scholarly journals The Dynamics of a Single Species in a Polluted Environment

2020 ◽  
pp. 1-12
Author(s):  
Raid Kamel Naji ◽  
Mona Ghassan Younis ◽  
Mohammad Naeemullah
Keyword(s):  
Mathematical Model ◽  
Equilibrium Point ◽  
Local Stability ◽  
Single Species ◽  
Global Dynamics ◽  
Polluted Environment ◽  
Nonlinear Mathematical Model ◽  
Proposed Model

This article proposed and analysed a nonlinear mathematical model that consist of a single species in a polluted environment (PE). The proposed model was also discussed in terms of its uniqueness, existence, and boundedness of the solution. Also, each possible equilibrium point was analysed for local stability, followed by investigation of the global dynamics of the system using the Lypanov functions. The effects of the presence of toxicants on the dynamics of a single species in the PE was numerically investigated

scholarly journals The effect of environmental tax on the survival of biological species in a polluted environment: a mathematical model

2010 ◽  
Vol 15 (3) ◽  
pp. 271-286 ◽  
Author(s):  
S. Agarwal ◽  
S. Devi
Keyword(s):  
Mathematical Model ◽  
Local Stability ◽  
Emission Rate ◽  
Concentration Level ◽  
Biological Species ◽  
Environmental Taxes ◽  
Environmental Tax ◽  
Polluted Environment ◽  
Nonlinear Mathematical Model ◽  
Runge Kutta Method

In this paper, a nonlinear mathematical model is proposed and analyzed for the survival of biological species affected by a pollutant present in the environment. It is considered that the emission of the pollutant into the environment is dynamic in nature and depends on the environmental tax imposed on the emitters. It is also assumed that the environmental tax is imposed to control the emission of pollutants only when the concentration level of pollutants in the environment crosses a limit over which the pollutants starts causing harm to the population under consideration. Criteria for local stability, global stability and permanence are obtained using theory of ordinary differential equations. Numerical simulations are carried out to investigate the dynamics of the system using fourth order Runge–Kutta Method. It is found that, as the emission rate of pollutants in the environment increases, the density of biological species decreases. It may also be pointed out that the biological species may even become extinct if the rate of emission of pollutants increases continuously. However, if some environmental taxes are imposed to control the rate of emission of these pollutants into the environment, the density of biological species can be maintained at a desired level.

Dynamics of populations with two sexes

2015 ◽  
Vol 08 (04) ◽  
pp. 1550049
Author(s):  
M. Cecilia Pérez ◽  
E. Adriana Saavedra ◽  
Mariano A. Ferrari
Keyword(s):  
Mathematical Model ◽  
Local Stability ◽  
Elephant Seal ◽  
Southern Elephant Seal ◽  
Real Population ◽  
Proposed Model ◽  
Males And Females ◽  
Direct Applicability ◽  
State Existence ◽  
Dynamics Of Populations

A mathematical model is presented in order to describe the dynamics of polygamous populations, bearing in mind single individuals of both sexes and the development of reproductive groups. In this context, the description leads us to consider positive homogeneous dynamical systems, establishing conditions for the stationary state existence and its local stability. A fourth pre-reproductive stage was considered, i.e. males and females spend part of their lives before being in condition to reproduce, as a first step to consider more general models. Finally, we parametrized the proposed model using southern elephant seal data, to analyze the direct applicability to a real population.

A MODEL FOR THE EFFECT OF TIME DELAY ON THE DYNAMICS OF A POPULATION LIVING IN A POLLUTED ENVIRONMENT

2004 ◽  
Vol 12 (01) ◽  
pp. 35-43 ◽  
Author(s):  
B. DUBEY
Keyword(s):  
Mathematical Model ◽  
Time Delay ◽  
Single Species ◽  
Polluted Environment ◽  
Species Population ◽  
Single Species Population

In this paper, a mathematical model is proposed and analyzed to study the effect of time delay on the dynamics of a single-species population living in a polluted environment. It is shown that time delay in the model has destabilizing effect on the system.

scholarly journals Sensitivity and mathematical model analysis on secondhand smoking tobacco

