Math. Model. Nat. Phenom.
Volume 15, 2020
Ecology and evolution
|Number of page(s)||26|
|Published online||15 December 2020|
Modeling the dynamics of Wolbachia-infected and uninfected Aedes aegypti populations by delay differential equations
Inria, Université de Lyon, Université Lyon 1,
2 São Paulo State University (UNESP), Institute of Biosciences, 18618-689 Botucatu, SP, Brazil
* Corresponding author: email@example.com
Accepted: 29 September 2020
Starting from an age structured partial differential model, constructed taking into account the mosquito life cycle and the main features of the Wolbachia-infection, we derived a delay differential model using the method of characteristics, to study the colonization and persistence of the Wolbachia-transinfected Aedes aegypti mosquito in an environment where the uninfected wild mosquito population is already established. Under some conditions, the model can be reduced to a Nicholson-type delay differential system; here, the delay represents the duration of mosquito immature phase that comprises egg, larva and pupa. In addition to mortality and oviposition rates characteristic of the life cycle of the mosquito, other biological features such as cytoplasmic incompatibility, bacterial inheritance, and deviation on sex ratio are considered in the model. The model presents three equilibriums: the extinction of both populations, the extinction of Wolbachia-infected population and persistence of uninfected one, and the coexistence. The conditions of existence for each equilibrium are obtained analytically and have been interpreted biologically. It is shown that the increase of the delay can promote, through Hopf bifurcation, stability switch towards instability for the nonzero equilibriums. Overall, when the delay increases and crosses predetermined thresholds, the populations go to extinction.
Mathematics Subject Classification: 34K13 / 34K18 / 34K20 / 34K21 / 92D25 / 92D40
Key words: Age and stage structured partial differential system / delay differential system / local and global asymptotic stability / Hopf bifurcation
© The authors. Published by EDP Sciences, 2020
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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