Simple Models for Avian Influenza

Ye, Xingyang; Li, Xuepeng

doi:10.1216/rmj-2008-38-5-1813

Cited by 3 publications

(4 citation statements)

References 6 publications

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“…The case of integer order model, ie, the counterpart with ν =1 of has been largely investigated in the literature; see, eg, Ye and Li . Model describes the interactions among the birds.…”

Section: Model Formulationmentioning

confidence: 99%

“…The case of integer order model, ie, the counterpart with = 1 of (2.1) has been largely investigated in the literature; see, eg, Ye and Li. 6 Model (2.1) describes the interactions among the birds. The parameter A is the constant recruitment rate at which new individuals come into the population in unit time, of which a fraction p(0 ≤ p < 1) is latent.…”

Section: Model Formulationmentioning

confidence: 99%

“…In order to understand the mechanism of the spread of avian influenza, a number of mathematical compartmental models have been introduced; see, eg, previous studies . However, most of these studies focused on an integer order compartmental epidemic model as a key tool for their investigation.…”

Section: Introductionmentioning

confidence: 99%

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A fractional order epidemic model and simulation for avian influenza dynamics

2019

Math Methods in App Sciences

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We present a nonlinear fractional order epidemic model to investigate the spreading dynamical behavior of the avian influenza. The population of the model contains susceptible individuals, asymptomatic but infective latent individuals, and infective individuals. We first establish the existence, uniqueness, nonnegativity, and positive invariance of the solution, then we study the reproduction number of the model and the stability of the disease‐free equilibrium. We observe that the reproduction number varies with the order of the fractional derivative ν. In terms of epidemics, this suggests that varying ν induces a change in the avian's epidemic status. Furthermore, we derive the sufficient conditions for the existence and the stability of the endemic equilibrium. Finally, we carry out some numerical simulations to validate the analytical results. We find from simulations that the solution of the fractional order model tends to a stationary state over a longer period of time with decreasing the value of the fractional derivative, and the size of epidemic decreases with decreasing ν.

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“…The case of integer order model, ie, the counterpart with ν =1 of has been largely investigated in the literature; see, eg, Ye and Li . Model describes the interactions among the birds.…”

Section: Model Formulationmentioning

confidence: 99%

Section: Model Formulationmentioning

confidence: 99%

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A fractional order epidemic model and simulation for avian influenza dynamics

2019

Math Methods in App Sciences

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“…Various of mathematical compartmental models have been introduced to study the mechanism of the spread of avian influenza. 1,4–8 However, most of these studies focused on an integer-order compartmental epidemic model as a key tool for their investigation. In recent years, it has frequently been observed in many areas of engineering, physics, life sciences, and elsewhere that models based on fractional order derivatives can provide better agreement between measured and simulated data than classical models based on integer order derivatives 9,10 and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Dynamical analysis of a fractional-order avian-human influenza epidemic model with logistic growth for avian population

Lin

2020

Journal of Algorithms & Computational Technology

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In this paper, a fractional order avian-human influenza epidemic model with logistic growth for avian population is investigated. The dynamical behavior of this model is discussed. We first establish the existence, uniqueness, non-negativity and positive invariance of the solution. Then we analyze the existence of various equilibrium points, and some sufficient conditions are derived to ensure the global asymptotic stability of the disease free equilibrium point and endemic equilibrium point. Finally, we take some numerical simulations to validate the analytical results.

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An SEI–SI avian–human influenza model with diffusion and nonlocal delay

Tang

Lin

2014

Applied Mathematics and Computation

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Simple Models for Avian Influenza

Cited by 3 publications

References 6 publications

A fractional order epidemic model and simulation for avian influenza dynamics

A fractional order epidemic model and simulation for avian influenza dynamics

Dynamical analysis of a fractional-order avian-human influenza epidemic model with logistic growth for avian population

An SEI–SI avian–human influenza model with diffusion and nonlocal delay

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