A mathematical model explores the contributions of bending and stretching forces to shoot gravitropism in Arabidopsis

Abstract 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.

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Evaluating the impacts of release in São Paulo State (Brazil) on the epidemic of covid-19 based on mathematical model

10.1101/2020.08.03.20167221 ◽

2020 ◽

Author(s):

Hyun Mo Yang ◽

Luis Pedro Pedro Lombardi Junior ◽

Ariana Campos Yang ◽

Fabio Fernandes Morato Castro

Keyword(s):

Mathematical Model ◽

Sao Paulo ◽

Model Parameters ◽

Isolated Population ◽

São Paulo ◽

Paulo State ◽

History Of ◽

São Paulo State ◽

Using Data ◽

The Impact

To flatten the curve of the natural epidemic of covid-19, many countries adopted lockdown or isolation resulting in the containment of the SARS-CoV-2 transmission. However, an important question arises about the strategies of release of isolated persons to avoid overloaded hospitals and increased deaths. São Paulo State (Brazil) implemented the isolation of the population in non- essential activities on March 24, and the progressive flexibilization considering the characteristics of each location (release of the isolated population) initiated on June 15. A mathematical model based on the natural history of covid-19 was applied to describe the epidemiological scenario with isolation in São Paulo State, and assess the impact of release on the covid-19 epidemic. Using data collected from São Paulo State, we estimated the model parameters to obtain the curves of the epidemic, the number of deaths, and the clinical evolution of covid-19. The epidemic under isolation was the framework to evaluate the strategies of the release, that is, how these curves are changed with the release of isolated persons. We evaluated three strategies of release. First two strategies considered four releases in the isolated population in four equal proportions, but successive releases elapsed by 14 and 21 days. In each strategy the beginning of the release was on June 29 and July 13, when the effective reproduction number Ref was evaluated. The third strategy aimed at the protection of the elder subpopulation. We observed that the delay to begin the release and the increased elapse between successive releases resulted in a better scenario by decreasing severe covid-19 cases and, consequently, to avoid overloaded hospitals. We also observed that the release delayed to achieve lower values for Ref and infectious persons retarded in several months the quick increasing phase of the forthcoming epidemic. However, this epidemic can be flattened or even suppressed by isolation of infectious persons by mass testing and/or by rigid adoption of protective measures and social distancing.

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A Mathematical Model of Contact Tracing during the 2014–2016 West African Ebola Outbreak

Mathematics ◽

10.3390/math9060608 ◽

2021 ◽

Vol 9 (6) ◽

pp. 608

Author(s):

Danielle Burton ◽

Suzanne Lenhart ◽

Christina J. Edholm ◽

Benjamin Levy ◽

Michael L. Washington ◽

...

Keyword(s):

Mathematical Model ◽

Disease Management ◽

Ebola Virus ◽

Virus Disease ◽

Infected Individual ◽

Vital Role ◽

West African ◽

Contact Tracing ◽

The Novel ◽

Using Data

The 2014–2016 West African outbreak of Ebola Virus Disease (EVD) was the largest and most deadly to date. Contact tracing, following up those who may have been infected through contact with an infected individual to prevent secondary spread, plays a vital role in controlling such outbreaks. Our aim in this work was to mechanistically represent the contact tracing process to illustrate potential areas of improvement in managing contact tracing efforts. We also explored the role contact tracing played in eventually ending the outbreak. We present a system of ordinary differential equations to model contact tracing in Sierra Leonne during the outbreak. Using data on cumulative cases and deaths, we estimate most of the parameters in our model. We include the novel features of counting the total number of people being traced and tying this directly to the number of tracers doing this work. Our work highlights the importance of incorporating changing behavior into one’s model as needed when indicated by the data and reported trends. Our results show that a larger contact tracing program would have reduced the death toll of the outbreak. Counting the total number of people being traced and including changes in behavior in our model led to better understanding of disease management.

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Abnormal Spinal Cord Myelination due to Oligodendrocyte Dysfunction in a Model of Huntington’s Disease

Journal of Huntington s Disease ◽

10.3233/jhd-210495 ◽

2021 ◽

pp. 1-8

Author(s):

Costanza Ferrari Bardile ◽

Harwin Sidik ◽

Reynard Quek ◽

Nur Amirah Binte Mohammad Yusof ◽

Marta Garcia-Miralles ◽

...

