scholarly journals Stability Analysis and Clinic Phenomenon Simulation of a Fractional-Order HBV Infection Model

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Yongmei Su ◽  
Sinuo Liu ◽  
Shurui Song ◽  
Xiaoke Li ◽  
Yongan Ye
Keyword(s):  
Fractional Order ◽  
Equilibrium Points ◽  
Mass Action ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Infection Model ◽  
Order Model ◽  
Infected Cells ◽  
Set Up ◽  
Hbv Model

In this paper, a fractional-order HBV model was set up based on standard mass action incidences and quasisteady assumption. The basic reproductive number R0 and the cytotoxic T lymphocytes’ immune-response reproductive number R1 were derived. There were three equilibrium points of the model, and stable analysis of each equilibrium point was given with corresponding hypothesis about R0 or R1. Some numerical simulations were also given based on HBeAg clinical data, and the simulation showed that there existed positive logarithmic correlation between the number of infected cells and HBeAg, which was consistent with the clinical facts. The simulation also showed that the clinical individual differences should be reflected by the fractional-order model.

Modeling and stability analysis of the spread of novel coronavirus disease COVID-19

2021 ◽  
pp. 2150035
Author(s):  
A. George Maria Selvam ◽  
Jehad Alzabut ◽  
D. Abraham Vianny ◽  
Mary Jacintha ◽  
Fatma Bozkurt Yousef
Keyword(s):  
Fractional Order ◽  
Disease Transmission ◽  
Equilibrium Points ◽  
Sufficient Conditions ◽  
Basic Reproductive Number ◽  
Phase Portraits ◽  
Transmission Model ◽  
Reproductive Number ◽  
Discrete Version ◽  
Novel Coronavirus

Towards the end of 2019, the world witnessed the outbreak of Severe Acute Respiratory Syndrome Coronavirus-2 (COVID-19), a new strain of coronavirus that was unidentified in humans previously. In this paper, a new fractional-order Susceptible–Exposed–Infected–Hospitalized–Recovered (SEIHR) model is formulated for COVID-19, where the population is infected due to human transmission. The fractional-order discrete version of the model is obtained by the process of discretization and the basic reproductive number is calculated with the next-generation matrix approach. All equilibrium points related to the disease transmission model are then computed. Further, sufficient conditions to investigate all possible equilibria of the model are established in terms of the basic reproduction number (local stability) and are supported with time series, phase portraits and bifurcation diagrams. Finally, numerical simulations are provided to demonstrate the theoretical findings.

scholarly journals A case study of 2019-nCOV cases in Argentina with the real data based on daily cases from March 03, 2020 to March 29, 2021 using classical and fractional derivatives

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Pushpendra Kumar ◽  
Vedat Suat Erturk ◽  
Marina Murillo-Arcila ◽  
Ramashis Banerjee ◽  
A. Manickam
Keyword(s):  
Fractional Order ◽  
Trust Region ◽  
Simulated Data ◽  
Real Data ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Order Model ◽  
The Real ◽  
The Stability ◽  
Parameter Values

AbstractIn this study, our aim is to explore the dynamics of COVID-19 or 2019-nCOV in Argentina considering the parameter values based on the real data of this virus from March 03, 2020 to March 29, 2021 which is a data range of more than one complete year. We propose a Atangana–Baleanu type fractional-order model and simulate it by using predictor–corrector (P-C) method. First we introduce the biological nature of this virus in theoretical way and then formulate a mathematical model to define its dynamics. We use a well-known effective optimization scheme based on the renowned trust-region-reflective (TRR) method to perform the model calibration. We have plotted the real cases of COVID-19 and compared our integer-order model with the simulated data along with the calculation of basic reproductive number. Concerning fractional-order simulations, first we prove the existence and uniqueness of solution and then write the solution along with the stability of the given P-C method. A number of graphs at various fractional-order values are simulated to predict the future dynamics of the virus in Argentina which is the main contribution of this paper.

