly variation in importation by traveller group (e.g., reason for travel and country of departure) and enabled a framework for measuring the impact of pre-departure testing requirements. Quantifying the contributors of importation risk through mathematical simulation can support the design of appropriate public health policy on border measures.

Integrated drying model of lychee as a function of temperature and relative humidity

Drying is a universal method applied for food preservation. To date, several models have been developed to evaluate drying kinetics. In this study, lychee was dried employing a hot air dryer, and the drying kinetics was evaluated by comparing the Newtonian model, Henderson and Pabis model, Page model, and Logarithmic model. However, temperature and relative humidity, the key driving forces for drying kinetics, are not considered by these models. Thus, an integrated drying model, as a function of temperature and relative humidity, was developed to predict the hot air-drying kinetics and mass transfer phenomena of lychee followed by the calibration and validation of the model with independent experimental datasets. The model validation consisted of Nash- Sutcliffe model coefficient (E ), coefficient of determination ( R 2 ) and index of agreement ( d ) and all of them were found close to 1 indicating perfect model fit. Besides, the developed model was applied for process optimization and scenario analysis. The drying rate constant was found as a function of temperature and relative humidity that was high at high temperature and low relative humidity. Interestingly, temperature showed a higher effect on the drying rate constant compared to relative humidity. Overall, the present study will open a new window to developing further drying model of lychee to optimize quality its quality parameters.

A deep learning-based approach for predicting COVID-19 diagnosis

This paper focuses on forecasting the total count of confirmed COVID-19 cases in Saudi Arabia through a range of methodologies, including ARIMA, mathematical modeling, and deep learning network (DQN) techniques. Its primary aim is to anticipate the verified COVID-19 cases in Saudi Arabia, aiding in decision-making for life-saving interventions by enhancing awareness of COVID-19 infection. Mathematical modeling and ARIMA are employed for their efficacy in forecasting, while DQN approaches, particularly through comparative analysis, are utilized for prediction. This comparative analysis evaluates the predictive capacities of ARIMA, mathematical modeling, and DQN techniques, aiming to pinpoint the most reliable method for forecasting positive COVID-19 cases. The modeling encompasses COVID-19 cases in Saudi Arabia, the United Kingdom (UK), and Tunisia (TU) spanning from 2020 to 2021. Predicting the number of individuals likely to test positive for COVID-19 poses a challenge, requiring adherence to fundamental assumptions in mathematical and ARIMA projections. The proposed methodology was implemented on a local server. The DQN algorithm formulates a reward function to uphold target functional performance while balancing training and testing periods. The findings indicate that DQN technology surpasses conventional approaches in efficiency and accuracy for predictions.

COVID-19 inequalities in England: a mathematical modelling study of transmission risk and clinical vulnerability by socioeconomic status

BACKGROUND

The COVID-19 pandemic resulted in major inequalities in infection and disease burden between areas of varying socioeconomic deprivation in many countries, including England. Areas of higher deprivation tend to have a different population structure-generally younger-which can increase viral transmission due to higher contact rates in school-going children and working-age adults. Higher deprivation is also associated with a higher presence of chronic comorbidities, which were convincingly demonstrated to be risk factors for severe COVID-19 disease. These two major factors need to be combined to better understand and quantify their relative importance in the observed COVID-19 inequalities.

METHODS

We used UK Census data on health status and demography stratified by decile of the Index of Multiple Deprivation (IMD), which is a measure of socioeconomic deprivation. We calculated epidemiological impact using an age-stratified COVID-19 transmission model, which incorporated different contact patterns and clinical health profiles by decile. To separate the contribution of each factor, we considered a scenario where the clinical health profile of all deciles was at the level of the least deprived. We also considered the effectiveness of school closures and vaccination of over 65-year-olds in each decile.

RESULTS

In the modelled epidemics in urban areas, the most deprived decile experienced 9% more infections, 13% more clinical cases, and a 97% larger peak clinical size than the least deprived; we found similar inequalities in rural areas. Twenty-one per cent of clinical cases and 16% of deaths in England observed under the model assumptions would not occur if all deciles experienced the clinical health profile of the least deprived decile. We found that more deaths were prevented in more affluent areas during school closures and vaccination rollouts.

CONCLUSIONS

This study demonstrates that both clinical and demographic factors synergise to generate health inequalities in COVID-19, that improving the clinical health profile of populations would increase health equity, and that some interventions can increase health inequalities.

A two-phase thin-film model for cell-induced gel contraction incorporating osmotic effects

We present a mathematical model of an experiment in which cells are cultured within a gel, which in turn floats freely within a liquid nutrient medium. Traction forces exerted by the cells on the gel cause it to contract over time, giving a measure of the strength of these forces. Building upon our previous work (Reoch et al. in J Math Biol 84(5):31, 2022), we exploit the fact that the gels used frequently have a thin geometry to obtain a reduced model for the behaviour of a thin, two-dimensional cell-seeded gel. We find that steady-state solutions of the reduced model require the cell density and volume fraction of polymer in the gel to be spatially uniform, while the gel height may vary spatially. If we further assume that all three of these variables are initially spatially uniform, this continues for all time and the thin film model can be further reduced to solving a single, non-linear ODE for gel height as a function of time. The thin film model is further investigated for both spatially-uniform and varying initial conditions, using a combination of analytical techniques and numerical simulations. We show that a number of qualitatively different behaviours are possible, depending on the composition of the gel (i.e., the chemical potentials) and the strength of the cell traction forces. However, unlike in the earlier one-dimensional model, we do not observe cases where the gel oscillates between swelling and contraction. For the case of initially uniform cell and gel density, our model predicts that the relative change in the gels' height and length are equal, which justifies an assumption previously used in the work of Stevenson et al. (Biophys J 99(1):19-28, 2010). Conversely, however, even for non-uniform initial conditions, we do not observe cases where the length of the gel changes whilst its height remains constant, which have been reported in another model of osmotic swelling by Trinschek et al. (AIMS Mater Sci 3(3):1138-1159, 2016; Phys Rev Lett 119:078003, 2017).

