scholarly journals A Mathematical Model to Study the Effectiveness of Some of the Strategies Adopted in Curtailing the Spread of COVID-19

2020 ◽  
Vol 2020 ◽  
pp. 1-6 ◽  
Author(s):  
Isa Abdullahi Baba ◽  
Bashir Abdullahi Baba ◽  
Parvaneh Esmaili
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Numerical Simulations ◽  
Government Policy ◽  
Local Stability ◽  
Equilibrium Points ◽  
Compartmental Models ◽  
Effective Strategy ◽  
Local Stability Analysis ◽  
The Government

In this paper, we developed a model that suggests the use of robots in identifying COVID-19-positive patients and which studied the effectiveness of the government policy of prohibiting migration of individuals into their countries especially from those countries that were known to have COVID-19 epidemic. Two compartmental models consisting of two equations each were constructed. The models studied the use of robots for the identification of COVID-19-positive patients. The effect of migration ban strategy was also studied. Four biologically meaningful equilibrium points were found. Their local stability analysis was also carried out. Numerical simulations were carried out, and the most effective strategy to curtail the spread of the disease was shown.

DYNAMICS OF A SEGMENTATION CLOCK MODEL WITH DISCRETE AND DISTRIBUTED DELAYS

2010 ◽  
Vol 03 (04) ◽  
pp. 399-416 ◽  
Author(s):  
PENG FENG
Keyword(s):  
Stability Analysis ◽  
Numerical Simulations ◽  
Local Stability ◽  
Time Delays ◽  
Distributed Delay ◽  
Distributed Delays ◽  
Clock Model ◽  
Segmentation Clock ◽  
Local Stability Analysis ◽  
First Case

In this paper, we study the effects of time delays on the dynamics of a segmentation clock model with both discrete and distributed delays. Two cases are considered. The first case corresponds to the model with only distributed delay. The second case involves both discrete and distributed delay. Local stability analysis is carried out for all cases. Numerical simulations are also performed to illustrate the results.

scholarly journals A Mathematical Modeling of Tuberculosis Dynamics with Hygiene Consciousness as a Control Strategy

2020 ◽  
pp. 38-48
Author(s):  
Phineas Z. Mawira ◽  
David M. Malonza
Keyword(s):  
Stability Analysis ◽  
Global Stability ◽  
Control Strategy ◽  
Local Stability ◽  
Equilibrium Points ◽  
Asymptotically Stable ◽  
Linear Ordinary Differential Equations ◽  
Global Stability Analysis ◽  
Local Stability Analysis ◽  
Disease Free

Tuberculosis, an airborne infectious disease, remains a major threat to public health in Kenya. In this study, we derived a system of non-linear ordinary differential equations from the SLICR mathematical model of TB to study the effects of hygiene consciousness as a control strategy against TB in Kenya. The effective basic reproduction number (R0) of the model was determined by the next generation matrix approach. We established and analyzed the equilibrium points. Using the Routh-Hurwitz criterion for local stability analysis and comparison theorem for global stability analysis, the disease-free equilibrium (DFE) was found to be locally asymptotically stable given that R0 < 1.  Also by using the Routh-Hurwitz criterion for local stability analysis and Lyapunov function and LaSalle’s invariance principle for global stability analysis, the endemic equilibrium (EE) point was found to be locally asymptotically stable given that R0 > 1. Using MATLAB ode45 solver, we simulated the model numerically and the results suggest that hygiene consciousness can helpin controlling TB disease if incorporated effectively.

Modelling the impacts of lockdown and isolation on the eradication of COVID-19

BIOMATH ◽  
2020 ◽  
Vol 9 (2) ◽  
pp. 2009107
Author(s):  
Joel N. Ndam
Keyword(s):  
Stability Analysis ◽  
Social Isolation ◽  
Local Stability ◽  
Effective Means ◽  
Asymptotically Stable ◽  
Effective Strategy ◽  
Local Stability Analysis ◽  
Strict Enforcement ◽  
Model Equations ◽  
Disease Free

A model describing the dynamics of COVID-19 is formulated and examined. The model is meant to address the impacts of lockdown and social isolation as strategies for the eradication of the pandemic. Local stability analysis indicate that the equilibria are locally-asymptotically stable for R0<1 and R_0>1 for the disease-free equilibrium and the endemic equilibrium respectively. Numerical simulations of the model equations show that lockdown is a more effective strategy in the eradication of the disease than social isolation. However, strict enforcement of both strategies is the most effective means that could end the disease within a shorter period of time.

