Modelling the $Wolbachia$ Strains for Dengue Fever Virus Control in the Presence of Seasonal Fluctuation
Year: 2021
Author: Yanan Xue, Lin Hu, Linfei Nie
Journal of Nonlinear Modeling and Analysis, Vol. 3 (2021), Iss. 2 : pp. 209–224
Abstract
Consider that infection with $Wolbachiacan$ limit a mosquito's ability to transmit Dengue fever virus through its saliva, a mathematical model describing the transmission of Dengue fever between vector mosquitoes and human, incorporating $Wolbachia$-carrying mosquito population and seasonal fluctuation, is proposed. Firstly, the stability and bifurcation of this model are investigated exactly in the case where seasonality can be neglected. Further, the basic reproductive number $\mathcal{R}_0^s$ for this model with seasonal variation is obtained, that is, if $\mathcal{R}_0^s$ is less than unity the disease is extinct and $\mathcal{R}_0^s$ is greater than unity the disease is uniformly persistent. Finally, numerical simulations verify the theoretical results. Theoretical results suggest that, compared with the mosquito reduction strategies (such as the elimination of mosquito breeding sites, killing of adult mosquitoes by spraying), introducing $Wolbachia$ strains is as effectual to fight against the transmission of Dengue virus.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.12150/jnma.2021.209
Journal of Nonlinear Modeling and Analysis, Vol. 3 (2021), Iss. 2 : pp. 209–224
Published online: 2021-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: Dengue fever $Wolbachiacan$ Seasonal fluctuation Stability and sensitivity analysis Extinction and persistence.