Mathematical Model
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2021 ◽  
Vol 3 (4) ◽  
pp. 34-39
Ziyang He ◽  
Bo Wen

In order to achieve the goal of protecting people from wildfire, we propose to build a safety house to reduce mortality. This paper mainly creates a mathematical model about the house’s temperature change. Assuming an ideal heat balance model, we use the method of Joint Cube Systems and Self Iteration to simulate the whole process of heat radiation again.

2021 ◽  
Naomi R Waterlow ◽  
Michiko Toizumi ◽  
Edwin van Leeuwen ◽  
Hien-Anh Thi Nguyen ◽  
Lay Myint-Yoshida ◽  

Influenza and Respiratory Syncytial Virus (RSV) interact within their host posing the concern for heterologous ecological changes following vaccination. We aimed to estimate the population level impact of their interaction. We developed a dynamic age-stratified two-pathogen mathematical model that includes pathogen interaction through competition for infection and enhanced severity of dual infections. We used parallel tempering to fit it's parameters to 11 years of enhanced hospital-based surveillance for acute respiratory illnesses (ARI) in children under 5 years old in Nha Trang, Vietnam. The data supported either a 41% (95%CrI: 36 - 54) reduction in heterologous acquisition during infection and for 10.0 days (95%CrI 7.1 -12.8) thereafter, or no cross protection. We estimate that co-infection increased the probability for an infection in <2y old children to be reported 7.2 fold (95%CrI 5.0 - 11.4); or 16.6 fold (95%CrI 14.5 - 18.4) in the respective scenarios. Absence of either pathogen was not to the detriment of the other. We find stronger evidence for severity enhancing than for acquisition limiting interaction. In this setting vaccination against either pathogen is unlikely to have a major detrimental effect on the burden of disease caused by the other.

2021 ◽  
Vol 1 ◽  
HoChan Cheon ◽  
Andrey Kan ◽  
Giulio Prevedello ◽  
Simone C. Oostindie ◽  
Simon J. Dovedi ◽  

Lymphocytes are the central actors in adaptive immune responses. When challenged with antigen, a small number of B and T cells have a cognate receptor capable of recognising and responding to the insult. These cells proliferate, building an exponentially growing, differentiating clone army to fight off the threat, before ceasing to divide and dying over a period of weeks, leaving in their wake memory cells that are primed to rapidly respond to any repeated infection. Due to the non-linearity of lymphocyte population dynamics, mathematical models are needed to interrogate data from experimental studies. Due to lack of evidence to the contrary and appealing to arguments based on Occam’s Razor, in these models newly born progeny are typically assumed to behave independently of their predecessors. Recent experimental studies, however, challenge that assumption, making clear that there is substantial inheritance of timed fate changes from each cell by its offspring, calling for a revision to the existing mathematical modelling paradigms used for information extraction. By assessing long-term live-cell imaging of stimulated murine B and T cells in vitro, we distilled the key phenomena of these within-family inheritances and used them to develop a new mathematical model, Cyton2, that encapsulates them. We establish the model’s consistency with these newly observed fine-grained features. Two natural concerns for any model that includes familial correlations would be that it is overparameterised or computationally inefficient in data fitting, but neither is the case for Cyton2. We demonstrate Cyton2’s utility by challenging it with high-throughput flow cytometry data, which confirms the robustness of its parameter estimation as well as its ability to extract biological meaning from complex mixed stimulation experiments. Cyton2, therefore, offers an alternate mathematical model, one that is, more aligned to experimental observation, for drawing inferences on lymphocyte population dynamics.

Fadime Öğülmüş Demircan ◽  
İbrahim Yücedağ ◽  
Metin Toz

Pressure ulcers are injuries caused by external conditions such as pressure, friction, shear, and humidity resulting from staying in the same position for a long time in bedridden patients. It is a serious problem worldwide when assessed in terms of hospital capacity, nursing staff employment and treatment costs. In this study, we developed a novel mathematical model based on one of our previous models to prevent pressure ulcers or delay injuries. The proposed model uses a human thermal model that includes skin temperature, hypothalamus temperature, regional perspiration coefficient, and unconsciously loss of water amount. Moreover, in our model, we defined a variable wetness parameter in addition to the parameters, pressure, temperature, and humidity. The proposed model is mathematically defined in detail and tested for a wide range of parameters to show the model’s effectiveness in determining the pressure ulcer formation risk. The model is also compared with a model from the literature that based on only the general parameters, pressure, temperature, and humidity. The obtained results showed that the model determines the risk of the occurrence of the pressure ulcer more precisely than the compared one.

