Mathematical Modelling of COVID-19 Transmission in Kenya: A Model with Reinfection Transmission Mechanism

In this study we propose a Coronavirus Disease 2019 (COVID-19) mathematical model that stratifies infectious subpopulations into: infectious asymptomatic individuals, symptomatic infectious individuals who manifest mild symptoms and symptomatic individuals with severe symptoms. In light of the recent revelation that reinfection by COVID-19 is possible, the proposed model attempt to investigate how reinfection with COVID-19 will alter the future dynamics of the recent unfolding pandemic. Fitting the mathematical model on the Kenya COVID-19 dataset, model parameter values were obtained and used to conduct numerical simulations. Numerical results suggest that reinfection of recovered individuals who have lost their protective immunity will create a large pool of asymptomatic infectious individuals which will ultimately increase symptomatic individuals with mild symptoms and symptomatic individuals with severe symptoms (critically ill) needing urgent medical attention. The model suggests that reinfection with COVID-19 will lead to an increase in cumulative reported deaths. Comparison of the impact of non pharmaceutical interventions on curbing COVID19 proliferation suggests that wearing face masks profoundly reduce COVID-19 prevalence than maintaining social/physical distance. Further, numerical findings reveal that increasing detection rate of asymptomatic cases via contact tracing, testing and isolating them can drastically reduce COVID-19 surge, in particular individuals who are critically ill and require admission into intensive care.

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THE DEVELOPMENT OF THE MATHEMATICAL MODEL OF PREDICTING THE INDICATORS OF ACCREDITATION OF TECHNICAL UNIVERSITIES IN THE RUSSIAN FEDERATION

VESTNIK OF ASTRAKHAN STATE TECHNICAL UNIVERSITY SERIES MANAGEMENT COMPUTER SCIENCE AND INFORMATICS ◽

10.24143/2072-9502-2017-2-27-38 ◽

2017 ◽

pp. 27-38

Author(s):

Olga Mikhaylovna Tikhonova ◽

Alexander Fedorovich Rezchikov ◽

Vladimir Andreevich Ivashchenko ◽

Vadim Alekseevich Kushnikov

Keyword(s):

Mathematical Model ◽

System Dynamics ◽

Regression Model ◽

Oriented Graph ◽

Real Data ◽

Educational Process ◽

Proposed Model ◽

Linear Differential ◽

The University ◽

The Mathematical Model

The paper presents the system of predicting the indicators of accreditation of technical universities based on J. Forrester mechanism of system dynamics. According to analysis of cause-and-effect relationships between selected variables of the system (indicators of accreditation of the university) there was built the oriented graph. The complex of mathematical models developed to control the quality of training engineers in Russian higher educational institutions is based on this graph. The article presents an algorithm for constructing a model using one of the simulated variables as an example. The model is a system of non-linear differential equations, the modelling characteristics of the educational process being determined according to the solution of this system. The proposed algorithm for calculating these indicators is based on the system dynamics model and the regression model. The mathematical model is constructed on the basis of the model of system dynamics, which is further tested for compliance with real data using the regression model. The regression model is built on the available statistical data accumulated during the period of the university's work. The proposed approach is aimed at solving complex problems of managing the educational process in universities. The structure of the proposed model repeats the structure of cause-effect relationships in the system, and also provides the person responsible for managing quality control with the ability to quickly and adequately assess the performance of the system.

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On the Dragging Trajectory of Anchors in Clay for Merchant Ships

Journal of Marine Science and Engineering ◽

10.3390/jmse9020118 ◽

2021 ◽

Vol 9 (2) ◽

pp. 118

Author(s):

Xinqing Zhuang ◽

Keliang Yan ◽

Pan Gao ◽

Yihua Liu

Keyword(s):

