scholarly journals Volterra–Lyapunov Stability Analysis of the Solutions of Babesiosis Disease Model

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1272
Author(s):  
Fengsheng Chien ◽  
Stanford Shateyi
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Global Stability ◽  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Disease Model ◽  
Transmission Dynamics ◽  
Global Stability Analysis ◽  
Lyapunov Stability Analysis ◽  
Disease Free

This paper studies the global stability analysis of a mathematical model on Babesiosis transmission dynamics on bovines and ticks populations as proposed by Dang et al. First, the global stability analysis of disease-free equilibrium (DFE) is presented. Furthermore, using the properties of Volterra–Lyapunov matrices, we show that it is possible to prove the global stability of the endemic equilibrium. The property of symmetry in the structure of Volterra–Lyapunov matrices plays an important role in achieving this goal. Furthermore, numerical simulations are used to verify the result presented.

Global dynamics of hepatitis C viral infection with logistic proliferation

2016 ◽  
Vol 09 (04) ◽  
pp. 1650056
Author(s):  
Sandip Banerjee ◽  
Ram Keval ◽  
Sunita Gakkhar
Keyword(s):  
Mathematical Model ◽  
Hepatitis C Virus ◽  
Stability Analysis ◽  
Hepatitis C ◽  
Viral Infection ◽  
Global Stability ◽  
Geometric Approach ◽  
Global Dynamics ◽  
Viral Dynamics ◽  
Global Stability Analysis

A modified mathematical model of hepatitis C viral dynamics has been presented in this paper, which is described by four coupled ordinary differential equations. The aim of this paper is to perform global stability analysis using geometric approach to stability, based on the higher-order generalization of Bendixson’s criterion. The result is also supported numerically. An important epidemiological issue of eradicating hepatitis C virus has been addressed through the global stability analysis.

scholarly journals Stability analysis of a fractional ordered COVID-19 model

2021 ◽  
Vol 9 (1) ◽  
pp. 22-45 ◽  
Author(s):  
Meghadri Das ◽  
Guruprasad Samanta
Keyword(s):  
Stability Analysis ◽  
Global Stability ◽  
Compartmental Model ◽  
Equilibrium Points ◽  
Real Data ◽  
Transmission Dynamics ◽  
Sensitivity Index ◽  
Limited Information ◽  
First Case ◽  
Disease Free

Abstract The main purpose of this work is to study transmission dynamics of COVID-19 in Italy 2020, where the first case of Coronavirus disease 2019 (COVID-19) in Italy was reported on 31st January 2020. Taking into account the uncertainty due to the limited information about the Coronavirus (COVID-19), we have taken the modified Susceptible-Asymptomatic-Infectious-Recovered (SAIR) compartmental model under fractional order framework. We have formulated our model by subdividing infectious compartment into two sub compartments (reported and unreported) and introduced hospitalized class. In this work, we have studied the local and global stability of the system at different equilibrium points (disease free and endemic) and calculated sensitivity index for Italy scenario. The validity of the model is justified by comparing real data with the results obtained from simulations.

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.

Global stability analysis of pertussis transmission dynamics with maternally derived immunity compartment

2021 ◽  
Author(s):  
Aisha Aliyu Yakubu ◽  
Farah Aini Abdullah ◽  
Ahmad Izani Md Ismail ◽  
Yazariah Mohd Yatim
Keyword(s):  
Stability Analysis ◽  
Global Stability ◽  
Transmission Dynamics ◽  
Global Stability Analysis

scholarly journals On the Global Stability Analysis of Corona Virus Disease (COVID-19) Mathematical Model

2021 ◽  
pp. 81-87
Author(s):  
William Atokolo ◽  
Achonu Omale Joseph ◽  
Rose Veronica Paul ◽  
Abdul Sunday ◽  
Thomas Ugbojoide Onoja
Keyword(s):  
Stability Analysis ◽  
Global Stability ◽  
Initial Conditions ◽  
Virus Disease ◽  
Disease Model ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Global Stability Analysis ◽  
Corona Virus ◽  
The Stability

In this present work, we investigated the Global Stability Analysis of Corona virus disease model formulated by Atokolo et al in [11]. The COVID‑19 pandemic, also known as the coronavirus pandemic, is an ongoing pandemic that is ravaging the whole world. By constructing a Lyapunov function, we investigated the stability of the model Endemic Equilibrium state to be globally asymptotically stable. This results epidemiologically implies that the COVID-19 will invade the population in respective of the initial conditions (population) considered.

scholarly journals A Mathematical Model of Rabies Transmission Dynamics in Dogs Incorporating Public Health Education as a Control Strategy -A Case Study of Makueni County

2020 ◽  
pp. 1-11
Author(s):  
Jane S. Musaili ◽  
Isaac Chepkwony
Keyword(s):  
Public Health ◽  
Mathematical Model ◽  
Stability Analysis ◽  
Health Education ◽  
Control Strategy ◽  
Public Health Education ◽  
Transmission Dynamics ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Disease Free

Rabies is a zoonotic viral disease that aects all mammals including human beings. Dogs are responsible for 99% of human rabies cases and the disease is always fatal once the symptoms appear. In Kenya the disease is still endemic despite the fact that there are ecient vaccines for controlling the disease. In this project, we developed SIRS mathematical model using a system of ordinary dierential equations from the model to study the transmission dynamics of rabies virusin dogs using public health education as a control strategy. The reproduction number R0 was calculated using the Next Generation Matrix. Both disease free and endemics equilibrium points were determined and their stability analysis performed. From the stability analysis results it was found out that the disease free equilibrium point is both locally and globally asymptotically stable when R0 < 1 and the endemic equilibrium point is both locally and globally asymptotically stable when R0 > 1. Numerical simulations done using Matlab indicated that education of the public on administration of both pre and post exposure vaccines to dogs and responsible dog ownership leads to a decrease in the numbers of rabies virus infected dogs which shows that public health education is an ecient means for controlling rabies.

scholarly journals A model assessing potential benefits of isolation and mass testing on COVID-19: the case of Nigeria

2020 ◽  
Author(s):  
Faraimunashe Chirove ◽  
Chinwendu Emilian Madubueze ◽  
Zviiteyi Chazuka ◽  
Sunday Casmir Madubueze
Keyword(s):  
Stability Analysis ◽  
Global Stability ◽  
Mathematical Analysis ◽  
Final Size ◽  
Global Stability Analysis ◽  
Potential Benefits ◽  
Final Size Relation ◽  
Isolation Facilities ◽  
Size Relation ◽  
Disease Free

We consider a model with mass testing and isolation mimicking the current policies implemented in Nigeria and use the Nigerian daily cumulative cases to calibrate the model to obtain the optimal mass testing and isolation levels. Mathematical analysis was done and important thresholds such the peak size relation and final size relation were obtained. Global stability analysis of the disease-free equilibrium indicated that COVID-19 can be eradicated provided that $\mathcal{R}_0<1$ and unstable otherwise. Results from simulations revealed that an increase in mass testing and reduction of transmission from isolated individuals are associated with benefits of increasing detected cases, lowering peaks of symptomatic cases, increase in self-isolating cases, decrease in cumulative deaths and decrease in admissions into monitored isolation facilities in the case of Nigeria

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