Analysis of a Non-integer Order Model for the Coinfection of HIV and HSV-2

2020 ◽  
Vol 21 (3-4) ◽  
pp. 291-302
Author(s):  
Carla M. A. Pinto ◽  
Ana R. M. Carvalho
Keyword(s):  
Local Stability ◽  
Reproduction Number ◽  
Point Of View ◽  
Order Derivative ◽  
Order Model ◽  
Integer Order ◽  
Disease Free

AbstractWe propose a non-integer order model for the dynamics of the coinfection of HIV and HSV-2. We calculate the reproduction number of the model and study the local stability of the disease-free equilibrium. Simulations of the model for the variation of epidemiologically relevant parameters and the order of the non-integer order derivative, α, reveal interesting dynamics. These results are discussed from an epidemiologically point of view.

scholarly journals An SEIARD epidemic model for COVID-19 in Mexico: mathematical analysis and state-level forecast

2020 ◽  
Author(s):  
Ugo Avila-Ponce de León ◽  
Ángel G. C. Pérez ◽  
Eric Avila-Vales
Keyword(s):  
Disease Transmission ◽  
Local Stability ◽  
Reproduction Number ◽  
State Level ◽  
Model Parameters ◽  
Relative Importance ◽  
Current Outbreak ◽  
Sensibility Analysis ◽  
Next Generation Matrix ◽  
Disease Free

We propose an SEIARD mathematical model to investigate the current outbreak of coronavirus disease (COVID-19) in Mexico. Our model incorporates the asymptomatic infected individuals, who represent the majority of the infected population (with symptoms or not) and could play an important role in spreading the virus without any knowledge. We calculate the basic reproduction number (R0) via the next-generation matrix method and estimate the per day infection, death and recovery rates. The local stability of the disease free equilibrium is established in terms of R0. A sensibility analysis is performed to determine the relative importance of the model parameters to the disease transmission. We calibrate the parameters of the SEIARD model to the reported number of infected cases and fatalities for several states in Mexico by minimizing the sum of squared errors and attempt to forecast the evolution of the outbreak until August 2020.

scholarly journals Backward and Hopf bifurcation analysis of an SEIRS COVID-19 epidemic model with saturated incidence and saturated treatment response

2020 ◽  
Author(s):  
David A. Oluyori ◽  
Ángel G. C. Pérez ◽  
Victor A. Okhuese ◽  
Muhammad Akram
Keyword(s):  
Hopf Bifurcation ◽  
Local Stability ◽  
Complex Dynamics ◽  
Reproduction Number ◽  
Backward Bifurcation ◽  
Treatment Measures ◽  
Saturated Incidence ◽  
Second Wave ◽  
Saturated Treatment ◽  
Disease Free

AbstractIn this work, we further the investigation of an SEIRS model to study the dynamics of the Coronavirus Disease 2019 pandemic. We derive the basic reproduction number R0 and study the local stability of the disease-free and endemic states. Since the condition R0 < 1 for our model does not determine if the disease will die out, we consider the backward bifurcation and Hopf bifurcation to understand the dynamics of the disease at the occurrence of a second wave and the kind of treatment measures needed to curtail it. Our results show that the limited availability of medical resources favours the emergence of complex dynamics that complicates the control of the outbreak.

QUALITATIVE STUDY FOR A MULTI-DRUG RESISTANT TB MODEL WITH EXOGENOUS REINFECTION AND RELAPSE

2012 ◽  
Vol 05 (04) ◽  
pp. 1250031 ◽  
Author(s):  
LUJU LIU ◽  
XINCHUN GAO
Keyword(s):  
Local Stability ◽  
Reproduction Number ◽  
Transmission Model ◽  
Drug Resistant ◽  
Full Model ◽  
Tuberculosis Transmission ◽  
Reproduction Numbers ◽  
Existence And Stability ◽  
Disease Free ◽  
Exogenous Reinfection