Mathematical Model ◽

Structural Integrity ◽

Indirect Measurement ◽

Test System ◽

Flow Rule ◽

Burial Depth ◽

Proposed Model ◽

Depth Increase ◽

Two Parameters ◽

The Mathematical Model

Anchor dragging is a major threat to the structural integrity of submarine pipelines. A mathematical model in which the mechanical model of chain and the bearing model of anchor were coupled together. Based on the associated flow rule, an incremental procedure was proposed to solve the spatial state of anchor until it reaches the ultimate embedding depth. With an indirect measurement method for the anchor trajectory, a model test system was established. The mathematical model was validated against some model tests, and the effects of two parameters were studied. It was found that both the ultimate embedding depth of a dragging anchor and the distance it takes to reach the ultimate depth increase with the shank-fluke pivot angle, but decrease as the undrained shear strength of clay increases. The proposed model is supposed to be useful for the embedding depth calculation and guiding the design of the pipeline burial depth.

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Content Dependent Representation Selection Model for Systems Based on MPEG DASH

Electronics ◽

10.3390/electronics10151843 ◽

2021 ◽

Vol 10 (15) ◽

pp. 1843

Author(s):

Jelena Vlaović ◽

Snježana Rimac-Drlje ◽

Drago Žagar

Keyword(s):

Mathematical Model ◽

Spatial Information ◽

Relevant Literature ◽

Video Quality ◽

Similarity Index ◽

Video Encoding ◽

Adaptation Algorithm ◽

Subjective Testing ◽

Proposed Model ◽

The Mathematical Model

A standard called MPEG Dynamic Adaptive Streaming over HTTP (MPEG DASH) ensures the interoperability between different streaming services and the highest possible video quality in changing network conditions. The solutions described in the available literature that focus on video segmentation are mostly proprietary, use a high amount of computational power, lack the methodology, model notation, information needed for reproduction, or do not consider the spatial and temporal activity of video sequences. This paper presents a new model for selecting optimal parameters and number of representations for video encoding and segmentation, based on a measure of the spatial and temporal activity of the video content. The model was developed for the H.264 encoder, using Structural Similarity Index Measure (SSIM) objective metrics as well as Spatial Information (SI) and Temporal Information (TI) as measures of video spatial and temporal activity. The methodology that we used to develop the mathematical model is also presented in detail so that it can be applied to adapt the mathematical model to another type of an encoder or a set of encoding parameters. The efficiency of the segmentation made by the proposed model was tested using the Basic Adaptation algorithm (BAA) and Segment Aware Rate Adaptation (SARA) algorithm as well as two different network scenarios. In comparison to the segmentation available in the relevant literature, the segmentation based on the proposed model obtains better SSIM values in 92% of cases and subjective testing showed that it achieves better results in 83.3% of cases.

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Digital proximity tracing on empirical contact networks for pandemic control

Nature Communications ◽

10.1038/s41467-021-21809-w ◽

2021 ◽

Vol 12 (1) ◽

Author(s):

G. Cencetti ◽

G. Santin ◽

A. Longa ◽

E. Pigani ◽

A. Barrat ◽

...

Keyword(s):

Large Scale ◽

Disease Outbreaks ◽

Physical Distance ◽

Contact Tracing ◽

Reproductive Number ◽

Modeling Framework ◽

Infectious Disease Outbreaks ◽

Contact Patterns ◽

Contact Data ◽

The Impact

AbstractDigital contact tracing is a relevant tool to control infectious disease outbreaks, including the COVID-19 epidemic. Early work evaluating digital contact tracing omitted important features and heterogeneities of real-world contact patterns influencing contagion dynamics. We fill this gap with a modeling framework informed by empirical high-resolution contact data to analyze the impact of digital contact tracing in the COVID-19 pandemic. We investigate how well contact tracing apps, coupled with the quarantine of identified contacts, can mitigate the spread in real environments. We find that restrictive policies are more effective in containing the epidemic but come at the cost of unnecessary large-scale quarantines. Policy evaluation through their efficiency and cost results in optimized solutions which only consider contacts longer than 15–20 minutes and closer than 2–3 meters to be at risk. Our results show that isolation and tracing can help control re-emerging outbreaks when some conditions are met: (i) a reduction of the reproductive number through masks and physical distance; (ii) a low-delay isolation of infected individuals; (iii) a high compliance. Finally, we observe the inefficacy of a less privacy-preserving tracing involving second order contacts. Our results may inform digital contact tracing efforts currently being implemented across several countries worldwide.