Keyword(s):

Spinal Cord ◽

Huntington's Disease ◽

Huntington’S Disease ◽

Oligodendrocyte Progenitor Cells ◽

Wild Type ◽

Specific Expression ◽

Relative Contribution ◽

Related Proteins ◽

The Impact ◽

Cervical Area

Background: The relative contribution of grey matter (GM) and white matter (WM) degeneration to the progressive brain atrophy in Huntington’s disease (HD) has been well studied. The pathology of the spinal cord in HD is comparatively less well documented. Objective: We aim to characterize spinal cord WM abnormalities in a mouse model of HD and evaluate whether selective removal of mutant huntingtin (mHTT) from oligodendroglia rescues these deficits. Methods: Histological assessments were used to determine the area of GM and WM in the spinal cord of 12-month-old BACHD mice, while electron microscopy was used to analyze myelin fibers in the cervical area of the spinal cord. To investigate the impact of inactivation of mHTT in oligodendroglia on these measures, we used the previously described BACHDxNG2Cre mouse line where mHTT is specifically reduced in oligodendrocyte progenitor cells. Results: We show that spinal GM and WM areas are significantly atrophied in HD mice compared to wild-type controls. We further demonstrate that specific reduction of mHTT in oligodendroglial cells rescues the atrophy of spinal cord WM, but not GM, observed in HD mice. Inactivation of mHTT in oligodendroglia had no effect on the density of oligodendroglial cells but enhanced the expression of myelin-related proteins in the spinal cord. Conclusion: Our findings demonstrate that the myelination abnormalities observed in brain WM structures in HD extend to the spinal cord and suggest that specific expression of mHTT in oligodendrocytes contributes to such abnormalities.

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Predicting the longitudinal modulus of elasticity of Sitka spruce from cellulose orientation and abundance

Holzforschung ◽

10.1515/hf.2010.084 ◽

2010 ◽

Vol 64 (4) ◽

Cited By ~ 17

Author(s):

J. Paul McLean ◽

Robert Evans ◽

John R. Moore

Keyword(s):

Bulk Density ◽

Modulus Of Elasticity ◽

Microfibril Angle ◽

Sitka Spruce ◽

Picea Sitchensis ◽

Model Parameters ◽

Bending Tests ◽

Wood Stiffness ◽

Using Data ◽

Longitudinal Modulus

Abstract Sitka spruce (Picea sitchensis) is the most widely planted commercial tree species in the United Kingdom and Ireland. Because of the increasing use of this species for construction, the ability to predict wood stiffness is becoming more important. In this paper, a number of models are developed using data on cellulose abundance and orientation obtained from the SilviScan-3 system to predict the longitudinal modulus of elasticity (MOE) of small defect-free specimens. Longitudinal MOE was obtained from both bending tests and a sonic resonance technique. Overall, stronger relationships were found between the various measures of cellulose abundance and orientation and the dynamic MOE obtained from the sonic resonance measurements, rather than with the static MOE obtained from bending tests. There was only a moderate relationship between wood bulk density and dynamic MOE (R2=0.423), but this relationship was improved when density was divided by microfibril angle (R2=0.760). The best model for predicting both static and dynamic MOE involved the product of bulk density and the coefficient of variation in the azimuthal intensity profile (R2=0.725 and 0.862, respectively). The model parameters obtained for Sitka spruce differed from those obtained in earlier studies on Pinus radiata and Eucalyptus delegatensis, indicating that the model might require recalibration before it can be applied to different species.

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2767. Variation in Incidence of Pediatric Herpes Zoster by First- and Second-Dose Varicella Vaccine Formulations

Open Forum Infectious Diseases ◽

10.1093/ofid/ofz360.2444 ◽

2019 ◽

Vol 6 (Supplement_2) ◽

pp. S975-S976

Author(s):

Sheila Weinmann ◽

Stephanie Irving ◽

Padma Koppolu ◽

Allison Naleway ◽

Edward Belongia ◽

...