One tuberculosis transmission model is formulated by incorporating exogenous reinfection, relapse, and two treatment stages of infectious TB cases. The global stability of the unique disease-free equilibrium is obtained by applying the comparison principle if the effective reproduction number for the full model is less than unity. The existence and stability of the boundary equilibria are given by introducing the invasion reproduction numbers. Furthermore, the existence and local stability of the endemic equilibrium are addressed under some conditions.

scholarly journals Kestabilan Model Epidemi Seir dengan Matriks Hurwitz

2016 ◽  
Vol 11 (2) ◽  
pp. 74
Author(s):  
Roni Tri Putra ◽  
Sukatik - ◽  
Sri Nita
Keyword(s):  
Basic Reproduction Number ◽  
Epidemic Model ◽  
Local Stability ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Asymptotically Stable ◽  
Stability Of Equilibrium ◽  
Disease Free ◽  
The Basic Reproduction Number

In this paper, it will be studied local stability of equilibrium points of  a SEIR epidemic model with infectious force in latent, infected and immune period. From the model it will be found investigated the existence and its stability of points its equilibrium by Hurwitz matrices. The local stability of equilibrium points is depending on the value of the basic reproduction number  If   the disease free equilibrium is local asymptotically stable.

scholarly journals The local stability of a modified multi-strain SIR model for emerging viral strains

PLoS ONE ◽  
2020 ◽  
Vol 15 (12) ◽  
pp. e0243408
Author(s):  
Miguel Fudolig ◽  
Reka Howard
Keyword(s):  
Local Stability ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Sir Model ◽  
Original Strain ◽  
Viral Strain ◽  
Sir Epidemic Model ◽  
Sir Epidemic ◽  
Cross Immunity ◽  
Disease Free

We study a novel multi-strain SIR epidemic model with selective immunity by vaccination. A newer strain is made to emerge in the population when a preexisting strain has reached equilbrium. We assume that this newer strain does not exhibit cross-immunity with the original strain, hence those who are vaccinated and recovered from the original strain become susceptible to the newer strain. Recent events involving the COVID-19 virus shows that it is possible for a viral strain to emerge from a population at a time when the influenza virus, a well-known virus with a vaccine readily available, is active in a population. We solved for four different equilibrium points and investigated the conditions for existence and local stability. The reproduction number was also determined for the epidemiological model and found to be consistent with the local stability condition for the disease-free equilibrium.

scholarly journals Analysis of a Model for Coronavirus Spread

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 820 ◽  
Author(s):  
Youcef Belgaid ◽  
Mohamed Helal ◽  
Ezio Venturino
Keyword(s):  
Dynamical System ◽  
Mathematical Model ◽  
Global Stability ◽  
Basic Reproduction Number ◽  
Local Stability ◽  
Reproduction Number ◽  
Early Stage ◽  
Asymptomatic Individuals ◽  
Restrictive Measures ◽  
Disease Free

The spread of epidemics has always threatened humanity. In the present circumstance of the Coronavirus pandemic, a mathematical model is considered. It is formulated via a compartmental dynamical system. Its equilibria are investigated for local stability. Global stability is established for the disease-free point. The allowed steady states are an unlikely symptomatic-infected-free point, which must still be considered endemic due to the presence of asymptomatic individuals; and the disease-free and the full endemic equilibria. A transcritical bifurcation is shown to exist among them, preventing bistability. The disease basic reproduction number is calculated. Simulations show that contact restrictive measures are able to delay the epidemic’s outbreak, if taken at a very early stage. However, if lifted too early, they could become ineffective. In particular, an intermittent lock-down policy could be implemented, with the advantage of spreading the epidemics over a longer timespan, thereby reducing the sudden burden on hospitals.

