Study On The Dynamic Properties Of Stochastic Mosquito Population Model

Mosquito-borne diseases are a serious public health problem worldwide,which makes more and more scholars interested in the research of mosquito population models.However,mosquitoes are very sensitive to changes in their environment,and deterministic mosquito population models are insufficient to describe real-world mosquito-borne disease problems.Therefore,it is more practical to study the dynamic properties of stochastic mosquito population models affected by environmental noise.In this paper,stochastic analysis,stochastic dynamical systems,probability theory and biological mathematics are used to study the dynamical properties of stochastic mosquito population models.The first chapter mainly introduces the research background,research significance,main content and innovation of the random mosquito population model.At the same time,the preparatory knowledge related to the research of this paper and the frame structure of the whole research content are introduced.The second chapter mainly studies the asymptotic behavior of random mosquito population models with Markov chains.First,the existence and uniqueness of the positive solution of the stochastic mosquito population model with Markov chains is proved by using Markov properties and approximation methods.Secondly,when the long-term growth rate of sterile mosquitoes is λ=0,it is proved that the distribution of the stochastic mosquito population model is weakly convergent to a constant by using the control convergence theorem,Fatou’s lemma and contradictory method;When the long-term growth rate of sterile mosquitoes is λ＞0,it is proved that the total variation of the transition probability of the stochastic mosquito population model converges to an invariant measure by using the strong Feller property and the Fredholm alternative theorem;When the long-term growth rate of sterile mosquitoes is λ＜0,the ergodicity and comparison theorem are used to prove that the distribution of wild mosquitoes in the stochastic mosquito population model weakly converges to a unique invariant measure.Finally,the moment-boundedness of the solution of the stochastic mosquito population model with Markov chains is proved by using Fubini’s theorem and boundary analysis method.The third chapter mainly studies the extinction and persistence of stochastic mosquito population models with multiple noise effects.First,the Feller property of the solution of the stochastic mosquito population model with multiple noise effects is proved by ingeniously constructing the Lyapunov function.Secondly,using the iterative logarithm theorem,Borel-Cantelli lemma,Chebyshev’s inequality and other theories,the extinction property of the solution of the stochastic mosquito population model with multiple noise effects is proved.Finally,the persistence of a stochastic mosquito population model with multiple noise effects is demonstrated by using strong Markov property,Dispersion of collections,and Related Properties of Probability.