Keyword(s):

Herpes Zoster ◽

Varicella Vaccine ◽

Vaccine Dose ◽

Varicella Vaccination ◽

Vaccine Formulation ◽

Wild Type ◽

Varicella Zoster ◽

Dose Formulation ◽

Using Data ◽

Rate Ratios

Abstract Background Varicella (VAR) and measles-mumps-rubella (MMR) vaccines are recommended for children at ages 12–15 months and 4–6 years. These are administered as separate MMR and VAR vaccines (MMR+VAR) or as combined measles-mumps-rubella-varicella (MMRV) vaccine. Herpes zoster (HZ), caused by wild-type or vaccine-strain varicella-zoster virus, can occur in children after varicella vaccination. It is unknown whether HZ incidence after varicella vaccination varies by vaccine formulation or simultaneous receipt of MMR. Methods Using data from six integrated health systems, we examined HZ incidence among children who turned 12 months old during 2003–2008 and received varicella and MMR vaccines according to routine recommendations. All HZ cases ≥ 21 days after first varicella vaccination were identified using ICD-9 codes from inpatient, outpatient, emergency room encounters, and claims data, through 2014. HZ incidence was examined by vaccine formulation (MMR+VAR, MMRV, or VAR without same-day MMR) and doses received and compared using incidence rate ratios (IRR). Results Among 199,797 children, we identified 601 HZ cases. Crude HZ incidence after first-dose MMR+VAR (18.6 [95% CI 11.1–29.2] cases/100,000 person-years) was similar to the rate after first-dose MMRV (17.9 [95% CI 10.6–28.3] cases/100,000 person-years), but approximately double the rate among those with first-dose VAR without same-day MMR (7.5 [95% CI 3.1–15.0] cases/100,000 person-years); see Table 1. The IRR for HZ after first-dose MMR+VAR or MMRV, compared with VAR, was 2.5 (95% CI 1.4–4.4; P = 0.002). When examining any first or second dose formulation, crude HZ incidence was lower after the second varicella vaccine dose (13.9 cases/100,000 person-years), than in the period before the second dose (i.e., between first and second doses or after the first dose in children with only one dose; 21.8 cases/100,000 person-years, P < 0.0001). HZ incidence was also lower after two varicella vaccine doses in each of the three first-dose formulation groups. Conclusion HZ incidence among children varied by first-dose varicella vaccine formulation and number of varicella vaccine doses. Regardless of the first-dose varicella vaccine formulation, children who received two vaccine doses had lower HZ incidence after the second dose. Disclosures All authors: No reported disclosures.

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The identification of a device based on a Peltier element by the least squares method

Proceedings of the Russian higher school Academy of sciences ◽

10.17212/1727-2769-2020-1-2-17-27 ◽

2020 ◽

pp. 17-27

Author(s):

Vladimir Grinkevich ◽

Keyword(s):

Mathematical Model ◽

Least Squares ◽

Least Squares Method ◽

Control Object ◽

Object Identification ◽

Model Parameters ◽

Peltier Element ◽

Transport Delay ◽

Non Linear ◽

The Mathematical Model

The evaluation of the mathematical model parameters of a non-linear object with a transport delay is considered in this paper. A temperature controlled stage based on a Peltier element is an identification object in the paper. Several input signal implementations are applied to the input of the identification object. The least squares method is applied for the calculation of the non-linear differential equitation parameters which describe the identification object. The least squares method is used due to its simplicity and the possibility of identification non-linear objects. The parameters values obtained in the process of identification are provided. The plots of temperature changes in the temperature control system with a controller designed based on the mathematical model of the control object obtained as a result of identification are shown. It is found that the mathematical model obtained in the process of identification may be applied to design controllers for non-linear systems, in particular for a temperature stage based on a Peltier element, and for self-tuning controllers. However, the least square method proposed in the paper cannot estimate the transport delay time. Therefore it is required to evaluate the time delay by temperature transient processes. Dynamic object identification is applied when it is required to obtain a mathematical model structure and evaluate the parameters by an input and output control object signal. Also, identification is applied for auto tuning of controllers. A mathematical model of a control object is required to design the controller which is used to provide the required accuracy and stability of control systems. Peltier elements are applied to design low-power and small- size temperature stage . Hot benches based on a Peltier element can provide the desired temperature above and below ambient temperature.