A continuum model for the elongation and orientation of Von Willebrand factor with applications in arterial flow

The blood protein Von Willebrand factor (VWF) is critical in facilitating arterial thrombosis. At pathologically high shear rates, the protein unfolds and binds to the arterial wall, enabling the rapid deposition of platelets from the blood. We present a novel continuum model for VWF dynamics in flow based on a modified viscoelastic fluid model that incorporates a single constitutive relation to describe the propensity of VWF to unfold as a function of the scalar shear rate. Using experimental data of VWF unfolding in pure shear flow, we fix the parameters for VWF's unfolding propensity and the maximum VWF length, so that the protein is half unfolded at a shear rate of approximately 5000 s - 1 . We then use the theoretical model to predict VWF's behaviour in two complex flows where experimental data are challenging to obtain: pure elongational flow and stenotic arterial flow. In pure elongational flow, our model predicts that VWF is 50% unfolded at approximately 2000 s - 1 , matching the established hypothesis that VWF unfolds at lower shear rates in elongational flow than in shear flow. We demonstrate the sensitivity of this elongational flow prediction to the value of maximum VWF length used in the model, which varies significantly across experimental studies, predicting that VWF can unfold between 2000 and 3200 s - 1 depending on the selected value. Finally, we examine VWF dynamics in a range of idealised arterial stenoses, predicting the relative extension of VWF in elongational flow structures in the centre of the artery compared to high shear regions near the arterial walls.

Kinetics and regulation of coagulation factor X activation by intrinsic tenase on phospholipid membranes

BACKGROUND

Factor X activation by the phospholipid-bound intrinsic tenase complex is a critical membrane-dependent reaction of blood coagulation. Its regulation mechanisms are unclear, and a number of questions regarding diffusional limitation, pathways of assembly and substrate delivery remain open.

METHODS

We develop and analyze here a detailed mechanism-driven computer model of intrinsic tenase on phospholipid surfaces. Three-dimensional reaction-diffusion-advection and stochastic simulations were used where appropriate.

RESULTS

Dynamics of the system was predominantly non-stationary under physiological conditions. In order to describe experimental data, we had to assume both membrane-dependent and solution-dependent delivery of the substrate. The former pathway dominated at low cofactor concentration, while the latter became important at low phospholipid concentration. Factor VIIIa-factor X complex formation was the major pathway of the complex assembly, and the model predicted high affinity for their lipid-dependent interaction. Although the model predicted formation of the diffusion-limited layer of substrate for some conditions, the effects of this limitation on the fXa production were small. Flow accelerated fXa production in a flow reactor model by bringing in fIXa and fVIIIa rather than fX.

CONCLUSIONS

This analysis suggests a concept of intrinsic tenase that is non-stationary, employs several pathways of substrate delivery depending on the conditions, and is not particularly limited by diffusion of the substrate.

Kill rates by immune cells: Ratio-dependent, or mass action?

We describe a cell-based fixed-lattice model to simulate immune cell and tumor cell interaction involving MHC recognition, and FasL vs perforin lysis. We are motivated by open questions about the mechanisms behind observed kill rates of tumor cells by different types of effector cells. These mechanisms play a big role in the effectiveness of many cancer immunotherapies. The model is a stochastic cellular automaton on a hexagonal grid.

The effects of spatially-constrained treatment regions upon a model of wombat mange

The use of therapeutic agents is a critical option to manage wildlife disease, but their implementation is usually spatially constrained. We seek to expand knowledge around the effectiveness of management of environmentally-transmitted Sarcoptes scabiei on a host population, by studying the effect of a spatially constrained treatment regime on disease dynamics in the bare-nosed wombat Vombatus ursinus. A host population of wombats is modelled using a system of non-linear partial differential equations, a spatially-varying treatment regime is applied to this population and the dynamics are studied over a period of several years. Treatment could result in mite decrease within the treatment region, extending to a lesser degree outside, with significant increases in wombat population. However, the benefits of targeted treatment regions within an environment are shown to be dependent on conditions at the start (endemic vs. disease free), as well as on the locations of these special regions (centre of the wombat population or against a geographical boundary). This research demonstrates the importance of understanding the state of the environment and populations before treatment commences, the effects of re-treatment schedules within the treatment region, and the transient large-scale changes in mite numbers that can be brought about by sudden changes to the environment. It also demonstrates that, with good knowledge of the host-pathogen dynamics and the spatial terrain, it is possible to achieve substantial reduction in mite numbers within the target region, with increases in wombat numbers throughout the environment.

