Dynamical behavior of a stochastic SIRS epidemic model

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Table of contents

Abstract
1 Introduction
1.1 Population dynamics
1.1.1 Single species growth
1.1.2 Biological interaction
1.1.3 Lotka-Volterra systems
1.2 Mathematical modelling of infectious disease
1.3 Models and obtained results
2 Spatial heterogeneity, fast migration and coexistence of Intraguild Predation Dynamics
2.1 Introduction
2.2 Model
2.3 Model reduction
2.3.1 Fast equilibrium
2.3.2 Aggregated model
2.4 Results and discussions
2.5 Conclusion and perspectives
3 E↵ect of small versus large clusters of fish school on the yield of a purse-seine small pelagic fishery including a marine protected area
3.1 Introduction
3.2 Complete Model
3.3 Building the aggregated model
3.3.1 First step of aggregation: very fast fish movements
3.3.2 Second step of aggregation: fast changes in clusters size .
3.4 Comparison with one-step aggregation
3.5 Harvest Optimization
3.6 Discussion and perspectives
4 Dynamics of species in a model with two predators and one prey
4.1 Introduction
4.2 Definitions and notation
4.3 The model with general coefficients
4.4 The model with periodic coefficients
4.5 Numerical examples and conclusion
5 Population dynamics in random environments
5.1 Dynamical behavior of a stochastic SIRS epidemic model
5.1.1 Introduction
5.1.2 Preliminary
5.1.3 Dynamical behavior of solutions
5.1.4 The semigroup and the stability in distribution
5.1.5 Simulation and discussion
5.2 Evolution of Lotka-Volterra predator-prey systems under telegraph noise
5.2.1 Model
5.2.2 Predator-prey system with carrying capacity
5.2.3 Predator-prey system with the absence of carrying capacity
5.2.4 Discussion and conclusion
6 Conclusion
Bibliography