2020 ◽  
Vol 28 (1) ◽  
Author(s):  
Birliew Fekede ◽  
Benyam Mebrate
Keyword(s):  
Mathematical Model ◽  
Equilibrium Point ◽  
Equilibrium Points ◽  
Reproductive Number ◽  
Primary Case ◽  
Susceptible Population ◽  
Proposed Model ◽  
Relative Change ◽  
Well Posed ◽  
Mathematical Model Analysis

AbstractIn this paper, we are concerned with a mathematical model of secondhand smoker. The model is biologically meaningful and mathematically well posed. The reproductive number $$R_{0}$$ R 0 is determined from the model, and it measures the average number of secondary cases generated by a single primary case in a fully susceptible population. If $$R_{0}<1,$$ R 0 < 1 , the smoking-free equilibrium point is stable, and if $$R_{0}>1,$$ R 0 > 1 , endemic equilibrium point is unstable. We also provide numerical simulation to show stability of equilibrium points. In addition, sensitivity analysis of parameters involving in the dynamic system of the proposed model has been included. The parameters involving in reproductive number measure the relative change in $$R_{0}$$ R 0 when the value of the parameter changes.

A MODEL FOR AN INSHORE-OFFSHORE FISHERY

2003 ◽  
Vol 11 (01) ◽  
pp. 27-41 ◽  
Author(s):  
B. DUBEY ◽  
P. SINHA ◽  
P. CHANDRA
Keyword(s):  
Mathematical Model ◽  
Global Stability ◽  
Local Stability ◽  
Optimal Harvesting ◽  
Discount Rates ◽  
Nonlinear Mathematical Model ◽  
Optimal Harvesting Policy ◽  
Fishery Resources ◽  
Control Instrument

In this paper, a nonlinear mathematical model to study the dynamics of an inshore-offshore fishery under variable harvesting is proposed and analyzed. Criteria for local stability, instability and global stability of the system are derived. The optimal harvesting policy is discussed by considering taxation as a control instrument. It is shown that the fishery resources can be protected from overexploitation by increasing the tax and discount rates.

scholarly journals Controlling Pest by Integrated Pest Management: A Dynamical Approach

2020 ◽  
Vol 5 (4) ◽  
pp. 769-786
Author(s):  
Vandana Kumari ◽  
Sudipa Chauhan ◽  
Joydip Dhar
Keyword(s):  
Mathematical Model ◽  
Equilibrium Point ◽  
Integrated Pest Management ◽  
Pest Management ◽  
Chemical Control ◽  
Local Stability ◽  
Equilibrium Points ◽  
Uniform Boundedness ◽  
Management Technique ◽  
Pest Population

Integrated Pest Management technique is used to formulate a mathematical model by using biological and chemical control impulsively. The uniform boundedness and the existence of pest extinction and nontrivial equilibrium points is discussed. Further, local stability of pest extinction equilibrium point is studied and it has been derived that if T≤T_max, the pest extinction equilibrium point is locally stable and for T>T_max, the system is permanent. It has also been obtained that how delay helps in eradicating pest population more quickly. Finally, analytic results have been validated numerically.

scholarly journals Mathematical Model for Coronavirus Disease 2019 (COVID-19) Containing Isolation Class

2020 ◽  
Vol 2020 ◽  
pp. 1-7 ◽  
Author(s):  
Anwar Zeb ◽  
Ebraheem Alzahrani ◽  
Vedat Suat Erturk ◽  
Gul Zaman
Keyword(s):  
Mathematical Model ◽  
Finite Difference ◽  
Local Stability ◽  
Dynamical Behavior ◽  
Order Method ◽  
Human Contact ◽  
Proposed Model ◽  
Fourth Order Method ◽  
Nsfd Scheme ◽  
Nonstandard Finite Difference

The deadly coronavirus continues to spread across the globe, and mathematical models can be used to show suspected, recovered, and deceased coronavirus patients, as well as how many people have been tested. Researchers still do not know definitively whether surviving a COVID-19 infection means you gain long-lasting immunity and, if so, for how long? In order to understand, we think that this study may lead to better guessing the spread of this pandemic in future. We develop a mathematical model to present the dynamical behavior of COVID-19 infection by incorporating isolation class. First, the formulation of model is proposed; then, positivity of the model is discussed. The local stability and global stability of proposed model are presented, which depended on the basic reproductive. For the numerical solution of the proposed model, the nonstandard finite difference (NSFD) scheme and Runge-Kutta fourth order method are used. Finally, some graphical results are presented. Our findings show that human to human contact is the potential cause of outbreaks of COVID-19. Therefore, isolation of the infected human overall can reduce the risk of future COVID-19 spread.