Modulating autophagy to treat diseases: A revisited review on in silico methods

BACKGROUND

Autophagy refers to the conserved cellular catabolic process relevant to lysosome activity and plays a vital role in maintaining the dynamic equilibrium of intracellular matter by degrading harmful and abnormally accumulated cellular components. Accumulating evidence has recently revealed that dysregulation of autophagy by genetic and exogenous interventions may disrupt cellular homeostasis in human diseases. In silico approaches as powerful aids to experiments have also been extensively reported to play their critical roles in the storage, prediction, and analysis of massive amounts of experimental data. Thus, modulating autophagy to treat diseases by in silico methods would be anticipated.

AIM OF REVIEW

Here, we focus on summarizing the updated in silico approaches including databases, systems biology network approaches, omics-based analyses, mathematical models, and artificial intelligence (AI) methods that sought to modulate autophagy for potential therapeutic purposes, which will provide a new insight into more promising therapeutic strategies.

KEY SCIENTIFIC CONCEPTS OF REVIEW

Autophagy-related databases are the data basis of the in silico method, storing a large amount of information about DNA, RNA, proteins, small molecules and diseases. The systems biology approach is a method to systematically study the interrelationships among biological processes including autophagy from a macroscopic perspective. Omics-based analyses are based on high-throughput data to analyze gene expression at different levels of biological processes involving autophagy. mathematical models are visualization methods to describe the dynamic process of autophagy, and its accuracy is related to the selection of parameters. AI methods use big data related to autophagy to predict autophagy targets, design targeted small molecules, and classify diverse human diseases for potential therapeutic applications.

Application of a mathematical model to clarify the statistical characteristics of a pan-tissue DNA methylation clock

DNA methylation clocks estimate biological age based on DNA methylation profiles. This study developed a mathematical model to describe DNA methylation aging and the establishment of a pan-tissue DNA methylation clock. The model simulates the aging dynamics of DNA methylation profiles based on passive demethylation as well as the process of cross-sectional bulk data acquisition. As a result, this study identified two conditions under which the pan-tissue DNA methylation clock can successfully predict biological age: one condition is that the target tissues are sufficiently well represented in the training dataset, and the other condition is that the target sample contains cell subsets that are common among different tissues. When either of these conditions is met, the clock performs well. It is also suggested that the epigenetic age of all samples in the target tissue tends to be either over or underestimated when biological age prediction fails. The model can reveal the statistical characteristics of DNA methylation clocks.

Sensory omics combined with mathematical modeling for integrated analysis of retronasal Muscat flavor in table grapes

This study focused on analyzing the aroma formation mechanism of retronasal muscat flavor in table grapes. The sensory characteristics and fragrance components of table grape juice with different intensities of Muscat were investigated using GC-Quadrupole-MS, quantitative descriptive analysis and three-alternate forced choice. Free monoterpenoids were the main contributors to the retronasal Muscat flavor. The contribution of Muscat compounds to this flavor was quantified by Stevens coefficient, the most and the least sensitive compounds to concentration changes were citronellol and linalool, respectively. To predict the Muscat flavor intensity by mathematical modeling, established a model between Muscat flavor intensity and monoterpenoids concentration, and an optimal partial least squares regression model with a linear relationship between natural logarithms was obtained. These findings provide reference for understanding the formation mechanism of specific aromas in fruits and provide a basis for the development and quality control of processed products such as Muscat flavor grape juice.

Sialic Acid Mediated Endothelial and Hepatic Uptake: A Mechanism based Mathematic Model Elucidating the Complex Pharmacokinetics and Pharmacodynamics of Efmarodocokin Alfa, a Variably Glycosylated Fusion Protein

Sialic acid (SA) is crucial for protecting glycoproteins from clearance. Efmarodocokin alfa (IL-22Fc), a fusion protein agonist that links IL-22 to the crystallizable fragment (Fc) of human IgG4, contains 8 N-glycosylation sites and exhibits heterogeneous and variable terminal sialylation biodistribution. This presents a unique challenge for Pharmacokinetic (PK) and Pharmacodynamic (PD) analysis and cross-species translation. In this study, we sought to understand how varying SA levels and heterogeneous distribution contribute to IL-22Fc's complex PKPD properties. We initially used homogenous drug material with varying SA levels to examine PKPD in mice. Population PKPD analysis based on mouse data revealed that SA was a critical covariate simultaneously accounting for the substantial between subject variability (BSV) in clearance (CL), distribution clearance (CLd), and volume of distribution (Vd). In addition to the well-established mechanism by which SA inhibits ASGPR activity, we hypothesized a novel mechanism by which decrease in SA increases the drug uptake by endothelial cells. This decrease in SA, leading to more endothelial uptake, was supported by the neonatal Fc receptor (FcRn) dependent cell-based transcytosis assay. The population analysis also suggested in vivo EC50 (IL-22Fc stimulating Reg3β) was independent on SA, while the in-vitro assay indicated a contradictory finding of SA-in vitro potency relationship. We created a mechanism based mathematical (MBM) PKPD model incorporating the decrease in SA mediated endothelial and hepatic uptake, and successfully characterized the SA influence on IL-22Fc PK, as well as the increased PK exposure being responsible for increased PD. Thereby, the MBM model supported that SA has no direct impact on EC50, aligning with the population PKPD analysis. Subsequently, using the MBM PKPD model, we employed 5 subpopulation simulations to reconstitute the heterogeneity of drug material. The simulation accurately predicted the PKPD of heterogeneously and variably sialylated drug in mouse, monkey and human. The successful prospective validation confirmed the MBM's ability to predict IL-22Fc PK across variable SA levels, homogenous to heterogeneous material, and across species (R2=0.964 for clearance prediction). Our model prediction suggests an average of 1 mol/mol SA increase leads to a 50% increase in drug exposure. This underlines the significance of controlling sialic acid levels during lot-to-lot manufacturing.