Stability and Hopf bifurcation of a delayed virus infection model with latently infected cells and Beddington–DeAngelis incidence

2020 ◽  
Vol 13 (05) ◽  
pp. 2050045
Author(s):  
Junxian Yang ◽  
Shoudong Bi
Keyword(s):  
Immune Response ◽  
Hopf Bifurcation ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Infection Model ◽  
Asymptotically Stable ◽  
Response Delay ◽  
Globally Asymptotically Stable ◽  
Latently Infected ◽  
Infected Cells

In this paper, the dynamical behaviors for a five-dimensional virus infection model with Latently Infected Cells and Beddington–DeAngelis incidence are investigated. In the model, four delays which denote the latently infected delay, the intracellular delay, virus production period and CTL response delay are considered. We define the basic reproductive number and the CTL immune reproductive number. By using Lyapunov functionals, LaSalle’s invariance principle and linearization method, the threshold conditions on the stability of each equilibrium are established. It is proved that when the basic reproductive number is less than or equal to unity, the infection-free equilibrium is globally asymptotically stable; when the CTL immune reproductive number is less than or equal to unity and the basic reproductive number is greater than unity, the immune-free infection equilibrium is globally asymptotically stable; when the CTL immune reproductive number is greater than unity and immune response delay is equal to zero, the immune infection equilibrium is globally asymptotically stable. The results show that immune response delay may destabilize the steady state of infection and lead to Hopf bifurcation. The existence of the Hopf bifurcation is discussed by using immune response delay as a bifurcation parameter. Numerical simulations are carried out to justify the analytical results.

scholarly journals Stability analysis of fractional order SEIR model for malaria disease in Khyber Pakhtunkhwa

2021 ◽  
Vol 54 (1) ◽  
pp. 326-334
Author(s):  
Noor Badshah ◽  
Haji Akbar
Keyword(s):  
Stability Analysis ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Equilibrium Points ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Next Generation ◽  
Seir Model ◽  
Khyber Pakhtunkhwa

Abstract We discussed stability analysis of susceptible-exposed-infectious-removed (SEIR) model for malaria disease through fractional order and check that malaria is epidemic or endemic in Khyber Pakhtunkhwa (Pakistan). We show that the model has two types of equilibrium points and check their stability through Routh-Hurwitz criterion. We find basic reproductive number using next-generation method. Finally, numerical simulations are also presented.

scholarly journals Modelling the effect of vertical transmission in the dynamics of HIV/AIDS in an age-structured population

2003 ◽  
Vol 21 (1) ◽  
pp. 82 ◽  
Author(s):  
J. Y. T. Mugisha ◽  
L. S. Luboobi
Keyword(s):  
Vertical Transmission ◽  
Equilibrium Points ◽  
Age Groups ◽  
Endemic Equilibrium ◽  
Mass Action ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
First Case ◽  
Age Structured ◽  
Hiv Aids

We use a continuous age-structured model of McKendrick-von-Foerster type to derive a two-age groups HIV/AIDS epidemic model. In the analysis of the model, keen interest is put on the role of vertical transmission in the dynamics of the spread of the epidemic. The model is analysed in two scenarios: the case when the force of infection is a constant and the case when we have it as a mass action. In the first case, the only possible equilibrium is the endemic equilibrium. In this situation, we show that if all babies born to infected mothers are HIV-free we have the basic reproductive number R0 = 0 and as such the epidemic will die out. In the second case, we show that both the disease-free and endemic equilibrium points exist. We also derive conditions for their stability.

ANALYSIS OF A STOCHASTIC HBV INFECTION MODEL WITH NONLINEAR INCIDENCE RATE

2019 ◽  
Vol 27 (03) ◽  
pp. 399-421 ◽  
Author(s):  
HONGWEN HUI ◽  
LIN-FEI NIE
Keyword(s):  
Numerical Simulations ◽  
Deterministic Model ◽  
Sufficient Conditions ◽  
Stochastic Perturbation ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Infection Model ◽  
Exponentially Stable ◽  
Infected Cells ◽  
Theoretical Results

Considering that environmental factors, diet, subconscious mind and other uncertainties play an important role in the process of delaying and treating diseases, we propose, in this paper, an amended Hepatitis B virus (HBV) model with stochastic perturbation, and investigate the longtime dynamics of this stochastic model. First, if the basic reproductive number of the corresponding deterministic model is less than 1, some sufficient conditions for almost surely exponentially stable in the sense of the infected cells and free virus are established, and the stationary probability density function of the uninfected sell is also obtained. Further, some sufficient conditions for the existence of the stationary distribution are obtained for the basic reproductive number more than 1. In addition, oscillatory behaviors of this model about the equilibrium of the corresponding deterministic model are discussed. Finally, numerical simulations demonstrate the main theoretical results and show stochastic virus model has more dynamic behaviors relative to its corresponding deterministic model. Theoretical results and numerical simulations imply that the intensity and “type (divided into positive and negative)” of white noise play very important roles in the treatment of infectious disease, which can make the disease more and more repetitive and unpredictable. Of course, comfortable environment, reasonable diet, optimistic mood and other positive uncertainty factors have active effects on the treatment and delaying of diseases, but not the converse.

scholarly journals A Fractional Order Model for Viral Infection with Cure of Infected Cells and Humoral Immunity

