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Global dynamics of avian influenza epidemic models with psychological effect.

Liu S, Pang L, Ruan S, Zhang X - Comput Math Methods Med (2015)

Bottom Line: The dynamical behavior of the model is studied by using the basic reproduction number.The results demonstrate that the saturation effect within avian population and the psychological effect in human population cannot change the stability of equilibria but can affect the number of infected humans if the disease is prevalent.Numerical simulations are given to support the theoretical results and sensitivity analyses of the basic reproduction number in terms of model parameters that are performed to seek for effective control measures for avian influenza.

View Article: PubMed Central - PubMed

Affiliation: School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China.

ABSTRACT
Cross-sectional surveys conducted in Thailand and China after the outbreaks of the avian influenza A H5N1 and H7N9 viruses show a high degree of awareness of human avian influenza in both urban and rural populations, a higher level of proper hygienic practice among urban residents, and in particular a dramatically reduced number of visits to live markets in urban population after the influenza A H7N9 outbreak in China in 2013. In this paper, taking into account the psychological effect toward avian influenza in the human population, a bird-to-human transmission model in which the avian population exhibits saturation effect is constructed. The dynamical behavior of the model is studied by using the basic reproduction number. The results demonstrate that the saturation effect within avian population and the psychological effect in human population cannot change the stability of equilibria but can affect the number of infected humans if the disease is prevalent. Numerical simulations are given to support the theoretical results and sensitivity analyses of the basic reproduction number in terms of model parameters that are performed to seek for effective control measures for avian influenza.

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The plots indicate that different values of the other parameter influence the values of Ih(t) when one parameter is fixed and ℛ0 < 1. (a) Parameter c influences the values of Ih(t) with b = 0.001; (b) parameter b influences the values of Ih(t) with c = 0.001.
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fig4: The plots indicate that different values of the other parameter influence the values of Ih(t) when one parameter is fixed and ℛ0 < 1. (a) Parameter c influences the values of Ih(t) with b = 0.001; (b) parameter b influences the values of Ih(t) with c = 0.001.

Mentions: Similarly, when parameter b is fixed, we can observe that the number of infected humans decreases with the increase of parameter c (see Figure 4(a)). When we fix parameter c and let parameter b change, we obtain a similar result (see Figure 4(b)). When both parameters b and c change simultaneously, we can see that the number of infected humans decreases obviously with the increase of parameters b and c (see Figure 5).


Global dynamics of avian influenza epidemic models with psychological effect.

Liu S, Pang L, Ruan S, Zhang X - Comput Math Methods Med (2015)

The plots indicate that different values of the other parameter influence the values of Ih(t) when one parameter is fixed and ℛ0 < 1. (a) Parameter c influences the values of Ih(t) with b = 0.001; (b) parameter b influences the values of Ih(t) with c = 0.001.
© Copyright Policy - open-access
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC4377454&req=5

fig4: The plots indicate that different values of the other parameter influence the values of Ih(t) when one parameter is fixed and ℛ0 < 1. (a) Parameter c influences the values of Ih(t) with b = 0.001; (b) parameter b influences the values of Ih(t) with c = 0.001.
Mentions: Similarly, when parameter b is fixed, we can observe that the number of infected humans decreases with the increase of parameter c (see Figure 4(a)). When we fix parameter c and let parameter b change, we obtain a similar result (see Figure 4(b)). When both parameters b and c change simultaneously, we can see that the number of infected humans decreases obviously with the increase of parameters b and c (see Figure 5).

Bottom Line: The dynamical behavior of the model is studied by using the basic reproduction number.The results demonstrate that the saturation effect within avian population and the psychological effect in human population cannot change the stability of equilibria but can affect the number of infected humans if the disease is prevalent.Numerical simulations are given to support the theoretical results and sensitivity analyses of the basic reproduction number in terms of model parameters that are performed to seek for effective control measures for avian influenza.

View Article: PubMed Central - PubMed

Affiliation: School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China.

ABSTRACT
Cross-sectional surveys conducted in Thailand and China after the outbreaks of the avian influenza A H5N1 and H7N9 viruses show a high degree of awareness of human avian influenza in both urban and rural populations, a higher level of proper hygienic practice among urban residents, and in particular a dramatically reduced number of visits to live markets in urban population after the influenza A H7N9 outbreak in China in 2013. In this paper, taking into account the psychological effect toward avian influenza in the human population, a bird-to-human transmission model in which the avian population exhibits saturation effect is constructed. The dynamical behavior of the model is studied by using the basic reproduction number. The results demonstrate that the saturation effect within avian population and the psychological effect in human population cannot change the stability of equilibria but can affect the number of infected humans if the disease is prevalent. Numerical simulations are given to support the theoretical results and sensitivity analyses of the basic reproduction number in terms of model parameters that are performed to seek for effective control measures for avian influenza.

Show MeSH
Related in: MedlinePlus