Stabiizing The Steady State Solution of Lasser Fever: Problems and Prospect

In order to determine the possibility of using the method of mathematical modeling for making long-term forecasts of channel deformations of trunk line underwater crossing (TLUC) through water obstacles, a methodology for performing and analyzing the results of mathematical modeling of channel deformations in the TLUC zone across the Kuban River is considered. Within the framework of the work, the following tasks were solved: 1) the format and composition of the initial data necessary for mathematical modeling were determined; 2) the procedure for assigning the boundaries of the computational domain of the model was considered, the computational domain was broken down into the computational grid, the zoning of the computational domain was performed by the value of the roughness coefficient; 3) the analysis of the results of modeling the water flow was carried out without taking the bottom deformations into account, as well as modeling the bottom deformations, the specifics of the verification and calibration calculations were determined to build a reliable mathematical model; 4) considered the possibility of using the method of mathematical modeling to check the stability of the bottom in the area of TLUC in the presence of man-made dumping or protective structure. It has been established that modeling the flow hydraulics and structure of currents, making short-term forecasts of local high-altitude reshaping of the bottom, determining the tendencies of erosion and accumulation of sediments upstream and downstream of protective structures are applicable for predicting channel deformations in the zone of the TLUC. In all these cases, it is mandatory to have materials from engineering-hydro-meteorological and engineering-geological surveys in an amount sufficient to compile a reliable mathematical model.

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A prey–predator model and control of a nematodes pest using control in banana: Mathematical modeling and qualitative analysis

International Journal of Biomathematics ◽

10.1142/s1793524521500893 ◽

2021 ◽

pp. 2150089

Author(s):

Sudhakar Yadav ◽

Vivek Kumar

Keyword(s):

Mathematical Modeling ◽

Mathematical Model ◽

Local Stability ◽

Detection Method ◽

Initial Release ◽

Pest Detection ◽

Predator Model ◽

And Control ◽

The Mathematical Model ◽

Theoretical Results

This study develops a mathematical model for describing the dynamics of the banana-nematodes and its pest detection method to help banana farmers. Two criteria: the mathematical model and the type of nematodes pest control system are discussed. The sensitivity analysis, local stability, global stability, and the dynamic behavior of the mathematical model are performed. Further, we also develop and discuss the optimal control mathematical model. This mathematical model represents various modes of management, including the initial release of infected predators as well as the destroying of nematodes. The theoretical results are shown and verified by numerical simulations.

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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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Simple MSEIR Model for Measles Transmission

Asian Research Journal of Mathematics ◽

10.9734/arjom/2019/v12i330090 ◽

2019 ◽

pp. 1-11

Author(s):

Mojeeb Al-Rahman EL-Nor Osman ◽

Appiagyei Ebenezer ◽

Isaac Kwasi Adu

Keyword(s):

Mathematical Model ◽

Basic Reproduction Number ◽

Recovery Rate ◽

Birth Rate ◽

Reproduction Number ◽

Progression Rate ◽

Asymptotically Stable ◽

The Stability ◽

Disease Free ◽

The Basic Reproduction Number

In this paper, an Immunity-Susceptible-Exposed-Infectious-Recovery (MSEIR) mathematical model was used to study the dynamics of measles transmission. We discussed that there exist a disease-free and an endemic equilibria. We also discussed the stability of both disease-free and endemic equilibria. The basic reproduction number is obtained. If , then the measles will spread and persist in the population. If , then the disease will die out. The disease was locally asymptotically stable if and unstable if . ALSO, WE PROVED THE GLOBAL STABILITY FOR THE DISEASE-FREE EQUILIBRIUM USING LASSALLE'S INVARIANCE PRINCIPLE OF Lyaponuv function. Furthermore, the endemic equilibrium was locally asymptotically stable if , under certain conditions. Numerical simulations were conducted to confirm our analytic results. Our findings were that, increasing the birth rate of humans, decreasing the progression rate, increasing the recovery rate and reducing the infectious rate can be useful in controlling and combating the measles.

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Solutions of a Linearized Mathematical Model for Capillary Formation in Tumor Angiogenesis: An Initial Data Perturbation Approximation

Computational and Mathematical Methods in Medicine ◽

10.1155/2013/789402 ◽

2013 ◽

Vol 2013 ◽

pp. 1-7 ◽

Cited By ~ 1

Author(s):

Serdal Pamuk

Keyword(s):

Mathematical Model ◽

Initial Data ◽

Tumor Angiogenesis ◽

Cell Movement ◽

Steady State Solution ◽

Stability Criteria ◽

Data Perturbation ◽

Capillary Formation ◽

The Stability ◽

Perturbation Approximation

We present a mathematical model for capillary formation in tumor angiogenesis and solve it by linearizing it using an initial data perturbation method. This method is highly effective to obtain solutions of nonlinear coupled differential equations. We also provide a specific example resulting, that even a few terms of the obtained series solutions are enough to have an idea for the endothelial cell movement in a capillary. MATLAB-generated figures are provided, and the stability criteria are determined for the steady-state solution of the cell equation.

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Improved Positioning of Pneumatic Cylinder by Using Flexible Coupling between the Piston and Rod

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1243/pime_proc_1992_206_151_02 ◽

1992 ◽

Vol 206 (6) ◽

pp. 431-435 ◽

Cited By ~ 4

Author(s):

G V Krejnin ◽

I L Krivz ◽

L A Smelov

Keyword(s):

Mathematical Model ◽

Computer Simulation ◽

Parameter Optimization ◽

Degrees Of Freedom ◽

Control Parameter ◽

Pneumatic Cylinder ◽

Output Link ◽

Positioning Accuracy ◽

Flexible Coupling ◽

And Control

Positioning accuracy of a pneumatic piston drive with flexible coupling between the piston and rod is considered. Improved positioning was expected due to the fact that the rod friction is usually considerably less than the piston friction. When the piston stops under the action of its friction force the rod continues the motion, providing the precision positioning of the output link. A mathematical model of a positioning pneumatic piston drive with two degrees of freedom was generated. Computer simulation of the performance of short and long strokes showed the feasibility of the improved positioning which provided design and control parameter optimization.

