Using the sterile insect technique,in which sterile mosquitoes are released to reduce or eradicate the wild mosquito population,is an effective weapon to prevent transmission of mosquito-borne diseases. To study the i...Using the sterile insect technique,in which sterile mosquitoes are released to reduce or eradicate the wild mosquito population,is an effective weapon to prevent transmission of mosquito-borne diseases. To study the impact of the sterile insect technique on the disease transmissions,we formulate stage-structured discrete-time mathematical models,based on difference equations,for the interactive dynamics of the wild and sterile mosquitoes. We incorporate different strategies for releasing sterile mosquitoes,investigate the model dynamics,and compare the impact of the different release strategies.Numerical examples are also provided to demonstrate dynamical features of the models.展开更多
The sterile insect technique(SIT)has been applied as an alternative method to reduce or eradicate mosquito-borne diseases.To explore the impact of the sterile mosquitoes on controlling the wild mosquito populations,in...The sterile insect technique(SIT)has been applied as an alternative method to reduce or eradicate mosquito-borne diseases.To explore the impact of the sterile mosquitoes on controlling the wild mosquito populations,in this paper,we further extend the work in[J.Li,New revised simple models for interactive wild and sterile mosquito populations and their dynamics,J.Biol.Dyn.11(S2)(2017)316-333]and formulate delayed models for interactive wild and sterile mosquitoes,which can depict wild mosquito population undergoing distinct stages of development during a lifetime.By performing mathematical analysis,the threshold dynamics of the proposed models are explored,respectively.In particular,Hopf bifurcation phenomena are observed as the delay T is varying.Numerical examples illustrateourfindings.展开更多
In this paper,a delayed mosquito population suppression model,where the number of sexually active sterile mosquitoes released is regarded as a given nonnegative function,and the birth process is density dependent by c...In this paper,a delayed mosquito population suppression model,where the number of sexually active sterile mosquitoes released is regarded as a given nonnegative function,and the birth process is density dependent by considering larvae progression and the intra-specific competition within the larvae,is developed and studied.A threshold value r^(*)for the releases of sterile mosquitoes is determined,and it is proved that the origin is globally asymptotically stable if the number of sterile mosquitoes released is above the threshold value r^(*).Besides,the case when the number of sterile mosquitoes released stays at a constant level r is also considered.In the special case,it is also proved that the origin is globally asymptotically stable if and only if r>r^(*)and that the model exhibits other complicated dynamics such as bi-stability and semi-stability when r≤r^(*).Numerical examples are also provided to illustrate our main theoretical results.展开更多
基金supported partially by U.S.National Science Foundation grant DMS-0931213
文摘Using the sterile insect technique,in which sterile mosquitoes are released to reduce or eradicate the wild mosquito population,is an effective weapon to prevent transmission of mosquito-borne diseases. To study the impact of the sterile insect technique on the disease transmissions,we formulate stage-structured discrete-time mathematical models,based on difference equations,for the interactive dynamics of the wild and sterile mosquitoes. We incorporate different strategies for releasing sterile mosquitoes,investigate the model dynamics,and compare the impact of the different release strategies.Numerical examples are also provided to demonstrate dynamical features of the models.
基金supported partially by National Natural Science Foundation of China (11871415)Foundation of Henan Educational Committee under Contract (22B110013)the Henan Province Distinguished Professor Program (LC).
文摘The sterile insect technique(SIT)has been applied as an alternative method to reduce or eradicate mosquito-borne diseases.To explore the impact of the sterile mosquitoes on controlling the wild mosquito populations,in this paper,we further extend the work in[J.Li,New revised simple models for interactive wild and sterile mosquito populations and their dynamics,J.Biol.Dyn.11(S2)(2017)316-333]and formulate delayed models for interactive wild and sterile mosquitoes,which can depict wild mosquito population undergoing distinct stages of development during a lifetime.By performing mathematical analysis,the threshold dynamics of the proposed models are explored,respectively.In particular,Hopf bifurcation phenomena are observed as the delay T is varying.Numerical examples illustrateourfindings.
基金supported by the National Natural Science Foundation of China (No.12171193)the Science and Technology Key Project of Henan Province of China (No.222102110028)the Key scientific research projects of colleges and universities in Henan Province of China (Nos.22B110006,22A110012 and 20B110008).
文摘In this paper,a delayed mosquito population suppression model,where the number of sexually active sterile mosquitoes released is regarded as a given nonnegative function,and the birth process is density dependent by considering larvae progression and the intra-specific competition within the larvae,is developed and studied.A threshold value r^(*)for the releases of sterile mosquitoes is determined,and it is proved that the origin is globally asymptotically stable if the number of sterile mosquitoes released is above the threshold value r^(*).Besides,the case when the number of sterile mosquitoes released stays at a constant level r is also considered.In the special case,it is also proved that the origin is globally asymptotically stable if and only if r>r^(*)and that the model exhibits other complicated dynamics such as bi-stability and semi-stability when r≤r^(*).Numerical examples are also provided to illustrate our main theoretical results.