2021 ◽  
Vol 10 (3) ◽  
pp. 24-30
S. Piltyay ◽  
A. Bulashenko ◽  
V. Shuliak ◽  
O. Bulashenko

In this article we present the results of mathematical simulation, development and optimization of a waveguide polarizer with a diaphragm and pins. A mathematical model was developed using the proposed approach on the example of a waveguide polarizer with one diaphragm and two pins. The diaphragm and pins were modeled as inductive or capacitive elements for two types of linear polarization of the fundamental modes. The applied model uses a wave scattering matrix. The total matrix of a polarizer was obtained using wave matrices of transmission of individual elements of the device structure. Using the elements of the common S-parameters the electromagnetic characteristics of the device, which is considered, were obtained. To check the performance of the developed mathematical model, it was simulated in a software using the finite element technique in the frequency domain. The designed structure of the polarizer is adjustable due to mechanical change in the length of the pins. The developed waveguide polarizer with one diaphragm and two pins provides a reflection coefficient of less than 0.36 and a transmission coefficient of more than 0.93 for two types of polarizations. Therefore, a new theoretical method was developed in the article for analysis of scattering matrix elements of a waveguide polarizer with diaphragms and pins. It can also be used for the development of new tunable waveguide polarizers, filters and other components with diaphragms and pins.

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Hui Ye ◽  
Zaiming Liu ◽  
Long Zhou ◽  
Qiang Cai

This study was to use the partial differential mathematical model to analyze the magnetic resonance imaging (MRI) images of cerebral ischemia-reperfusion injury (CIRI) and to dynamically observe the role of L-theanine in CIRI based on this. 30 patients with cerebral ischemia in a hospital in a certain area were selected and divided into a cerebral ischemia group and a L-theanine treatment group. The two groups of patients were examined by MRI within 48 hours, and the relative apparent diffusion coefficient (rADC) of the cerebral ischemic part of the patients was determined. The partial differential mathematical model was used for data processing to obtain the function of cerebral ischemia time and infarct area, and the data of patients in the cerebral ischemia group and L-theanine treatment group were compared and analyzed. The results showed that the partial differential mathematical model could effectively analyze the linear relationship between the rADC value and time in the treatment of CIRI using L-theanine. The rADC values of the four points of interest in the L-theanine treatment group all increased with time, and there was a positive correlation between the variables X and Y. In observing the efficacy indicators of L-theanine, the L-theanine treatment group showed a significant advantage in the neurospecific enolase (NSE) content compared with the cerebral ischemia group ( P < 0.01 ), and the neurological function score of the L-theanine treatment group gradually decreased and showed a statistically obvious difference on the 7th day of treatment ( P < 0.05 ). In summary, it was verified in this study that the role of L-theanine in the treatment of CIRI was of a great and positive significance for the subsequent treatment of patients with cerebral ischemia, providing reliable theoretical basis and data basis for clinical treatment of CIRI.

