Modeling and scientific computing for the transmission dynamics of Avian influenza with half-saturated incidence

This paper presents the mathematical analysis of the dynamical system for avian influenza. The proposed model considers a nonlinear dynamical model of birds and human. The half-saturated incidence rate is used for the transmission of avian influenza infection. Rigorous mathematical results are presented for the proposed models. The local and global dynamics of each model are presented and proven that when [Formula: see text], then the disease-free equilibrium of each model is stable both locally and globally, and when [Formula: see text], then the endemic equilibrium is stable both locally and globally. The numerical results obtained for the proposed model shows that influenza could be eliminated from the community if the threshold is not greater than unity.

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Mathematical modeling approach to the transmission dynamics of pine wilt disease with saturated incidence rate

International Journal of Biomathematics ◽

10.1142/s1793524518500353 ◽

2018 ◽

Vol 11 (03) ◽

pp. 1850035 ◽

Cited By ~ 4

Author(s):

Muhammad Altaf Khan ◽

Kamil Shah ◽

Yasir Khan ◽

Saeed Islam

Keyword(s):

Incidence Rate ◽

Local Stability ◽

Pine Wilt Disease ◽

Wilt Disease ◽

Pine Wilt ◽

Proposed Model ◽

Saturated Incidence Rate ◽

Saturated Incidence ◽

Disease Free ◽

Endemic State

The present paper investigates the dynamics of pine wilt disease with saturated incidence rate. The proposed model is stable both locally and globally. The local stability of the disease-free equilibrium is determined by the basic reproduction [Formula: see text]. The disease-free equilibrium is stable locally and globally whenever [Formula: see text]. If [Formula: see text], then the endemic state is stable both locally and globally. Further, a brief discussion with conclusion on the numerical results of the proposed model is presented.

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The dynamics of a delayed deterministic and stochastic epidemic SIR models with a saturated incidence rate

Random Operators and Stochastic Equations ◽

10.1515/rose-2018-0021 ◽

2018 ◽

Vol 26 (4) ◽

pp. 235-245 ◽

Cited By ~ 1

Author(s):

Modeste N’zi ◽

Ilimidi Yattara

Keyword(s):

Stochastic Model ◽

White Noise ◽

Incidence Rate ◽

Deterministic Model ◽

Contact Rate ◽

Almost Sure Stability ◽

Saturated Incidence Rate ◽

Saturated Incidence ◽

Global Positive Solution ◽

Disease Free

AbstractWe treat a delayed SIR (susceptible, infected, recovered) epidemic model with a saturated incidence rate and its perturbation through the contact rate using a white noise. We start with a deterministic model and then add a perturbation on the contact rate using a white noise to obtain a stochastic model. We prove the existence and uniqueness of the global positive solution for both deterministic and stochastic delayed differential equations. Under suitable conditions on the parameters, we study the global asymptotic stability of the disease-free equilibrium of the deterministic model and the almost sure stability of the disease-free equilibrium of the stochastic model.

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Mathematical Analysis and Stochastic Stability of Nonlinear Epidemic Model with Incidence Rate

Asian Research Journal of Mathematics ◽

10.9734/arjom/2020/v16i730199 ◽

2020 ◽

pp. 8-19

Author(s):

Laid Chahrazed

Keyword(s):

Incidence Rate ◽

Epidemic Model ◽

Basic Reproductive Number ◽

Reproductive Number ◽

Globally Asymptotically Stable ◽

Saturated Incidence Rate ◽

Saturated Incidence ◽

The Stability ◽

Disease Free ◽

Temporary Immunity

In this work, we consider a nonlinear epidemic model with temporary immunity and saturated incidence rate. Size N(t) at time t, is divided into three sub classes, with N(t)=S(t)+I(t)+Q(t); where S(t), I(t) and Q(t) denote the sizes of the population susceptible to disease, infectious and quarantine members with the possibility of infection through temporary immunity, respectively. We have made the following contributions: The local stabilities of the infection-free equilibrium and endemic equilibrium are; analyzed, respectively. The stability of a disease-free equilibrium and the existence of other nontrivial equilibria can be determine by the ratio called the basic reproductive number, This paper study the reduce model with replace S with N, which does not have non-trivial periodic orbits with conditions. The endemic -disease point is globally asymptotically stable if R0 ˃1; and study some proprieties of equilibrium with theorems under some conditions. Finally the stochastic stabilities with the proof of some theorems. In this work, we have used the different references cited in different studies and especially the writing of the non-linear epidemic mathematical model with [1-7]. We have used the other references for the study the different stability and other sections with [8-26]; and sometimes the previous references.

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Asymptotic behavior of a stochastic delayed avian influenza model with saturated incidence rate

Mathematical Biosciences and Engineering ◽

10.3934/mbe.2020289 ◽

2020 ◽

Vol 17 (5) ◽

pp. 5341-5368

Author(s):

Yanyan Du ◽

◽

Ting Kang ◽

Qimin Zhang ◽

Keyword(s):

Asymptotic Behavior ◽

Avian Influenza ◽

Incidence Rate ◽

Saturated Incidence Rate ◽

Saturated Incidence

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On global dynamics of COVID-19 by using SQIR type model under non-linear saturated incidence rate

Alexandria Engineering Journal ◽

10.1016/j.aej.2020.08.040 ◽

2021 ◽

Vol 60 (1) ◽

pp. 393-399

Author(s):

Ebrahem A. Algehyne ◽

Rahim ud Din

Keyword(s):