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The Impact of Elongation on Change in Electrical Resistance of Electrically Conductive Yarns Woven into Fabric

Materials ◽

10.3390/ma14123390 ◽

2021 ◽

Vol 14 (12) ◽

pp. 3390

Author(s):

Željko Knezić ◽

Željko Penava ◽

Diana Šimić Penava ◽

Dubravko Rogale

Keyword(s):

Mathematical Model ◽

Electrical Resistance ◽

Electrically Conductive ◽

Textile Materials ◽

Measurement Results ◽

Conductive Yarns ◽

Yarn Count ◽

As Relationship ◽

The Impact ◽

The Mathematical Model

Electrically conductive yarns (ECYs) are gaining increasing applications in woven textile materials, especially in woven sensors suitable for incorporation into clothing. In this paper, the effect of the yarn count of ECYs woven into fabric on values of electrical resistance is analyzed. We also observe how the direction of action of elongation force, considering the position of the woven ECY, effects the change in the electrical resistance of the electrically conductive fabric. The measurements were performed on nine different samples of fabric in a plain weave, into which were woven ECYs with three different yarn counts and three different directions. Relationship curves between values of elongation forces and elongation to break, as well as relationship curves between values of electrical resistance of fabrics with ECYs and elongation, were experimentally obtained. An analytical mathematical model was also established, and analysis was conducted, which determined the models of function of connection between force and elongation, and between electrical resistance and elongation. The connection between the measurement results and the mathematical model was confirmed. The connection between the mathematical model and the experimental results enables the design of ECY properties in woven materials, especially textile force and elongation sensors.

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An Optimized Mathematical Model for Items Supplies Planning of a Logistic System

Modern Applied Science ◽

10.5539/mas.v10n10p133 ◽

2016 ◽

Vol 10 (10) ◽

pp. 133

Author(s):

Mohammad Ali Nasiri Khalili ◽

Mostafa Kafaei Razavi ◽

Morteza Kafaee Razavi

Keyword(s):

Mathematical Model ◽

Mixed Integer ◽

Logistics System ◽

Proposed Model ◽

Multiple Objective Decision Making ◽

System Requirements ◽

Purchasing Logistics ◽

The Cost ◽

The Mathematical Model ◽

First Time

Items supplies planning of a logistic system is one of the major issue in operations research. In this article the aim is to determine how much of each item per month from each supplier logistics system requirements must be provided. To do this, a novel multi objective mixed integer programming mathematical model is offered for the first time. Since in logistics system, delivery on time is very important, the first objective is minimization of time in delivery on time costs (including lack and maintenance costs) and the cost of purchasing logistics system. The second objective function is minimization of the transportation supplier costs. Solving the mathematical model shows how to use the Multiple Objective Decision Making (MODM) can provide the ensuring policy and transportation logistics needed items. This model is solved with CPLEX and computational results show the effectiveness of the proposed model.

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The Impact Analysis of Revolute Pair Clearance to the End Pose Accuracy of Welding Robot

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.778.259 ◽

2015 ◽

Vol 778 ◽

pp. 259-263

Author(s):

Fa Jun Zhang ◽

Lin Zi Li ◽

Hui Lin ◽

Yin Lin Pu ◽

Zhu Xin

Keyword(s):

Mathematical Model ◽

Impact Analysis ◽

Joint Clearance ◽

Welding Robot ◽

Movement Characteristic ◽

Movement Stability ◽

Simulation Results ◽

The Impact ◽

The Mathematical Model ◽

Welding Position

Various uncertain factors affect the movement of the welding robot, thus welding gun tend to deviate from the theory of welding position which reduces the welding accuracy, of which the revolute pair clearance have an greater effect on the movement of the welding robot. In order to study the influence of revolute pair clearance to the end pose accuracy of welding robot, the mathematical model of revolute pair clearance was established, and the software SolidWorks was used for establishing the welding robot model, making simulations of the mechanical arm with joint clearance and no joint clearance. At last, the movement characteristic of the hinge shaft is attained. The simulation results showed that the shaft velocity and displacement of mechanical arm with joint clearance has a certain degree of fluctuation, which affecting the end pose accuracy of welding robot , and reducing the movement stability and the welding accuracy of welding robot.

