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Dynamics of a Mosquito Egg-Larvae Model with Seasonality

Dynamics of a mosquito egg-larvae model with seasonality
Authors: Jesús Bellver-Arnau; Alessandro Margheri; Carlota Rebelo;

Dynamics of a Mosquito Egg-Larvae Model with Seasonality

Abstract

AbstractWe propose a two stages mosquito egg-larvae model with seasonality as a simplification of a four stages one. For the simplified model we characterize the dynamics in terms of the vectorial reproduction number, $$R_0$$ R 0 , obtaining extinction if $$R_0\le 1$$ R 0 ≤ 1 and convergence to a unique positive periodic orbit if $$R_0>1$$ R 0 > 1 . We illustrate each case with an example, by providing general conditions on the periodic coefficients for its occurrence. These examples are further developed using numerical simulations where the periodic parameters satisfy the conditions obtained. In the $$R_0>1$$ R 0 > 1 case, real climatic data is used for inferring the parameter behaviour. For the four stage system, using alternative oviposition rate functions, we present a result which generalizes others given for models with delays and even with diffusion to the case in which competition between the larvae is introduced. The analytical study of our initial four stages system when $$R_0\ge 1$$ R 0 ≥ 1 remains open, since we were not able to prove that in this case the system is dissipative.

Country
Spain
Keywords

Monotone systems, Mosquito life cycle, systems with seasonality, Mathematical Concepts, Stability of solutions to ordinary differential equations, Pest management, vectorial reproduction number, Models, Biological, Vectorial reproduction number, mosquito life cycle, Systems with seasonality, Diffusion, Population dynamics (general), Culicidae, Larva, Animals, Original Article, Female, periodic attractor, Periodic solutions to ordinary differential equations, monotone systems, Periodic attractor

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
2
Average
Average
Average
Green
hybrid