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Resource-Driven Encounters and the Induction of Disease Among Consumers

10.1101/091850 ◽

2016 ◽

Author(s):

Rebecca K. Borchering ◽

Steve E. Bellan ◽

Jason M. Flynn ◽

Juliet R.C. Pulliam ◽

Scott A. McKinley

Keyword(s):

National Park ◽

Interaction Model ◽

Spatially Explicit ◽

Encounter Rate ◽

Model Parameters ◽

Expected Number ◽

Spatially Explicit Model ◽

Consumer Population ◽

Using Data ◽

The Relationship

AbstractSubmitted Manuscript 2016. Territorial animals share a variety of common resources, which can be a major driver of conspecific encounter rates. We examine how changes in resource availability influence the rate of encounters among individuals in a consumer population by implementing a spatially explicit model for resource visitation behavior by consumers. Using data from 2009 and 2010 in Etosha National Park, we verify our model's prediction that there is a saturation effect in the expected number of jackals that visit a given carcass site as carcasses become abundant. However, this does not directly imply that the overall resource-driven encounter rate among jackals decreases. This is because the increase in available carcasses is accompanied by an increase in the number of jackals that detect and potentially visit carcasses. Using simulations and mathematical analysis of our consumer-resource interaction model, we characterize key features of the relationship between resource-driven encounter rate and model parameters. These results are used to investigate a standing hypothesis that the outbreak of a fatal disease among zebras can potentially lead to an outbreak of an entirely different disease in the jackal population, a process we refer to as indirect induction of disease.

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A modelling approach to estimate the sensitivity of pooled faecal samples for isolation of Salmonella in pigs

Journal of The Royal Society Interface ◽

10.1098/rsif.2005.0057 ◽

2005 ◽

Vol 2 (4) ◽

pp. 365-372 ◽

Cited By ~ 38

Author(s):

Mark E Arnold ◽

Alasdair Cook ◽

Rob Davies

Keyword(s):

Mathematical Model ◽

Individual Sample ◽

Sensitive Test ◽

Sample Weight ◽

Sample Weights ◽

Test Sensitivity ◽

Faecal Samples ◽

Using Data ◽

The Individual ◽

Modelling Approach

The objective of this study was to develop and parametrize a mathematical model of the sensitivity of pooled sampling of faeces to detect Salmonella infection in pigs. A mathematical model was developed to represent the effect of pooling on the probability of Salmonella isolation. Parameters for the model were estimated using data obtained by collecting 50 faecal samples from each of two pig farms. Each sample was tested for Salmonella at individual sample weights of 0.1, 0.5, 1, 10 and 25 g and pools of 5, 10 and 20 samples were created from the individual samples. The highest test sensitivity for individual samples was found at 10 g (90% sensitivity), with the 25 g test sensitivity equal to 83%. For samples of less than 10 g, sensitivity was found to reduce with sample weight. Incubation for 48 h was found to produce a more sensitive test than incubation for 24 h. Model results found increasing sensitivity with more samples in the pool, with the pools of 5, 10 and 20 being more sensitive than individual sampling, and the pools of 20 being the most sensitive of those considered.

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A mathematical model of common-cold epidemics on Tristan da Cunha

Journal of Hygiene ◽

10.1017/s0022172400021677 ◽

1971 ◽

Vol 69 (3) ◽

pp. 423-433 ◽

Cited By ~ 14

Author(s):

B. J. Hammond ◽

D. A. J. Tyrrell

Keyword(s):

Mathematical Model ◽

Common Cold ◽

Average Duration ◽

Model Parameters ◽

Epidemic Threshold ◽

Tristan Da Cunha ◽

Simulation Techniques ◽

Time Courses ◽

The Mathematical Model ◽

Computer Simulation Techniques

SUMMARYRecords of seven common-cold outbreaks on the island of Tristan da Cunha are compared with the corresponding time courses given by the mathematical model of Kermack & McKendrick (1927) and with an alternative model that directly involves a constant average duration of individual infection. Using computer simulation techniques the latter model is shown to be preferred and is then closely matched to the field data to obtain values for the model parameters. Consideration is then given to the intensity of epidemics predicted by the model and to the distribution of the actual epidemics relative to the theoretical epidemic threshold.

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