Mathematical modeling of optimal coagulant dosage for tofu preparation using MgCl2

To explore the association between the optimal coagulant for tofu and the components of soybeans,30 different kinds of soybeans were selected, and tested for their optimal coagulant MgCl2 content. The optimal amount of coagulant was taken as the dependent variable, and the soybean Composition were taken as independent variables for the correlation analysis. The results showed that there was a positive correlation between the optimal coagulant content and the content of histidine, 7S β-conglycinin, B1aB1bB2B3B4 of 11 s glycincin, and α'-subunit of 7S β-conglycinin, negative correlation with lysine. The regression formula is y = -1.186 + 3.457*B1aB1bB2B3B4 + 2.304*7S + 0.351*histidine - 0.084*lysine + 4.696*α', and the model is validated to be within 10 % of the error value and has a high degree of confidence. This study provides theoretical support for realizing the green production of traditional soybean products.

Review of mathematical models of Neisseria gonorrhoeae vaccine impact: Implications for vaccine development

An effective prophylactic vaccine for prevention of Neisseria gonorrhoeae infection would have a major impact on sexual and reproductive health worldwide. Interest in developing gonorrhoea vaccines is growing due to the reported high rates of N. gonorrhoeae infections globally, and the threat of antimicrobial resistance. Several gonorrhoea vaccine candidates are currently under evaluation and various mathematical models have been used to assess the potential population-level impact a gonorrhoea vaccine may have once available. Here we review key aspects of gonorrhoea vaccine mathematical modelling studies, including model structures, populations considered, and assumptions used as well as vaccine characteristics and implementation scenarios investigated. The predicted vaccine impact varied between studies, ranging from as little as ∼17 % reduction in N. gonorrhoeae prevalence after 30 years up to 100 % reduction after 5 years. However, all studies predicted that even a partially effective gonorrhoea vaccine could have a substantial impact in reducing N. gonorrhoeae prevalence or incidence, particularly when high coverage is achieved within either important risk groups or the overall sexually active population. As expected, higher vaccine efficacy against acquisition of N. gonorrhoeae and longer duration of protection were linked to greater reductions in infections. A vaccine that alters onward transmission could also substantially reduce infections. Several gaps and research needs have been identified by researchers in the field and via this narrative literature review. For example, future modelling to inform gonorrhoea vaccine development and implementation should consider additional populations that are at high risk of N. gonorrhoeae infection, especially in low- and middle-income settings, as well as the impact of vaccination on the potential adverse sexual and reproductive health outcomes of infection. In addition, more detailed and robust epidemiological, biological, and behavioural data is needed to enable more accurate and robust modelling of gonorrhoea vaccine impact to inform future scientific and public health decision-making.

Mathematical model explains differences in Omicron and Delta SARS-CoV-2 dynamics in Caco-2 and Calu-3 cells

Within-host infection dynamics of Omicron dramatically differs from previous variants of SARS-CoV-2. However, little is still known about which parameters of virus-cell interplay contribute to the observed attenuated replication and pathogenicity of Omicron. Mathematical models, often expressed as systems of differential equations, are frequently employed to study the infection dynamics of various viruses. Adopting such models for results of in vitro experiments can be beneficial in a number of aspects, such as model simplification (e.g., the absence of adaptive immune response and innate immunity cells), better measurement accuracy, and the possibility to measure additional data types in comparison with in vivo case. In this study, we consider a refinement of our previously developed and validated model based on a system of integro-differential equations. We fit the model to the experimental data of Omicron and Delta infections in Caco-2 (human intestinal epithelium model) and Calu-3 (lung epithelium model) cell lines. The data include known information on initial conditions, infectious virus titers, and intracellular viral RNA measurements at several time points post-infection. The model accurately explains the experimental data for both variants in both cell lines using only three variant- and cell-line-specific parameters. Namely, the cell entry rate is significantly lower for Omicron, and Omicron triggers a stronger cytokine production rate (i.e., innate immune response) in infected cells, ultimately making uninfected cells resistant to the virus. Notably, differences in only a single parameter (e.g., cell entry rate) are insufficient to obtain a reliable model fit for the experimental data.

