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 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.

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.

scholarly journals TRANSMISSION DYNAMICS OF DENGUE IN COSTA RICA: THE ROLE OF HOSPITALIZATIONS

2019 ◽  
Vol 27 (1) ◽  
pp. 241-266
Author(s):  
FABIO SANCHEZ ◽  
JORGE ARROYO-ESQUIVEL ◽  
PAOLA VÁSQUEZ
Keyword(s):  
Costa Rica ◽  
Compartmental Model ◽  
Control Strategies ◽  
Transmission Dynamics ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Specific Parameter ◽  
Public Health Officials ◽  
Disease Free

For decades, dengue virus has caused major problems for public health officials in tropical and subtropical countries around the world. We construct a compartmental model that includes the role of hospitalized individuals in the transmission dynamics of dengue in Costa Rica. The basic reproductive number, R0, is computed, as well as a sensitivity analysis on R0 parameters. The global stability of the disease-free equilibrium is established. Numerical simulations under specific parameter scenarios are performed to determine optimal prevention/control strategies.

scholarly journals “Stability Analysis of Three Species Ammensalism Model with Time Delay”

2019 ◽  
Vol 8 (2S11) ◽  
pp. 3664-3670
Keyword(s):  
Numerical Simulation ◽  
Stability Analysis ◽  
Time Delay ◽  
Global Stability ◽  
Analytical Study ◽  
Present Model ◽  
Ecological Model ◽  
Equilibrium Points

The present model is devoted to an analytical study of a three species syn-ecological model which the 1 st species ( ) N1 ammensal on the 2 nd species ( ) N2 and 2 nd species ( ) N2 ammensal on the 3 rd species ( ) N3 . Here 1 st species and 2 nd species are neutral to each other. A time delay is established between 1 st species and 2 nd species and 2 nd species and 3rd species. All attainable equilibrium points of the model are known and native stability for each case is mentioned and also the global stability of co-existing state is discussed by constructing appropriate Lyapunov operate. Further, precise solutions of perturbed equations are derived. The steadiness analysis is supported by numerical simulation victimization MatLab.

scholarly journals Global Stability of Malaria Transmission Dynamics Model with Logistic Growth

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Abadi Abay Gebremeskel
Keyword(s):  
Sensitivity Analysis ◽  
Global Stability ◽  
Malaria Transmission ◽  
Equilibrium Points ◽  
Transmission Dynamics ◽  
Logistic Growth ◽  
Asymptotically Stable ◽  
Dynamics Model ◽  
Globally Asymptotically Stable ◽  
The Impact

Mathematical models become an important and popular tools to understand the dynamics of the disease and give an insight to reduce the impact of malaria burden within the community. Thus, this paper aims to apply a mathematical model to study global stability of malaria transmission dynamics model with logistic growth. Analysis of the model applies scaling and sensitivity analysis and sensitivity analysis of the model applied to understand the important parameters in transmission and prevalence of malaria disease. We derive the equilibrium points of the model and investigated their stabilities. The results of our analysis have shown that if R0≤1, then the disease-free equilibrium is globally asymptotically stable, and the disease dies out; if R0>1, then the unique endemic equilibrium point is globally asymptotically stable and the disease persists within the population. Furthermore, numerical simulations in the application of the model showed the abrupt and periodic variations.

scholarly journals Modeling the impact of early interventions on the transmission dynamics of coronavirus infection

F1000Research ◽  
2021 ◽  
Vol 10 ◽  
pp. 518
Author(s):  
Christopher Saaha Bornaa ◽  
Baba Seidu ◽  
Yakubu Ibrahim Seini
Keyword(s):  
Death Rate ◽  
Deterministic Model ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Transmission Probability ◽  
Transmission Dynamics ◽  
Early Interventions ◽  
Coronavirus Infection ◽  
The Impact ◽  
Disease Free

A deterministic model is proposed to describe the transmission dynamics of coronavirus infection with early interventions. Epidemiological studies have employed modeling to unravel knowledge that transformed the lives of families, communities, nations and the entire globe. The study established the stability of both disease free and endemic equilibria. Stability occurs when the reproduction number, R0, is less than unity for both disease free and endemic equilibrium points. The global stability of the disease-free equilibrium point of the model is established whenever the basic reproduction number R0 is less than or equal to unity. The reproduction number is also shown to be directly related to the transmission probability (β), rate at which latently infected individuals join the infected class (δ) and rate of recruitment (Λ). It is inversely related to natural death rate (μ), rate of early treatment (τ1), rate of hospitalization of infected individuals (θ) and Covid-induced death rate (σ). The analytical results established are confirmed by numerical simulation of the model.

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

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.

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

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.

MODELING THE SCHISTOSOMIASIS ON THE ISLETS IN NANJING

2012 ◽  
Vol 05 (04) ◽  
pp. 1250037 ◽  
Author(s):  
LONGXING QI ◽  
JING-AN CUI ◽  
YUAN GAO ◽  
HUAIPING ZHU
Keyword(s):  
Differential Equations ◽  
Global Stability ◽  
Field Study ◽  
Rattus Norvegicus ◽  
Compartmental Model ◽  
Endemic Equilibrium ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Parasitic Diseases ◽  
Disease Free

A compartmental model is established for schistosomiasis infection in Qianzhou and Zimuzhou, two islets in the center of Yangtzi River near Nanjing, P. R. China. The model consists of five differential equations about the susceptible and infected subpopulations of mammalian Rattus norvegicus and Oncomelania snails. We calculate the basic reproductive number R0 and discuss the global stability of the disease free equilibrium and the unique endemic equilibrium when it exists. The dynamics of the model can be characterized in terms of the basic reproductive number. The parameters in the model are estimated based on the data from the field study of the Nanjing Institute of Parasitic Diseases. Our analysis shows that in a natural isolated area where schistosomiasis is endemic, killing snails is more effective than killing Rattus norvegicus for the control of schistosomiasis.

Sign in / Sign up

Export Citation Format

Share Document