Existence and stability of a unique and exact two periodic orbits for an interactive wild and sterile mosquito model

DOI10.1016/j.jde.2020.07.019zbMath1457.34084OpenAlexW3085991565MaRDI QIDQ2003930

Jian She Yu

Publication date: 13 October 2020

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2020.07.019

zbMATH Keywords

uniquenessasymptotic stabilitysterile mosquitoesat most two periodic solutionsexact two periodic solutionsmosquito population suppression

Mathematics Subject Classification ID

Epidemiology (92D30) Periodic solutions to ordinary differential equations (34C25) Population dynamics (general) (92D25) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Discontinuous ordinary differential equations (34A36) Qualitative investigation and simulation of ordinary differential equation models (34C60) Global stability of solutions to ordinary differential equations (34D23) Asymptotic properties of solutions to ordinary differential equations (34D05)

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Cites Work

• \textit{Wolbachia} spread dynamics in stochastic environments
• Qualitative analysis for a Wolbachia infection model with diffusion
• Discrete-time models with mosquitoes carrying genetically-modified bacteria
• Simple paratransgenic mosquitoes models and their dynamics
• Optimal control of Aedes aegypti mosquitoes by the sterile insect technique and insecticide
• Models to assess how best to replace dengue virus vectors with \textit{Wolbachia}-infected mosquito populations
• Assessing the efficiency of \textit{Wolbachia} driven \textit{Aedes} mosquito suppression by delay differential equations
• Wolbachia spreading dynamics in mosquitoes with imperfect maternal transmission
• The threshold infection level for \textit{Wolbachia} invasion in random environments
• \textit{Wolbachia} spread dynamics in multi-regimes of environmental conditions
• Wolbachia infection dynamics by reaction-diffusion equations
• Bifurcation analysis of a wild and sterile mosquito model
• The impact of mating competitiveness and incomplete cytoplasmic incompatibility on \textit{Wolbachia}-driven mosquito population suppression
• Global asymptotic stability in an interactive wild and sterile mosquito model
• A stage structured model of delay differential equations for \textit{Aedes} mosquito population suppression
• Bifurcation analysis of a mosquito population model for proportional releasing sterile mosquitoes
• Complex Wolbachia infection dynamics in mosquitoes with imperfect maternal transmission
• Simple mathematical models for interacting wild and transgenic mosquito populations
• ModelingWolbachiaSpread in Mosquitoes Through Delay Differential Equations
• Dynamics of interactive wild and sterile mosquitoes with time delay
• Differential equations models for interacting wild and transgenic mosquito populations
• Modeling Mosquito Population Suppression Based on Delay Differential Equations
• ModelingWolbachiainfection in mosquito population via discrete dynamical models
• Dynamics of Mosquitoes Populations with Different Strategies for Releasing Sterile Mosquitoes