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.

Mean-square Stability of Stochastic Age-dependent Delay Population Systems with Jumps

In this paper, we present the compensated stochastic θ method for stochastic age-dependent delay population systems（SADDPSs） with Poisson jumps. The definition of mean-square stability of the numerical solution is given and a sufficient condition for mean-square stability of the numerical solution is derived. It is shown that the compensated stochastic θ method inherits stability property of the numerical solutions. Finally,the theoretical results are also confirmed by a numerical experiment.

Deterministic approaches for head lice infestations and treatments

Pediculus humanus capitis are human ectoparasites which cause infestations,mostly in children,worldwide.Understanding the life cycle of head lice is an important step in knowing how to treat lice infestations,as the parasite behavior depends considerably on its age and gender.In this work we propose a mathematical model for head lice population dynamics in hosts who could be or not quarantined and treated.Considering a lice population structured by age and gender we formulate the model as a system of hyperbolic PDEs,which can be reduced to compartmental systems of delay or ordinary differential equations.Besides studying fundamental properties of the model,such as existence,uniqueness and nonnegativity of solutions,we show the existence of(in certain cases multiple)equilibria at which the infestation persists on the host’s head.Aiming to assess the performance of treatments against head lice infestations,by mean of computer experiments and numerical simulations we investigate four possible treatment strategies.Our main results can be summarized as follows:(i)early detection is crucial for quick and efficient eradication of lice infestations;(ii)dimeticone-based products applied every 4 days effectively remove lice in at most three applications even in case of severe infestations and(iii)minimization of the reinfection risk,e.g.by mean of synchronized treatments in families/classrooms is recommended.