2018 ◽  
Vol 2018 ◽  
pp. 1-12
Author(s):  
Adnane Boukhouima ◽  
Khalid Hattaf ◽  
Noura Yousfi
Keyword(s):  
Viral Infection ◽  
Humoral Immunity ◽  
Host Cells ◽  
Infection Model ◽  
Order Model ◽  
Fractional Order Model ◽  
Infected Cells ◽  
Fractional Differential ◽  
Well Posed ◽  
Viral Infection Model

In this paper, we study the dynamics of a viral infection model formulated by five fractional differential equations (FDEs) to describe the interactions between host cells, virus, and humoral immunity presented by antibodies. The infection transmission process is modeled by Hattaf-Yousfi functional response which covers several forms of incidence rate existing in the literature. We first show that the model is mathematically and biologically well-posed. By constructing suitable Lyapunov functionals, the global stability of equilibria is established and characterized by two threshold parameters. Finally, some numerical simulations are presented to illustrate our theoretical analysis.

scholarly journals Nonlinear Dynamics and Chaos in a Fractional-Order HIV Model

2009 ◽  
Vol 2009 ◽  
pp. 1-12 ◽  
Author(s):  
Haiping Ye ◽  
Yongsheng Ding
Keyword(s):  
Fractional Order ◽  
Equation Model ◽  
Viral Diversity ◽  
Human Immune System ◽  
Order Model ◽  
Hiv Model ◽  
Interior Equilibrium ◽  
Infected Cells ◽  
The One ◽  
Predictor Corrector

We introduce fractional order into an HIV model. We consider the effect of viral diversity on the human immune system with frequency dependent rate of proliferation of cytotoxic T-lymphocytes (CTLs) and rate of elimination of infected cells by CTLs, based on a fractional-order differential equation model. For the one-virus model, our analysis shows that the interior equilibrium which is unstable in the classical integer-order model can become asymptotically stable in our fractional-order model and numerical simulations confirm this. We also present simulation results of the chaotic behaviors produced from the fractional-order HIV model with viral diversity by using an Adams-type predictor-corrector method.

scholarly journals Global Stability for a Viral Infection Model with Saturated Incidence Rate

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Huaqin Peng ◽  
Zhiming Guo
Keyword(s):  
Viral Infection ◽  
Global Stability ◽  
Incidence Rate ◽  
Sufficient Conditions ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Infection Model ◽  
Saturated Incidence Rate ◽  
Saturated Incidence ◽  
Viral Infection Model

A viral infection model with saturated incidence rate and viral infection with delay is derived and analyzed; the incidence rate is assumed to be a specific nonlinear formβxv/(1+αv). The existence and uniqueness of equilibrium are proved. The basic reproductive numberR0is given. The model is divided into two cases: with or without delay. In each case, by constructing Lyapunov functionals, necessary and sufficient conditions are given to ensure the global stability of the models.

scholarly journals Microsimulation of SARS-CoV-2 Transmission in Society

2021 ◽  
Author(s):  
Anthony R Green ◽  
Daniel Keep ◽  
Ian Piper
Keyword(s):  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Infection Model ◽  
Infection Rates ◽  
Social Distancing ◽  
Source Of Infection ◽  
Population Sizes ◽  
Doubling Times ◽  
Good Agreement ◽  
Infection Spread

The outbreak of the pandemic disease, COVID-19, has shown that the approaches by different countries has resulted in a range of infection rates through their societies. This has arisen from the varying personal behaviour and tactical use of lockdown strategies within each country. We report the use of microsimulation of a simulated community in Australia, using a discrete infection model within a community of residences, places of work and recreation to demonstrate the applicability of this method to both the current pandemic and to infection more generally. Simulations without any societal intervention on infection spread provided base simulations that could be compared with social and societal controls in the future and which were compared with the initial doubling times of country outbreaks across the world. Different population sizes were represented in some simulations and in other simulations the effects of either social distancing or the use of facial masks as personal behaviours was investigated within the community. Good agreement is found between the initial doubling times for several countries and the simulations that suggests that modelling infection as a collection of individual infections provides an alternative to current epidemiological models. The variation of the basic reproductive number, R0, with time and population size, suggests that one of the fundamentals assumptions in SIR type models is wrong, but varies according to the properties of the population being modelled. Investigation of the infection spread shows that the number of super-spreaders varies with the size of the population and occurs through contacts in clubs, supermarkets, schools and theatres where the source of infection is an employee and where there are high numbers of contacts. The simulations of individual control show that the benefits of social distancing or wearing masks is only fully realised where there is considerable compliance within society to these measures.

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