A stochastic model for topographically influenced cell migration

Migrating cells traverse a range of topographic configurations presented by the native extracellular environment to conduct their physiologic functions. It is well documented cells can modulate their behaviour in response to different topographic features, finding promising applications in biomaterial and bioimplant design. It is useful, in these areas of research, to be able to predict which topographic arrangements could be used to promote certain patterns of migration prior to laboratory experimentation. Despite a profusion of study and interest shown in these fields by experimentalists, the related modelling literature is as yet relatively sparse and tend to focus more on either cell-matrix interaction or morphological responses of cells. We propose a mathematical model for individual cell migration based on an Ornstein-Uhlenbeck process, and set out to see if the model can be used to predict migration patterns on 2-d isotropic and anisotropic topographies, whose characteristics can be broadly described as either uniform flat, uniform linear with variable ridge density or non-uniform disordered with variable feature density. Results suggest the model is capable of producing realistic patterns of migration for flat and linear topographic patterns, with calibrated output closely approximating NIH3T3 fibroblast migration behaviour derived from an experimental dataset, in which migration linearity increased with ridge density and average speed was highest at intermediate ridge densities. Exploratory results for non-uniform disordered topographies suggest cell migration patterns may adopt disorderedness present in the topography and that 'distortion' introduced to linear topographic patterns may not impede linear guidance of migration, given its magnitude is bounded within certain limits. We conclude that an Ornstein-Uhlenbeck based model for topographically influenced migration may be useful to predict patterns of migration behaviour for certain isotropic (flat) and anisotropic (linear) topographies in the NIH3T3 fibroblast cell line, but additional investigation is required to predict with confidence migration patterns for non-uniform disordered topographic arrangements.

Macrophage-induced reduction of bacteriophage density limits the efficacy of in vivo pulmonary phage therapy

The rise of antimicrobial resistance has led to renewed interest in evaluating phage therapy. In murine models highly effective treatment of acute pneumonia caused by Pseudomonas aeruginosa relies on the synergistic antibacterial activity of bacteriophages with neutrophils. Here, we show that depletion of alveolar macrophages (AM) shortens the survival of mice without boosting the P. aeruginosa load in the lungs. Unexpectedly, upon bacteriophage treatment, pulmonary levels of P. aeruginosa were significantly lower in AM-depleted than in immunocompetent mice. To explore potential mechanisms underlying the benefit of AM-depletion in treated mice, we developed a mathematical model. Integration of model simulations suggest that AM reduce bacteriophage density in the lungs. We experimentally confirmed that the in vivo decay of phage is faster in immunocompetent compared to AM-depleted animals. These findings demonstrate the involvement of feedback between bacteriophage, bacteria, and the immune system in shaping the outcomes of phage therapy in clinical settings.

Temporal features of goals, substitutions, and fouls in football games in the five major European league from 2018 to 2021

The "Big Five" European football leagues, comprising England's Premier League, Germany's Bundesliga, Spain's La Liga, Italy's Serie A, and France's Ligue 1, command significant attention. While the occurrence of goals, substitutions, and fouls in football games is often considered random, of the presence of an inherent inevitability is unclear. To investigate, we analyzed a public dataset detailing timing of goals, substitutions, and yellow cards in regular time from WhoScored across three seasons (2018-2019, 2019-2020, 2020-2021) in the top five European football leagues. We employed various mathematical descriptive models (including linear, sigmoid, and gaussian functions) to measure the temporal tendency of goals, substitutions, and yellow cards. Our results indicate that, whether in the first or second half of the match, the temporal distribution of these elements exhibits evenness a (indicative of randomness). However, specific characteristics were discerned through distinct model parameters, capturing novel phenomena that were intuitively illustrated. Furthermore, we explored the interaction of the timing of goals, substitutions, and yellow cards. In this analysis we found that scoring in the second half leads to more substitutions and yellow cards. Changing players in the second half corresponded with more goals, while the impact of yellow card fouls showed no differences in goals in the first and second halves. Our research is the first to systematically study the laws of modern football matches, providing valuable guidance and reference for many football coaches.

Mathematical modeling of combined therapies for treating tumor drug resistance

Drug resistance is one of the most intractable issues to the targeted therapy for cancer diseases. To explore effective combination therapy schemes, we propose a mathematical model to study the effects of different treatment schemes on the dynamics of cancer cells. Then we characterize the dynamical behavior of the model by finding the equilibrium points and exploring their local stability. Lyapunov functions are constructed to investigate the global asymptotic stability of the model equilibria. Numerical simulations are carried out to verify the stability of equilibria and treatment outcomes using a set of collected model parameters and experimental data on murine colon carcinoma. Simulation results suggest that immunotherapy combined with chemotherapy contributes significantly to the control of tumor growth compared to monotherapy. Sensitivity analysis is performed to identify the importance of model parameters on the variations of model outcomes.

Optimization design of brushless DC motor based on improved JAYA algorithm

Brushless direct current motor is widely used in industrial production because of its simple structure, wide speed range and low noise. To improve the operation efficiency of brushless DC motor and reduce the production and application costs, the optimization of brushless DC motor is analyzed by introducing the JAYA algorithm. This method determines the optimal parameters of a brushless DC motor using the theory of electromagnetic structure parameter selection and efficiency calculation. The population diversity of the JAYA algorithm is improved through an empirical learning strategy, and an adaptive strategy is introduced to balance the development ability and search performance of the algorithm. This ensures population diversity and improves convergence speed. The experiment showcases that the improved JAYA algorithm has a lower rank average in unimodal function operations, demonstrating stronger local development ability and better stability. It exhibits strong search ability in many local optima of multimodal functions. Moreover, the motor's average efficiency after optimization is 94.48%. The algorithm reaches the global optimum after approximately 40 iterations and offers faster convergence speed and higher accuracy. The adaptive JAYA algorithm is stable at around 93% when the number of iterations reaches 90, with a maximum efficiency of 95.3%. It is 5-12 percentage points higher than the other three comparison algorithms. The optimal solution of the motor parameters in the adaptive JAYA algorithm is closest to the theoretical parameter optimization value, meeting both the constraints of variables and the constraints of the model. The stator diameter, tooth magnetic induction, winding current density, air gap magnetic induction, and stator yoke magnetic induction values are 201.5 mm, 1.8 T, 2.049 A/mm2, 0.63 T, and 0.91 T, respectively. The research overcomes the problem of parameter optimization in the optimization design of brushless DC motor, improving their economic value of brushless DC motor in industrial production and application.

