Mathematical Biosciences and Engineering, 2019, 16(3): 1625-1653. doi: 10.3934/mbe.2019078

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Global dynamics of an age-structured malaria model with prevention

Zhong-Kai Guo, Hai-Feng Huo, Hong Xiang

1 College of Electrical and Information Engineering, Lanzhou University of Technology, Lanzhou, Gansu, 730050, Peoples Republic of China
2 Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou, Gansu, 730050, Peoples Republic of China

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Special Issues: Mathematical Modeling of Mosquito-Borne Diseases

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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 ${R}_{0}$ and show that ${R}_{0}$ completely determines the global dynamics of the model, that is, if ${R}_{0}$<1 the="" disease-free="" equilibrium="" is="" globally="" asymptotically="" stable="" if="" 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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