Dynamic behavior of swine influenza transmission during the breed-slaughter process

Fangyuan Chen; Rong Yuan; Fangyuan Chen; Rong Yuan

doi:10.3934/mbe.2020312

Mathematical Biosciences and Engineering

2020, Volume 17, Issue 5: 5849-5863. doi: 10.3934/mbe.2020312

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Dynamic behavior of swine influenza transmission during the breed-slaughter process

Fangyuan Chen ^,,
Rong Yuan

School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China

Received: 20 May 2020 Accepted: 24 August 2020 Published: 02 September 2020

Global influenza pandemics have brought about various public health crises, such as the 2009 H1N1 swine flu. Actually, most swine influenza infections occur during the breed-slaughter process. However, there is little research about the mathematical model to elaborate on the swine influenza transmission with human-pig interaction. In this paper, a new breed-slaughter model with swine influenza transmission is proposed, and the equilibrium points of the model are calculated subsequently. Meanwhile, we analyze the existence of the equilibrium points by the persistence theory, and discuss their stability by the basic reproduction number. And then, we focus on the invasion process of infected domestic animals into the habitat of humans. Under certain conditions as in Theorem 2, we construct a propagating terrace linking human habitat to animal-human coexistent habitat, then to swine flu natural foci, which is divided by spreading speeds.
- swine influenza transmission,
- breed-slaughter model,
- basic reproduction number,
- propagating terrace,
- spreading speed
Citation: Fangyuan Chen, Rong Yuan. Dynamic behavior of swine influenza transmission during the breed-slaughter process[J]. Mathematical Biosciences and Engineering, 2020, 17(5): 5849-5863. doi: 10.3934/mbe.2020312

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Abstract

Global influenza pandemics have brought about various public health crises, such as the 2009 H1N1 swine flu. Actually, most swine influenza infections occur during the breed-slaughter process. However, there is little research about the mathematical model to elaborate on the swine influenza transmission with human-pig interaction. In this paper, a new breed-slaughter model with swine influenza transmission is proposed, and the equilibrium points of the model are calculated subsequently. Meanwhile, we analyze the existence of the equilibrium points by the persistence theory, and discuss their stability by the basic reproduction number. And then, we focus on the invasion process of infected domestic animals into the habitat of humans. Under certain conditions as in Theorem 2, we construct a propagating terrace linking human habitat to animal-human coexistent habitat, then to swine flu natural foci, which is divided by spreading speeds.

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