Modelling the Effects of Growth and Remodelling on the Density and Structure of Cancellous Bone

A two-stage model is proposed for investigating remodelling characteristics in bone over time and distance to the growth plate. The first stage comprises a partial differential equation (PDE) for bone density as a function of time and distance from the growth plate. This stage clarifies the contributions to changes in bone density due to remodelling and growth processes and tracks the rate at which new bone emanates from the growth plate. The second stage consists of simulating the remodelling process to determine remodelling characteristics. Implementing the second stage requires the rate at which bone moves away from the growth plate computed during the first stage. The second stage is also needed to confirm that remodelling characteristics predicted by the first stage may be explained by a realistic model for remodelling and to compute activation frequency. The model is demonstrated on microCT scans of tibia of juvenile female rats in three experimental groups: sham-operated control, oestrogen deprived, and oestrogen deprived followed by treatment. Model predictions for changes in bone density and remodelling characteristics agree with the literature. In addition, the model provides new insight into the role of treatment on the density of new bone emanating from the growth plate and provides quantitative descriptions of changes in remodelling characteristics beyond what has been possible to ascertain by experimentation alone.

Virus-mediated cell fusion of SARS-CoV-2 variants

SARS-CoV-2 has the ability to form large multi-nucleated cells known as syncytia. Little is known about how syncytia affect the dynamics of the infection or severity of the disease. In this manuscript, we extend a mathematical model of cell-cell fusion assays to estimate both the syncytia formation rate and the average duration of the fusion phase for five strains of SARS-CoV-2. We find that the original Wuhan strain has the slowest rate of syncytia formation (6.4×10-4/h), but takes only 4.0 h to complete the fusion process, while the Alpha strain has the fastest rate of syncytia formation (0.36 /h), but takes 7.6 h to complete the fusion process. The Beta strain also has a fairly fast syncytia formation rate (9.7×10-2/h), and takes the longest to complete fusion (8.4 h). The D614G strain has a fairly slow syncytia formation rate (2.8×10-3/h), but completes fusion in 4.0 h. Finally, the Delta strain is in the middle with a syncytia formation rate of 3.2×10-2/h and a fusing time of 6.1 h. We note that for these SARS-CoV-2 strains, there appears to be a tradeoff between the ease of forming syncytia and the speed at which they complete the fusion process.

Spatial analysis of Dengue through the reproduction numbers relating to socioeconomic features: Case studies on two Brazilian urban centers

The study of the propagation of infectious diseases in urban centers finds a close connection with their population's social characteristics and behavior. This work performs a spatial analysis of dengue cases in urban centers based on the basic reproduction numbers, R0, and incidence by planning areas (PAs), as well as their correlations with the Human Development Index (HDI) and the number of trips. We analyzed dengue epidemics in 2002 at two Brazilian urban centers, Belo Horizonte (BH) and Rio de Janeiro (RJ), using PAs as spatial units. Our results reveal heterogeneous spatial scenarios for both cities, with very weak correlations between R0 and both the number of trips and the HDI; in BH, the values of R0 show a less spatial heterogeneous pattern than in RJ. For BH, there are moderate correlations between incidence and both the number of trips and the HDI; meanwhile, they weakly correlate for RJ. Finally, the absence of strong correlations between the considered measures indicates that the transmission process should be treated considering the city as a whole.

Biofilms communities in the soil: characteristic and interactions using mathematical model

There are many different kinds of microorganisms in the soil, and many of them are biofilms because they can make supracellular compounds. Surface-associated microorganisms in a biofilm are encased in a hydrated extracellular polymeric substance that aids in adherence and survival. Numerous different kinds of microorganisms call the soil home. Strong interactions with and among species are made possible by biofilms; this, in turn, might increase the effectiveness with which organic compounds and poisons in soil are degraded. This encouraged us to take a close look at soil biofilm ecosystems, which we do in this paper. In this research, we will look at how soil biofilms arise and how that affects the composition of microbial communities and their function in the soil. Recent years have seen an uptick in interest in questions about biofilm structure and the social interactions of various bacteria. Many concepts elucidating the underlying mathematics of biofilm growth are also presented. Since biofilms are so widespread, this breakthrough in soil biofilm inquiry might help scientists understand soil microbiomes better. Mathematical models further extrapolate the relationships between microbial communities and gives a more precise information as to what is happening in a biofilm. Biofilms can help plants cope with a variety of environmental challenges. Soil quality, plant nourishment, plant protection, bioremediation, and climate change are all influenced by the interplay of biofilm communities. Thus, biofilms play an important role in the development of environmentally friendly and sustainable agriculture.

