A mathematical model of avian influenza with half-saturated incidence

2013 ◽  
Vol 133 (1) ◽  
pp. 23-38 ◽  
Author(s):  
Nyuk Sian Chong ◽  
Jean Michel Tchuenche ◽  
Robert J. Smith
Keyword(s):  
Mathematical Model ◽  
Avian Influenza ◽  
Saturated Incidence

scholarly journals Mathematical Model of Avian Influenza Epidemics with Vaccinating Poultry and Giving Treatment to Quarantined Infected Human

2019 ◽  
Author(s):  
Muhammad Kharis ◽  
Amidi Amidi ◽  
Arief Agoestanto
Keyword(s):  
Mathematical Model ◽  
Avian Influenza ◽  
Human Life ◽  
The Impact

Avian Influenza epidemics have an impact on human life both in the health and economic fields. This epidemic is one of major problem that causes the infected human get hospitalization. Some action are needed to prevent and reduce the impact of this outbreak. The actions which were done are vaccination in poultry, burning infected poultry, quarantining and giving treatment infected humans.

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

2020 ◽  
Vol 11 (04) ◽  
pp. 2050035
Author(s):  
Muhammad Altaf Khan ◽  
Saif Ullah ◽  
Yasir Khan ◽  
Muhammad Farhan
Keyword(s):  
Avian Influenza ◽  
Influenza Infection ◽  
Transmission Dynamics ◽  
Global Dynamics ◽  
Nonlinear Dynamical ◽  
Local And Global Dynamics ◽  
Proposed Model ◽  
Saturated Incidence Rate ◽  
Saturated Incidence ◽  
Disease Free

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.

Dynamics of an avian influenza model with half-saturated incidence

2019 ◽  
Vol 355 ◽  
pp. 399-416 ◽  
Author(s):  
Zhenfeng Shi ◽  
Xinhong Zhang ◽  
Daqing Jiang
Keyword(s):  
Avian Influenza ◽  
Saturated Incidence

A Pandemic Avian Influenza Mathematical Model

2009 ◽  
pp. 798-808
Author(s):  
Mohamed Derouich
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Avian Influenza ◽  
Influenza A ◽  
Human Infection ◽  
Influenza Viruses ◽  
Human Influenza ◽  
Influenza A Viruses ◽  
The World ◽  
Pandemic Avian Influenza

Throughout the world, seasonal outbreaks of influenza affect millions of people, killing about 500,000 individuals every year. Human influenza viruses are classified into 3 serotypes: A, B, and C. Only influenza A viruses can infect and multiply in avian species. During the last decades, important avian influenza epidemics have occurred and so far, the epidemics among birds have been transmitted to humans; but the most feared problem is the risk of pandemics that may be caused by person-to person transmission. The present mathematical model deals with the dynamics of human infection by avian influenza both in birds and in humans. Stability analysis is carried out and the behaviour of the disease is illustrated by simulation with different parameters values.

scholarly journals Analysis of the Dynamics of SI-SI-SEIR Avian Influenza A(H7N9) Epidemic Model with Re-infection

2020 ◽  
pp. 43-73
Author(s):  
Oluwafemi I. Bada ◽  
Abayomi S. Oke ◽  
Winfred N. Mutuku ◽  
Patrick O. Aye
Keyword(s):  
Mathematical Model ◽  
Avian Influenza ◽  
Global Stability ◽  
Numerical Simulations ◽  
Epidemic Model ◽  
Influenza A ◽  
Equilibrium Points ◽  
Local And Global Stability ◽  
Continuous Contact ◽  
Non Linear

The spread of Avian influenza in Asia, Europe and Africa ever since its emergence in 2003, has been endemic in many countries. In this study, a non-linear SI-SI-SEIR Mathematical model with re-infection as a result of continuous contact with both infected poultry from farm and market is proposed. Local and global stability of the three equilibrium points are established and numerical simulations are used to validate the results.

scholarly journals Stability Analysis of an Epidemic Model with Infected Immigrants and Optimal Vaccination

2019 ◽  
Vol 8 (2) ◽  
pp. 3071-3077
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Epidemic Model ◽  
Susceptible Individual ◽  
Susceptible Population ◽  
Vaccination Strategies ◽  
Saturated Incidence Rate ◽  
Saturated Incidence ◽  
The Impact ◽  
Disease Free

In this paper an SIR (Susceptible-infectious-recovered) epidemic model consisting of saturated incidence rate with vaccination to the susceptible individual in presence of infected immigrants is studied. Stabilities of disease free and endemic equilibrium are also analyzed. The impact of the infected immigrants in the spread of the illness in a populace is examined. A mathematical model has been used to investigate the inflow of the infected immigrants in a population who rapidly transmit the disease. By using appropriate vaccine level to the susceptible population, disease can be reduced. The main purpose of this work is minimizing the invectives and maximizes the recovered individuals. To attain this, apply optimal vaccination strategies by utilizing the pontryagin’s maximum principle (PMP). Speculative results are demonstrated through the numerical simulations

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