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Global dynamics of an age-structured malaria model with prevention

  • Received: 18 November 2018 Accepted: 30 January 2019 Published: 26 February 2019
  • In this paper, we formulate a new age-structured malaria model, which incorporates the age of prevention period of susceptible people, the age of latent period of human and the age of latent period of female Anopheles mosquitoes. We show that there exists a compact global attractor and obtain a sufficient condition for uniform persistence of the solution semiflow. We obtain the basic reproduction number $\mathcal{R}_{0}$ and show that $\mathcal{R}_{0}$ completely determines the global dynamics of the model, that is, if $\mathcal{R}_{0} < 1$, the disease-free equilibrium is globally asymptotically stable, if $\mathcal{R}_{0}>1$, there exists a unique endemic equilibrium that attracts all solutions for which malaria transmission occurs. Finally, we perform some numerical simulations to illustrate our theoretical results and give a brief discussion.

    Citation: Zhong-Kai Guo, Hai-Feng Huo, Hong Xiang. Global dynamics of an age-structured malaria model with prevention[J]. Mathematical Biosciences and Engineering, 2019, 16(3): 1625-1653. doi: 10.3934/mbe.2019078

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  • In this paper, we formulate a new age-structured malaria model, which incorporates the age of prevention period of susceptible people, the age of latent period of human and the age of latent period of female Anopheles mosquitoes. We show that there exists a compact global attractor and obtain a sufficient condition for uniform persistence of the solution semiflow. We obtain the basic reproduction number $\mathcal{R}_{0}$ and show that $\mathcal{R}_{0}$ completely determines the global dynamics of the model, that is, if $\mathcal{R}_{0} < 1$, the disease-free equilibrium is globally asymptotically stable, if $\mathcal{R}_{0}>1$, there exists a unique endemic equilibrium that attracts all solutions for which malaria transmission occurs. Finally, we perform some numerical simulations to illustrate our theoretical results and give a brief discussion.
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    © 2019 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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