Estimating the population effectiveness of interventions against COVID-19 in France: A modelling study

BACKGROUND

Non-pharmaceutical interventions (NPIs) and vaccines have been widely used to manage the COVID-19 pandemic. However, uncertainty persists regarding the effectiveness of these interventions due to data quality issues, methodological challenges, and differing contextual factors. Accurate estimation of their effects is crucial for future epidemic preparedness.

METHODS

To address this, we developed a population-based mechanistic model that includes the impact of NPIs and vaccines on SARS-CoV-2 transmission and hospitalization rates. Our statistical approach estimated all parameters in one step, accurately propagating uncertainty. We fitted the model to comprehensive epidemiological data in France from March 2020 to October 2021. With the same model, we simulated scenarios of vaccine rollout.

RESULTS

The first lockdown was the most effective, reducing transmission by 84 % (95 % confidence interval (CI) 83-85). Subsequent lockdowns had diminished effectiveness (reduction of 74 % (69-77) and 11 % (9-18), respectively). A 6 pm curfew was more effective than one at 8 pm (68 % (66-69) vs. 48 % (45-49) reduction), while school closures reduced transmission by 15 % (12-18). In a scenario without vaccines before November 2021, we predicted 159,000 or 168 % (95 % prediction interval (PI) 70-315) more deaths and 1,488,000 or 300 % (133-492) more hospitalizations. If a vaccine had been available after 100 days, over 71,000 deaths (16,507-204,249) and 384,000 (88,579-1,020,386) hospitalizations could have been averted.

CONCLUSION

Our results highlight the substantial impact of NPIs, including lockdowns and curfews, in controlling the COVID-19 pandemic. We also demonstrate the value of the 100 days objective of the Coalition for Epidemic Preparedness Innovations (CEPI) initiative for vaccine availability.

The impact of triple doses vaccination and other interventions for controlling the outbreak of COVID-19 cases and mortality in Australia: A modelling study

COVID-19 is a significant public health problem around the globe, including in Australia. Despite this, Australia's Ministry of Health has expanded COVID-19 control measures widely, logistical trials exist, and the disease burden still needs more clarity. One of the best methods to comprehend the dynamics of disease transmission is by mathematical modeling of COVID-19, which also makes it possible to quantify factors in many places, including Australia. In order to understand the dynamics of COVID-19 in Australia, we examine a mathematical modeling framework for the virus in this study. Australian COVID-19 actual incidence data from January to December 2021 was used to calibrate the model. We also performed a sensitivity analysis of the model parameters and found that the COVID-19 transmission rate was the primary factor in determining the basic reproduction number (R0). Gradually influential intervention policies were established, with accurate effect and coverage regulated with the help of COVID-19 experts in Australia. We simulated data for the period from April 2022 to August 2023. To ascertain which of these outcomes is most effective in lowering the COVID-19 burden, we here assessed the COVID-19 burden (as shown by the number of incident cases and mortality) under a range of intervention scenarios. Regarding the policy of single intervention, the fastest and most efficient way to lower the incidence of COVID-19 is via increasing the first-dose immunization rate, while an improved treatment rate for the afflicted population is also helps to lower mortality in Australia. Furthermore, our results imply that integrating more therapies at the same time increases their efficacy, particularly for mortality, which significantly reduced with a moderate effort, while lowering the number of COVID-19 instances necessitates a major and ongoing commitment.

The impact of Covid-19 vaccination in Aotearoa New Zealand: A modelling study

Aotearoa New Zealand implemented a Covid-19 elimination strategy in 2020 and 2021, which enabled a large majority of the population to be vaccinated before being exposed to the virus. This strategy delivered one of the lowest pandemic mortality rates in the world. However, quantitative estimates of the population-level health benefits of vaccination are lacking. Here, we use a validated mathematical model of Covid-19 in New Zealand to investigate counterfactual scenarios with differing levels of vaccine coverage in different age and ethnicity groups. The model builds on earlier research by adding age- and time-dependent case ascertainment, the effect of antiviral medications, improved hospitalisation rate estimates, and the impact of relaxing control measures. The model was used for scenario analysis and policy advice for the New Zealand Government in 2022 and 2023. We compare the number of Covid-19 hospitalisations, deaths, and years of life lost in each counterfactual scenario to a baseline scenario that is fitted to epidemiological data between January 2022 and June 2023. Our results estimate that vaccines saved 6650 (95% credible interval [4424, 10180]) lives, and prevented 74500 [51000, 115400] years of life lost and 45100 [34400, 55600] hospitalisations during this 18-month period. Making the same comparison before the benefit of antiviral medications is accounted for, the estimated number of lives saved by vaccines increases to 7604 [5080, 11942]. Due to inequities in the vaccine rollout, vaccination rates among Māori were lower than in people of European ethnicity. Our results show that, if vaccination rates had been equitable, an estimated 11%-26% of the 292 Māori Covid-19 deaths that were recorded in this time period could have been prevented. We conclude that Covid-19 vaccination greatly reduced health burden in New Zealand and that equity needs to be a key focus of future vaccination programmes.

Algorithm design of a combinatorial mathematical model for computer random signals

To improve the processing effect of computer random signals, the manuscript employs the intelligent signal recognition algorithm to design a combinatorial mathematical model for computer random signals, and studies the parameter estimation of conventional frequency hopping signal (FHS) based on optimizing kernel function (KF). First, the mathematical form and graphical representation of the ambiguity function of the conventional FHS are explored. Furthermore, a new KF is presented according to its fuzzy function (FF) and the parameters of conventional FHSs are estimated according to the time-frequency distribution corresponding to the KF. Then, simulation experiments are carried out in different types of interference noise environments. The proposed combinatorial mathematical model for computer random signals shows a practical impact, and can effectively improve the effect of random signal combination.