Fractional Model for Malaria Disease

2013 ◽  
Author(s):  
Carla M. A. Pinto ◽  
J. A. Tenreiro Machado
Keyword(s):  
Fractional Order ◽  
Initial Conditions ◽  
Dynamical Evolution ◽  
Order Model ◽  
Fractional Model ◽  
Integer Order ◽  
A Value ◽  
Parameter Values ◽  
Future Work ◽  
Disease Free

In this paper we study a fractional order model for malaria transmission. It is considered the integer order model proposed by Chitnis et al [1] and we generalize it up to become a fractional model. The new model is simulated for distinct values of the fractional order. Are considered two initial conditions and a set of parameter values satisfying a value of the reproduction number, R0, less than one, for the integer model. In this case, there is co-existence of a stable disease free equilibrium and an endemic equilibrium. The results are in agreement with the integer order model and reveal that we can extend the dynamical evolution up to new types of transients. Future work will focus on analytically prove some of the results obtained.

scholarly journals Mathematical Analysis of TB Model with Vaccination and Saturated Incidence Rate

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Ashenafi Kelemu Mengistu ◽  
Peter J. Witbooi
Keyword(s):  
Local Stability ◽  
Reproduction Number ◽  
Model System ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Latently Infected ◽  
Saturated Incidence Rate ◽  
Saturated Incidence ◽  
Disease Free ◽  
The Basic Reproduction Number

The model system of ordinary differential equations considers two classes of latently infected individuals, with different risk of becoming infectious. The system has positive solutions. By constructing a Lyapunov function, it is proved that if the basic reproduction number is less than unity, then the disease-free equilibrium point is globally asymptotically stable. The Routh-Hurwitz criterion is used to prove the local stability of the endemic equilibrium when R 0 > 1 . The model is illustrated using parameters applicable to Ethiopia. A variety of numerical simulations are carried out to illustrate our main results.

scholarly journals Dynamics of an SEIRS COVID-19 Epidemic Model with Saturated Incidence and Saturated Treatment Response: Bifurcation Analysis and Simulations

2021 ◽  
Vol 1 (1) ◽  
pp. 39-56
Author(s):  
David A. Oluyori ◽  
◽  
Angel G. C. Perez ◽  
Victor A. Okhuese ◽  
Muhammad Akram ◽  
...  
Keyword(s):  
Local Stability ◽  
Complex Dynamics ◽  
Reproduction Number ◽  
Backward Bifurcation ◽  
Treatment Measures ◽  
Saturated Incidence ◽  
Asymptomatic Infections ◽  
Second Wave ◽  
Saturated Treatment ◽  
Disease Free

In this work, we study the dynamics of the Coronavirus Disease 2019 pandemic using an SEIRS model with saturated incidence and treatment rates. We derive the basic reproduction number R_0 and study the local stability of the disease-free and endemic states. Since the condition R_0<1 for our model does not determine if the disease will die out, we study the backward bifurcation and Hopf bifurcation to understand the dynamics of the disease at the occurrence of a second wave and the kind of treatment measures needed to curtail it. We present some numerical simulations considering the symptomatic and asymptomatic infections and make a comparison with the reported COVID-19 data for Nigeria. Our results show that the limited availability of medical resources favours the emergence of complex dynamics that complicates the control of the outbreak

scholarly journals SVIR Epidemic Model with Non Constant Population

CAUCHY ◽  
2018 ◽  
Vol 5 (3) ◽  
pp. 102
Author(s):  
Joko Harianto ◽  
Titik Suparwati
Keyword(s):  
Equilibrium Point ◽  
Epidemic Model ◽  
Local Stability ◽  
Reproduction Number ◽  
Endemic Equilibrium ◽  
Asymptotically Stable ◽  
System Disease ◽  
Local Stability Analysis ◽  
Disease Free ◽  
The Basic Reproduction Number

In this article, we present an SVIR epidemic model with deadly deseases and non constant population. We only discuss the local stability analysis of the model. Initially the basic formulation of the model is presented. Two equilibrium point exists for the system; disease free and endemic equilibrium point. The local stability of the disease free and endemic equilibrium exists when the basic reproduction number less or greater than unity, respectively. If the value of R0 less than one then the desease free equilibrium point is locally asymptotically stable, and if its exceeds, the endemic equilibrium point is locally asymptotically stable. The numerical results are presented for illustration.

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