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Enhancement the Solar Still Performance Using Chimney Exhaust Gases

ASME 2021 15th International Conference on Energy Sustainability ◽

10.1115/es2021-63858 ◽

2021 ◽

Author(s):

Hamdy Hassan

Keyword(s):

Mathematical Model ◽

Theoretical Study ◽

Saline Water ◽

Kutta Method ◽

Solar Still ◽

Climate Conditions ◽

Exhaust Gases ◽

Runge Kutta Method ◽

The Impact ◽

The Mathematical Model

Abstract In this paper, a theoretical study is presented on enhancement of the solar still performance by using the exhaust gases passing inside a chimney under the still basin. The impact of the exhaust gases temperature on the solar still temperature, productivity, and efficiency are considered. The performance of solar still with chimney is compared with that of conventional solar still. The study is carried out under the hot and climate conditions of Upper Egypt. A complete transient mathematical model of the physical model including the solar still regions temperatures, productivity, and heat transfer between the solar still and the exhaust gases are constructed. The mathematical model is solved numerically by using fourth-order Runge-Kutta method and is programmed by using MATLAB. The mathematical model is validated using an experimental work. The results show that the solar still saline water temperature increases and productivity with using and rising the exhaust gases. Furthermore, the impact of using exhaust gases on the still performance in winter is greater than in summer. using chimney exhaust gases at 75 °C and 125 °C enhances the daily freshwater yield of the conventional still by more than three times and about six times in winter, respectively, and about two and half times and more than three times in summer, respectively.

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Methods of Mathematical Modeling of the Leaching Process of Cobalt-Containing Solutions

Solid State Phenomena ◽

10.4028/www.scientific.net/ssp.316.661 ◽

2021 ◽

Vol 316 ◽

pp. 661-666

Author(s):

Nataliya V. Mokrova

Keyword(s):

Mathematical Modeling ◽

Mathematical Model ◽

Chemical Kinetics ◽

Group Method ◽

Data Handling ◽

Multistage Processes ◽

Leaching Process ◽

Proposed Model ◽

Simulation Results ◽

The Mathematical Model

Current cobalt processing practices are described. This article discusses the advantages of the group argument accounting method for mathematical modeling of the leaching process of cobalt solutions. Identification of the mathematical model of the cascade of reactors of cobalt-producing is presented. Group method of data handling is allowing: to eliminate the need to calculate quantities of chemical kinetics; to get the opportunity to take into account the results of mixed experiments; to exclude the influence of random interference on the simulation results. The proposed model confirms the capabilities of the group method of data handling for describing multistage processes.

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Population Behavior in the Mathematical Model of the Spread of COVID19 Type SEIRS

Jurnal Inotera ◽

10.31572/inotera.vol6.iss2.2021.id147 ◽

2021 ◽

Vol 6 (2) ◽

pp. 83-88

Author(s):

Asmaidi As Med ◽

Resky Rusnanda

Keyword(s):

Mathematical Modeling ◽

Numerical Simulation ◽

Mathematical Model ◽

Everyday Life ◽

Applied Mathematics ◽

Living Things ◽

Simulation Results ◽

Parameter Values ◽

The Mathematical Model ◽

Disease Free

Mathematical modeling utilized to simplify real phenomena that occur in everyday life. Mathematical modeling is popular to modeling the case of the spread of disease in an area, the growth of living things, and social behavior in everyday life and so on. This type of research is included in the study of theoretical and applied mathematics. The research steps carried out include 1) constructing a mathematical model type SEIRS, 2) analysis on the SEIRS type mathematical model by using parameter values for conditions 1and , 3) Numerical simulation to see the behavior of the population in the model, and 4) to conclude the results of the numerical simulation of the SEIRS type mathematical model. The simulation results show that the model stabilized in disease free quilibrium for the condition and stabilized in endemic equilibrium for the condition .

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