P.V. Trusov ◽  
N.V. Zaitseva ◽  
M.Yu. Tsinker ◽  
A.V. Nekrasova

As part of the mathematical model of the human respiratory system, a submodel is considered for the study of the non-steady airflow with solid particles (suspended particulate matter (PM) / dust particles) and the deposition of particles of various sizes in the human nasal cavity. It is assumed that the nasal cavity is divided by the bone-cartilaginous septum into two symmetrical (relative to the nasal septum) parts; the average geometry of the right part of the human nasal cavity is considered. The inhaled air is considered as a multiphase mixture of homogeneous single-component gas and solid dust particles. The Eulerian-Lagrangian approach to modeling the motion of a multiphase mixture is used: a viscous liquid model is used to describe the motion of the carrier gas phase; the carried phase (dust particles) is modeled as separate inclusions of various sizes. The process of heating the inhaled air due to its contact with the walls is also taken into account. The features of the unsteady flow of a multiphase air mixture with dust particles were obtained using Ansys CFX for several scenarios. It has been noted that when studying the airflow in the nasal cavity, it is necessary to take into account the presence of turbulence, for which it is proposed to use the k-ω model. The velocity fields of inhaled air in the nasal cavity have been obtained; presented temperature distributions in the nasal cavity at different time points; made estimates of air heating at different temperatures of inhaled air; gave estimates of the proportion of deposited particles in the nasal cavity depending on the particle size for real machine-building production; presented trajectories of movement of suspended particles. Thus, it is shown that more than 99.7 % of particles with a diameter of more than 10 microns deposit in the human nasal cavity; as the particle diameter and mass decrease, the proportion of deposited particles decreases. Suspended particles with a size of less than 2.5 microns almost do not deposit in the nasal cavity. They can penetrate deeper into the lower airways and lungs of a person with the inhaled air and, having fibrogenic and toxic effect, can cause diseases. The results obtained are in good agreement with the results of individual studies performed by other scientists. Further development of the model involves studying airflow in the human lungs and modeling the formation of diseases caused by the harmful effects of environmental factors (including dust particles) entering the human body by inhalation.

Actuators ◽  
2021 ◽  
Vol 10 (11) ◽  
pp. 285
Zhen Lv ◽  
Muhammad Uzair ◽  
Xinjie Wang ◽  
Yafeng Liu

In this paper, a novel photovoltaic-electrostatic hybrid actuator with a slant lower electrode based on the PLZT ceramic is proposed. The mathematical model of photovoltaic-electrostatic hybrid actuator is established. Then, based on the mathematical model of photovoltaic-electrostatic hybrid actuator and the parameters identified, the mathematical simulation of the closed-loop displacement control for the photovoltaic-electrostatic hybrid actuator based on the PLZT ceramic is carried out. The results show that the displacement of the actuator can be controlled successfully at a particular value within the pull-in displacement by the light source. Furthermore, the response speed of the output displacement for photovoltaic-electrostatic hybrid actuator with a slant lower electrode is faster than that with a parallel lower electrode, offering a good potential to advance the current applications on micro-electro-mechanical system.

Energies ◽  
2021 ◽  
Vol 14 (21) ◽  
pp. 6974
Ivan V. Vasyukov ◽  
Alexander V. Pavlenko ◽  
Vladimir S. Puzin ◽  
Denis V. Batishchev ◽  
Irina A. Bolshenko

The issues of mathematical and numerical simulation of an electrical complex of a power plant based on hydrogen fuel cells with a voltage step-down converter were considered. The work was aimed at developing a mathematical model that would provide for determining the most loaded operation mode of the complex components. The existing mathematical models do not consider the effect of such processes as the charge and discharge of the battery backup power supply on the power plant components. They often do not consider the nonlinearity of the fuel cell output voltage. This paper offers a mathematical model of an electrical complex based on the circuit analysis. The model combines a well-known physical model of a fuel cell based on a potential difference and a model of a step-down converter with a battery backup power supply developed by the authors. A method of configuring a fuel cell model based on the experimental current–voltage characteristic by the least-squares method has been proposed. The developed model provides for determining currents and voltages in all components of the power plant both in the nominal operating mode and in the mode of limiting the power consumed from the fuel cell when the battery backup power supply is being charged. The correctness of the calculated ratios and the mathematical model has been confirmed experimentally. Using the proposed model, a 1300 W power plant with a specific power of 529.3 W∙h/kg was developed and tested.

A. Manickam ◽  
Pushpendra Kumar ◽  
K. Dasunaidu ◽  
V. Govindaraj ◽  
Dheeraj Kumar Joshi

A stochastic SIR influenza vertical transmission model is examined in this paper where vaccination and an incidence rate that is not linear are considered. To determine whether testosterone regulates lower sintering HPA axis function in males, we used a stochastic SIR epidemic procedure with divergent influences on ACTH and cortisol. The suppressive effects on cortisol can be attributed to a peripheral (adrenal) locus. Following that, we came to the conclusion that experimental solutions have been discovered and the requisite statistical findings have been examined. Finally, we deduce that the given mathematical model and the results are relevant to medical research. In the future, this research can be further extended to simulate more results in the medical field.

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