scholarly journals A mathematical Model for the Dynamics of COVID-19 Pandemy Involving the Infective Immigrants

2021 ◽  
pp. 295-307
Author(s):  
Ahmed A. Mohsen ◽  
Hassan F. AL-Husseiny ◽  
Khalid Hattaf ◽  
Bilal Boulfoul
Keyword(s):  
Mathematical Model ◽  
Equilibrium Point ◽  
Foreign Students ◽  
Dynamical Behavior ◽  
Foreign Workers ◽  
Proposed Model ◽  
Rapid Spread ◽  
The Stability ◽  
Control And Management ◽  
Stability Results

Since the first outbreak in Wuhan, China, in December 31, 2019, COVID-19    pandemy  ‎has been spreading to many countries in the world. The ongoing COVID-19 pandemy has caused a ‎major global crisis, with 554,767 total confirmed cases, 484,570 total recovered cases, and ‎‎12,306 deaths in Iraq as of February 2, 2020. In the absence of any effective therapeutics or drugs ‎and with an unknown epidemiological life cycle, predictive mathematical models can aid in ‎the understanding of both control and management of coronavirus disease. Among the important ‎factors that helped the rapid spread of the epidemy are immigration, travelers, foreign workers, and foreign students. In this work, we develop a mathematical model to study the dynamical ‎behavior of COVID-19 pandemy, involving immigrants' effects with the possibility of re-infection. ‎Firstly, we studied the positivity and roundedness of the solution of the proposed model. The stability ‎results of the model at the disease-free equilibrium point were presented when . Further, it was proven that the pandemic equilibrium point will persist uniformly when . Moreover, we ‎confirmed the occurrence of the local bifurcation (saddle-node, pitchfork, and transcritical). Finally, ‎theoretical analysis and numerical results were shown to be consistent.

scholarly journals Mathematical Analysis of Intraguild Interactions among Hosts, Parasitoids and Predators

2021 ◽  
Vol 52 (1) ◽  
pp. 171-187
Author(s):  
Hongming You ◽  
Kaijen Cheng
Keyword(s):  
Mathematical Model ◽  
Mathematical Analysis ◽  
Local Stability ◽  
Global Dynamics ◽  
Intraguild Interactions ◽  
Positivity Of Solution

In this work, we consider a mathematical model of an omnivorous ecosystem in which intermediate predators are infected by parasites. We first establish the boundeness and positivity of solution with conditions. Then the existence and local stability of all equilibria are clarified in R4. Finally, some global dynamics will be analyzed.  

EXISTENCE AND SURVIVAL OF TWO COMPETING SPECIES IN A POLLUTED ENVIRONMENT: A MATHEMATICAL MODEL

2001 ◽  
Vol 09 (02) ◽  
pp. 89-103 ◽  
Author(s):  
J. B. SHUKLA ◽  
A. K. AGRAWAL ◽  
B. DUBEY ◽  
P. SINHA
Keyword(s):  
Mathematical Model ◽  
Growth Rate ◽  
Emission Rate ◽  
Biological Species ◽  
Rate Coefficients ◽  
Washout Rate ◽  
Polluted Environment ◽  
Nonlinear Mathematical Model ◽  
Model Study ◽  
External Sources

In this paper, a nonlinear mathematical model to study the effect of a toxicant emitted into the environment from external sources on two competing biological species is proposed and analyzed. The cases of constant emission and instantaneous spill of a toxicant are considered in the model study. In the case of constant emission, it is shown that four usual outcomes of competition between two species may be altered under appropriate conditions which are mainly dependent on emission rate of toxicant into the environment, uptake concentrations of toxicant by the two species and their growth rate coefficients and carrying capacities. However, in the case of instantaneous spill, it is found that if the washout rate of toxicant is large, then the four outcomes of competition exist under usual conditions. It is also pointed out that the survival of the competitors, coexisting in absence of the toxicant, may be threatened if the constant emission of toxicant into their environment continues unabatedly.

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