What Influence Could the Acceptance of Visitors Cause on the Epidemic Dynamics of a Reinfectious Disease?: A Mathematical Model

The globalization in business and tourism becomes crucial more and more for the economical sustainability of local communities. In the presence of an epidemic outbreak, there must be such a decision on the policy by the host community as whether to accept visitors or not, the number of acceptable visitors, or the condition for acceptable visitors. Making use of an SIRI type of mathematical model, we consider the influence of visitors on the spread of a reinfectious disease in a community, especially assuming that a certain proportion of accepted visitors are immune. The reinfectivity of disease here means that the immunity gained by either vaccination or recovery is imperfect. With the mathematical results obtained by our analysis on the model for such an epidemic dynamics of resident and visitor populations, we find that the acceptance of visitors could have a significant influence on the disease's endemicity in the community, either suppressive or supportive.

Spatially-dependent model for rods and cones in the retina

We develop a mathematical model for photoreceptors in the retina. We focus on rod and cone outer segment dynamics and interactions with a nutrient source associated with the retinal pigment epithelium cells. Rod and cone densities (number per unit area of retinal surface) are known to have significant spatial dependence in the retina with cones located primarily near the fovea and the rods located primarily away from the fovea. Our model accounts for this spatial dependence of the rod and cone photoreceptor density as well as for the possibility of nutrient diffusion. We present equilibrium and dynamic solutions, discuss their relation to existing models, and estimate model parameters through comparisons with available experimental measurements of both spatial and temporal photoreceptor characteristics. Our model compares well with existing data on spatially-dependent regrowth of photoreceptor outer segments in the macular region of Rhesus Monkeys. Our predictions are also consistent with existing data on the spatial dependence of photoreceptor outer segment length near the fovea in healthy human subjects. We focus primarily on the healthy eye but our model could be the basis for future efforts designed to explore various retinal pathologies, eye-related injuries, and treatments of these conditions.

Prediction of effectiveness of universal rotavirus vaccination in Southwestern Vietnam based on a dynamic mathematical model

Vaccinating young children against rotavirus (RV) is a promising preventive strategy against rotavirus gastroenteritis (RVGE). We evaluated the relative risk reduction of RVGE induced by universal vaccination in Vietnam through dynamic model analysis. We developed an age-stratified dynamic Vaccinated-Susceptible-Infectious-Recovered-Susceptible model to analyze RV transmission and assess vaccine effectiveness (VE). We assumed 3 different vaccine efficacies: 55%, 70%, and 85%. For model calibration, we used a database of patients under 5 years of age admitted to Ho Chi Minh No.1 Hospital with RVGE between January 2013 and December 2018. Assuming a vaccination rate of 95%, the number of RVGE hospitalizations after 5 years from universal RV vaccination decreased from 92,502 cases to 45,626 with 85% efficacy, to 54,576 cases with 70% efficacy, and to 63,209 cases with 55% efficacy. Additionally, RVGE hospitalizations after 10 years decreased from 177,950 to 89,517 with 85% efficacy and to 121,832 cases with 55% efficacy. The relative risk reductions of RVGE after 10 years were 49.7% with 85% efficacy, 40.6% with 70% efficacy, and 31.5% with 55% efficacy. The VE was 1.10 times (95% CI, 1.01-1.22) higher in the 4-months to 1-year-old age group than in the other age groups (P = 0.038), when applying 85% efficacy with 95% coverage. In conclusion, despite its relatively lower efficacy compared to high-income countries, RV vaccination remains an effective intervention in Southwestern Vietnam. In particular, implementing universal RV vaccination with higher coverage would result in a decrease in RVGE hospitalizations among Vietnamese children under 5 years of age.

Impacts of Vaccination and Severe Acute Respiratory Syndrome Coronavirus 2 Variants Alpha and Delta on Coronavirus Disease 2019 Transmission Dynamics in Four Metropolitan Areas of the United States

To characterize Coronavirus Disease 2019 (COVID-19) transmission dynamics in each of the metropolitan statistical areas (MSAs) surrounding Dallas, Houston, New York City, and Phoenix in 2020 and 2021, we extended a previously reported compartmental model accounting for effects of multiple distinct periods of non-pharmaceutical interventions by adding consideration of vaccination and Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) variants Alpha (lineage B.1.1.7) and Delta (lineage B.1.617.2). For each MSA, we found region-specific parameterizations of the model using daily reports of new COVID-19 cases available from January 21, 2020 to October 31, 2021. In the process, we obtained estimates of the relative infectiousness of Alpha and Delta as well as their takeoff times in each MSA (the times at which sustained transmission began). The estimated infectiousness of Alpha ranged from 1.1x to 1.4x that of viral strains circulating in 2020 and early 2021. The estimated relative infectiousness of Delta was higher in all cases, ranging from 1.6x  to 2.1x. The estimated Alpha takeoff times ranged from February 1 to February 28, 2021. The estimated Delta takeoff times ranged from June 2 to June 26, 2021. Estimated takeoff times are consistent with genomic surveillance data.