scholarly journals Stability Analysis of Competing Insect Species for a Single Resource

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Sizah Mwalusepo ◽  
Henri E. Z. Tonnang ◽  
Estomih S. Massawe ◽  
Tino Johansson ◽  
Bruno Pierre Le Ru
Keyword(s):  
Stability Analysis ◽  
Local Stability ◽  
Equilibrium Points ◽  
Single Species ◽  
Insect Species ◽  
System Of Differential Equations ◽  
Competing Species ◽  
Local Study ◽  
Interior Equilibrium ◽  
Local Stability Analysis

The models explore the effects of resource and temperature on competition between insect species. A system of differential equations is proposed and analysed qualitatively using stability theory. A local study of the models is performed around axial, planar, and interior equilibrium points to successively estimate the effect of (i) one species interacting with a resource, (ii) two competing species for a single resource, and (iii) three competing species for a single resource. The local stability analysis of the equilibrium is discussed using Routh-Hurwitz criteria. Numerical simulation of the models is performed to investigate the sensitivity of certain key parameters. The models are used to predict population dynamics in the selected cases studied. The results show that when a single species interacts with a resource, the species will be able to establish and sustain a stable population. However, in competing situation, it is observed that the combinations of three parameters (half-saturation, growth rate, and mortality rate) determine which species wins for any given resource. Moreover, our results indicate that each species is the superior competitor for the resource for the range of temperature for which it has the lowest equilibrium resource.

Spread of Tuberculosis Among Smokers

2020 ◽  
pp. 49-73
Author(s):  
Purvi M. Pandya ◽  
Ekta N. Jayswal ◽  
Yash Shah
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Numerical Simulations ◽  
Psychological Health ◽  
Matrix Method ◽  
Equilibrium Points ◽  
Research Work ◽  
Linear Ordinary Differential Equations ◽  
Smoking Addiction ◽  
The Mathematical Model

Smoking tobacco has some hazardous implications on an individual's physical, physiological, and psychological health; health of the passive smokers near him or her; and on the surrounding environment. From carcinomas to auto-immune disorders, smoking has a role to play. Therefore, there arises a need to frame a systemic pathway to decipher relationship between smoking and a perilous disease such as tuberculosis. This research work focuses on how drugs or medications can affect individuals who are susceptible to tuberculosis because of smoking habits and also on individuals who have already developed symptoms of tuberculosis due to their smoking addiction. The mathematical model is formulated using non-linear ordinary differential equations, and then threshold is calculated for different equilibrium points using next generation matrix method. Stability analysis along with numerical simulations are carried out to validate the data.

scholarly journals Dynamics of a Cournot Duopoly Game with a Generalized Bounded Rationality

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-10 ◽  
Author(s):  
A. Al-khedhairi
Keyword(s):  
Stability Analysis ◽  
Bounded Rationality ◽  
Numerical Computation ◽  
Local Stability ◽  
Complex Dynamics ◽  
Equilibrium Points ◽  
Cournot Duopoly ◽  
Local Stability Analysis

In this paper, the dynamics of Cournot duopoly game with a generalized bounded rationality is considered. The fractional bounded rationality of the Cournot duopoly game is introduced. The conditions of local stability analysis of equilibrium points of the game are derived. The effect of fractional marginal profit on the game is investigated. The complex dynamics behaviors of the game are discussed by numerical computation when parameters are varied.

scholarly journals Stability behaviour of mathematical model MERS corona virus spread in population

Filomat ◽  
2019 ◽  
Vol 33 (12) ◽  
pp. 3947-3960 ◽  
Author(s):  
Muhammad Tahir ◽  
Syed Shah ◽  
Gul Zaman ◽  
Tahir Khan
Keyword(s):  
Stability Analysis ◽  
Local Stability ◽  
Equilibrium Points ◽  
Reproductive Number ◽  
Virus Spread ◽  
Global Stability Analysis ◽  
Local Stability Analysis ◽  
Proposed Model ◽  
Disease Free ◽  
Model Existence

In this subsection, we first formulated the proposed model in there infectious classes and then we derived the basic key value reproductive number, R0 with the help of next generation approach. Then we obtained all the endemic equilibrium points, as well as, local stability analysis, at disease free equilibria and, at endemic equilibria of the related model and shown stable. Further the global stability analysis either, at disease free equilibria, and at endemic equilibria is discussed by constructing Lyapunov function which show the validity of the concern model exist. In the last part of the article numerical simulation is presented for the model which support the model existence with the help of RK-4 method.

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