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
In this paper,a new mosquito population suppression model with stage and sex structure is constructed,which is composed of two sub-models switching each other.Sterile mosquitoes are released with period T and remain s...In this paper,a new mosquito population suppression model with stage and sex structure is constructed,which is composed of two sub-models switching each other.Sterile mosquitoes are released with period T and remain sexually active for time T.For the case T<T,three thresholds T^(*),m^(*)and c^(*)are determined for the release period T and release amount c.According to the values of T and c in different ranges determined by these thresholds,we study the dynamical behavior of the system for different release strategies,mainly including the existence and stability of the mosquito-extinction equilibrium and positive periodic solutions.Finally,some numerical simulations are performed to illustrate our results.展开更多
A bio-safe dengue control strategy is to use Wolbachia,which can induce incomplete cytoplasmic incompatibility(CI)and reduce the mating competitiveness of infected males.In this work,we formulate a delay differential ...A bio-safe dengue control strategy is to use Wolbachia,which can induce incomplete cytoplasmic incompatibility(CI)and reduce the mating competitiveness of infected males.In this work,we formulate a delay differential equation model,including both the larval and adult stages of wild mosquitoes,to assess the impacts of CI intensityξand mating competitivenessθof infected males on the suppression efficiency.Our analysis identifies a CI intensity thresholdξ*below which a successful suppression is impossible.Whenξ≥ξ*,the wild population will be eliminated ultimately if the releasing level exceeds the release amount threshold R*uniformly.The dependence of R*onξandθ,and the impact of temperature on suppression are further exhibited through numerical examples.Our analyses indicate that a slight reduction ofξis more devastating than significantly decrease ofθin the suppression efficiency.To suppress more than 95%wild mosquitoes during the peak season of dengue in Guangzhou,the optimal starting date for releasing is sensitive toξbut almost independent ofθ.One percent reduction ofξfrom 1 requires at least one week earlier in the optimal releasing starting date from 7 weeks ahead of the peak season of dengue.展开更多
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.
基金This work is supported by the National Natural Science Foundation of China(12071407,11901502)Training plan for young backbone teachers in Henan Province(2019GGJS157)+2 种基金Program for Science&Technology Innovation Talents in Universities of Henan Province(21HASTIT026)Program for Innovative Research Team(in Science and Technology)in the University of Henan Province(21IRTSTHN014)Natural Science Foundation of Henan Province(222300420016).
文摘In this paper,a new mosquito population suppression model with stage and sex structure is constructed,which is composed of two sub-models switching each other.Sterile mosquitoes are released with period T and remain sexually active for time T.For the case T<T,three thresholds T^(*),m^(*)and c^(*)are determined for the release period T and release amount c.According to the values of T and c in different ranges determined by these thresholds,we study the dynamical behavior of the system for different release strategies,mainly including the existence and stability of the mosquito-extinction equilibrium and positive periodic solutions.Finally,some numerical simulations are performed to illustrate our results.
基金supported by the National Natural Science Foundation of China(Nos.12026222,12071095)Program for Changjiang Scholars and Innovative Research Team in University(No.IRT 16R16)by the Natural Science Foundation of Guangdong Province(No.2017A030310597)。
文摘A bio-safe dengue control strategy is to use Wolbachia,which can induce incomplete cytoplasmic incompatibility(CI)and reduce the mating competitiveness of infected males.In this work,we formulate a delay differential equation model,including both the larval and adult stages of wild mosquitoes,to assess the impacts of CI intensityξand mating competitivenessθof infected males on the suppression efficiency.Our analysis identifies a CI intensity thresholdξ*below which a successful suppression is impossible.Whenξ≥ξ*,the wild population will be eliminated ultimately if the releasing level exceeds the release amount threshold R*uniformly.The dependence of R*onξandθ,and the impact of temperature on suppression are further exhibited through numerical examples.Our analyses indicate that a slight reduction ofξis more devastating than significantly decrease ofθin the suppression efficiency.To suppress more than 95%wild mosquitoes during the peak season of dengue in Guangzhou,the optimal starting date for releasing is sensitive toξbut almost independent ofθ.One percent reduction ofξfrom 1 requires at least one week earlier in the optimal releasing starting date from 7 weeks ahead of the peak season of dengue.