Asymptotic stability in a mosquito population suppression model with time delay

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.

One discrete dynamical model on the Wolbachia infection frequency in mosquito populations

How to prevent and control the outbreak of mosquito-borne diseases,such as malaria,dengue fever and Zika,is an urgent worldwide public health problem.The most conventional method for the control of these diseases is to directly kill mosquitoes by spraying insecticides or removing their breeding sites.However,the traditional method is not effective enough to keep the mosquito density below the epidemic risk threshold.With promising results international,the World Mosquito Program’s Wolbachia method is helping to reduce the occurrence of diseases transmitted by mosquitoes.In this paper,we introduce a generalized discrete model to study the dynamics of the Wolbachia infection frequency in mosquito populations where infected mosquitoes are impulsively released.This generalized model covers all the relevant existing models since 1959 as some special cases.After summarizing known results of discrete models deduced from the generalized one,we put forward some interesting open questions to be further investigated for the periodic impulsive releases.

Meteorological indicators of dengue epidemics in non-endemic Northwest Argentina

In the last two decades dengue cases increased significantly throughout the world,giving place to more frequent outbreaks in Latin America.In the non-endemic city of San Ramòn de la Nueva Orán,located in Northwest Argentina,large dengue outbreaks alternate with several years of smaller ones.This pattern,as well as the understanding of the underlying mechanisms,could be essential to design proper strategies to reduce epidemic size.We develop a stochastic model that includes climate variables,social structure,and mobility between a non-endemic city and an endemic area.Climatic variables were input of a mosquito population ecological model,which in turn was coupled to a meta-population,spatially explicit,epidemiological model.Human mobility was included into the model given the high border crossing to the northern country of Bolivia,where dengue transmission is sustained during the whole year.We tested different hypotheses regarding people mobility as well as climate variability by fitting numerical simulations to weekly clinical data reported from 2009 to 2016.After assessing the number of imported cases that triggered the observed outbreaks,our model allows to explain the observed epidemic pattern.We found that the number of vectors per host and the effective reproductive number are proxies for large epidemics.Both proxies are related with climate variability such as rainfall and temperature,opening the possibility to test these meteorological variables for forecast purposes.