Mathematical modeling of sterile insect technology for control of anopheles mosquito

Abstract

International audienceModelling the biomechanics of growing trees is a non-classical problem, as the usual framework of structural mechanics does not take into account the evolution of the domain geometry due to growth processes. Incremental approaches have been used in rod theory to bypass this problem and to model the addition of new material points on an existing deformed structure. However, these approaches are based on the explicit time numerical algorithm of an unknown continuous model, and thus, the accuracy of the numerical results obtained cannot be analysed. A new continuous space-time formulation has been recently proposed to model the biomechanical response of growing rods. The aim of this paper is to discretise the corresponding non-linear system of partial differential equations and the linearised system in order to compare the numerical results with analytical solutions of the linearised problem. The finite element method is implemented to compute the space boundary problem and different time integration schemes are considered to solve the associated initial value problem with a special attention to the forward Euler method which is the analogue of the previously used incremental approach. The numerical results point out that the accuracy of the time integration schemes strongly depends on the value of the parameters. The forward Euler method may present slow convergence property and errors with significant orders of magnitude. Nevertheless, attention must be paid to implicit methods since, for specific values of the parameters and large time steps, they may lead to spurious solutions that may come from numerical instabilities. Hence, the second order Heun's method is an interesting alternative even if it is more time consuming

Impact of environmental factors on mosquito dispersal in the prospect of sterile insect technique control

“…As an alternative to the proof of theorem 1, we could show that system (1) is monotonous and cooperative and apply the results developed by Anguelov et al [1].…”

“…If the release is far from the females, then sterile males will have lower chance to mate females, so, ρ s Λ s may represent the release of sterile males that would actually play a role in SIT. Following [1,23], we assume that the probability for an immature female to become a feeding female depends on the ratio (u M + λ s f s u M s )/(u M + u M s ), when sterile males are released. Note that ρ s is only relevant in the temporal model, as it provides some kind of spatial information on the releases.…”

“…Therefore, it is necessary to consider new sustainable alternatives or additional tools, like the Sterile Insect Technique (SIT). SIT consists in releasing sterilized male mosquitoes that will mate with wild females which won't be able to deposit hatching eggs [32] (see also [6,1,23] for extended references about SIT), driving slowly the wild population to decline. Thus, the release of sufficiently many sterile males over a sufficiently long period of time can lead to local reduction or elimination of the wild population.…”

Mathematical modelling and estimation of seasonal variation of mosquito population: a real case study

“…Malaria is one of the most prevalent vector-host diseases, whereby the disease is not transmitted directly from host to host, but through a vector [3,4,5,8,9,10]. There are many existing models based on climatic conditions considering mosquito control in homogeneous, non-homogeneous stage structured model to study and control the mosquito vector [11,12,16,17,18]. Several models have been developed to predict mosquito population dynamics.…”

A patchy model for Chikungunya-like diseases

“…In fact, using [5], we can show the following Theorem 1: Let A i,m (0) ≤ α i K i , then the following results hold 1) System (10) defines a cooperative dissipative dynamical system on R 2 + . 2) If N i,m ≤ 1, then the equilibrium E 0 is globally asymptotically stable on R 2 + .…”