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Analysis of the SARS-CoV-2 Outbreak in Northern Cyprus using a Mathematical Model

10.21203/rs.3.rs-28213/v1 ◽

2020 ◽

Author(s):

Tamer Sanlidag ◽

Nazife Sultanoglu ◽

Bilgen Kaymakamzade ◽

Evren Hincal ◽

Murat Sayan ◽

...

Keyword(s):

Mathematical Model ◽

Basic Reproduction Number ◽

Reproduction Number ◽

Equilibrium Points ◽

Real Data ◽

Northern Cyprus ◽

The Stability ◽

Disease Free ◽

The Basic Reproduction Number

Abstract The present study studied the dynamics of SARS-CoV-2 in Northern-Cyprus (NC) by using real data and a designed mathematical model. The model consisted of two equilibrium points, which were disease-free and epidemic. The stability of the equilibrium points was determined by the magnitude of the basic reproduction number (𝑹𝟎). If 𝑹𝟎 < 1, the disease eventually disappears, if 𝑹𝟎 ≥ 1, the presence of an epidemic is stated. 𝑹𝟎 has been calculated patient zero, with a range of 2.38 to 0.65. Currently, the 𝑹𝟎 for NC was found to be 0.65, indicating that NC is free from the SARS-CoV-2 epidemic.

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Analysis of the SARS-CoV-2 Outbreak in Northern Cyprus using a Mathematical Model

10.21203/rs.3.rs-28704/v1 ◽

2020 ◽

Author(s):

Tamer Sanlidag ◽

Nazife Sultanoglu ◽

Bilgen Kaymakamzade ◽

Evren Hincal ◽

Murat Sayan ◽

...

Keyword(s):

Mathematical Model ◽

Basic Reproduction Number ◽

Reproduction Number ◽

Equilibrium Points ◽

Real Data ◽

Northern Cyprus ◽

The Stability ◽

Disease Free ◽

The Basic Reproduction Number

Abstract The present study studied the dynamics of SARS-CoV-2 in Northern-Cyprus (NC) by using real data and a designed mathematical model. The model consisted of two equilibrium points, which were disease-free and epidemic. The stability of the equilibrium points was determined by the magnitude of the basic reproduction number (𝑹𝟎). If 𝑹𝟎 < 1, the disease eventually disappears, if 𝑹𝟎 ≥ 1, the presence of an epidemic is stated. 𝑹𝟎 has been calculated patient zero, with a range of 2.38 to 0.65. Currently, the 𝑹𝟎 for NC was found to be 0.65, indicating that NC is free from the SARS-CoV-2epidemic.

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QUALITATIVE ANALYSIS OF A MATHEMATICAL MODEL FOR CAPILLARY FORMATION IN TUMOR ANGIOGENESIS

Mathematical Models and Methods in Applied Sciences ◽

10.1142/s0218202503002362 ◽

2003 ◽

Vol 13 (01) ◽

pp. 19-33 ◽

Cited By ~ 14

Author(s):

SERDAL PAMUK

Keyword(s):

Mathematical Model ◽

Steady State ◽

Qualitative Analysis ◽

Transition Probability ◽

Steady State Solution ◽

State Solution ◽

Transition Probability Density ◽

Capillary Formation ◽

Long Time ◽

The Stability

Qualitative analysis of a mathematical model for capillary formation is presented under assumptions that enzyme and fibronectin concentrations are in quasi-steady state. The aim of this paper is to prove mathematically that the long-time tendency of endothelial cells will be towards the transition probability density function of enzyme and fibronectin. Endothelial cell steady-state solution is obtained and a numerical simulation is provided to show that there is a close agreement between the steady-state solution obtained analytically and the numerically calculated steady-state of the related initial value problem, which provides strong evidence for the stability of this steady-state.

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Analysis of infectious disease transmission and prediction through SEIQR epidemic model

Nonautonomous Dynamical Systems ◽

10.1515/msds-2020-0126 ◽

2021 ◽

Vol 8 (1) ◽

pp. 75-86

Author(s):

Swati Tyagi ◽

Shaifu Gupta ◽

Syed Abbas ◽

Krishna Pada Das ◽

Baazaoui Riadh

Keyword(s):

Mathematical Model ◽

Infectious Diseases ◽

Disease Transmission ◽

Disease Spread ◽

Infectious Disease Transmission ◽

Control Measurement ◽

Dynamics And Control ◽

The Stability ◽

And Control ◽

Special Case

Abstract In literature, various mathematical models have been developed to have a better insight into the transmission dynamics and control the spread of infectious diseases. Aiming to explore more about various aspects of infectious diseases, in this work, we propose conceptual mathematical model through a SEIQR (Susceptible-Exposed-Infected-Quarantined-Recovered) mathematical model and its control measurement. We establish the positivity and boundedness of the solutions. We also compute the basic reproduction number and investigate the stability of equilibria for its epidemiological relevance. To validate the model and estimate the parameters to predict the disease spread, we consider the special case for COVID-19 to study the real cases of infected cases from [2] for Russia and India. For better insight, in addition to mathematical model, a history based LSTM model is trained to learn temporal patterns in COVID-19 time series and predict future trends. In the end, the future predictions from mathematical model and the LSTM based model are compared to generate reliable results.

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