Incidence Rate ◽

Type Model ◽

Global Dynamics ◽

Non Linear ◽

Saturated Incidence Rate ◽

Saturated Incidence

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Deterministic and stochastic stability of an SIRS epidemic model with a saturated incidence rate

Random Operators and Stochastic Equations ◽

10.1515/rose-2017-0002 ◽

2017 ◽

Vol 25 (1) ◽

Cited By ~ 1

Author(s):

Modeste N’zi ◽

Jacques Tano

Keyword(s):

Incidence Rate ◽

Epidemic Model ◽

Deterministic Model ◽

Random Noise ◽

Stochastic Version ◽

Noise Perturbation ◽

Sirs Epidemic Model ◽

Saturated Incidence Rate ◽

Saturated Incidence ◽

Disease Free

AbstractIn this paper, we formulate an epidemic model for the spread of an infectious disease in a population of varying size. The total population is divided into three distinct epidemiological subclass of individuals (susceptible, infectious and recovered) and we study a deterministic and stochastic models with saturated incidence rate. The stochastic model is obtained by incorporating a random noise into the deterministic model. In the deterministic case, we briefly discuss the global asymptotic stability of the disease free equilibrium by using a Lyapunov function. For the stochastic version, we study the global existence and positivity of the solution. Under suitable conditions on the intensity of the white noise perturbation, we prove that there are a

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Stability and Persistence of an Avian Influenza Epidemic Model with Impacts of Climate Change

Discrete Dynamics in Nature and Society ◽

10.1155/2016/7871251 ◽

2016 ◽

Vol 2016 ◽

pp. 1-16 ◽

Cited By ~ 1

Author(s):

Xiao-Yan Zhao ◽

Shu-Min Guo ◽

Mini Ghosh ◽

Xue-Zhi Li

Keyword(s):

Climate Change ◽

Seasonal Variation ◽

Avian Influenza ◽

Epidemic Model ◽

Transmission Dynamics ◽

Stability Conditions ◽

Influenza Epidemic ◽

Threshold Conditions ◽

Disease Free ◽

Impacts Of Climate Change

The growing number of reported avian influenza cases has prompted awareness of the importance of research methods to control the spread of the disease. Seasonal variation is one of the important factors that affect the spread of avian influenza. This paper presents a “nonautonomous” model to analyze the transmission dynamics of avian influenza with the effects of climate change. We obtain and discuss the global stability conditions of the disease-free equilibrium; the threshold conditions for persistence, permanence, and extinction of the disease; and the parameters with periodicity for controlling and eliminating the avian influenza.

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A Mathematical Model of COVID-19 Pandemic: A Case Study of Bangkok, Thailand

Computational and Mathematical Methods in Medicine ◽

10.1155/2021/6664483 ◽

2021 ◽

Vol 2021 ◽

pp. 1-11

Author(s):

Pakwan Riyapan ◽

Sherif Eneye Shuaib ◽

Arthit Intarasit

Keyword(s):

Mathematical Model ◽

Reproduction Number ◽

Transmission Dynamics ◽

Asymptotically Stable ◽

Globally Asymptotically Stable ◽

Proposed Model ◽

Next Generation Matrix ◽

Disease Free ◽

The Basic Reproduction Number

In this study, we propose a new mathematical model and analyze it to understand the transmission dynamics of the COVID-19 pandemic in Bangkok, Thailand. It is divided into seven compartmental classes, namely, susceptible S , exposed E , symptomatically infected I s , asymptomatically infected I a , quarantined Q , recovered R , and death D , respectively. The next-generation matrix approach was used to compute the basic reproduction number denoted as R cvd 19 of the proposed model. The results show that the disease-free equilibrium is globally asymptotically stable if R cvd 19 < 1 . On the other hand, the global asymptotic stability of the endemic equilibrium occurs if R cvd 19 > 1 . The mathematical analysis of the model is supported using numerical simulations. Moreover, the model’s analysis and numerical results prove that the consistent use of face masks would go on a long way in reducing the COVID-19 pandemic.

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A SATURATED TREATMENT MODEL FOR THE TRANSMISSION DYNAMICS OF RABIES

MALAYSIAN JOURNAL OF COMPUTING ◽

10.24191/mjoc.v4i1.6119 ◽

2019 ◽

Vol 4 (1) ◽

pp. 201

Author(s):

A A Ayoade ◽

O J Peter ◽

T A Ayoola ◽

S Amadiegwu ◽

A A Victor

Keyword(s):

Incidence Rate ◽

Nonlinear Differential Equations ◽

Viral Disease ◽

Control Measures ◽

Transmission Dynamics ◽

Infectious Agents ◽

Multiple Control ◽

Saturated Incidence Rate ◽

Saturated Incidence ◽

Saturated Treatment

Rabies is a viral disease that claims about 59 000 lives globally every year. The ignorance of the fact that man can be a carrier of the disease makes every practical and theoretical approach towards the study of the disease a good development. In this work, a mathematical model is designed to incorporate a saturated incidence rate such that the incidence rate is saturated around the infectious agents. The model is studied qualitatively via stability theory of nonlinear differential equations to assess the effects of general awareness, constant vaccination and the saturated treatment on the transmission dynamics of rabies disease. The effective reproduction number is derived and the numerical simulation is carried out to verify the analytical results. It is discovered that while general awareness plays pivotal roles in averting rabies death, multiple control measures have the tendency of driving rabies to extinction.

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