The aim of this presentation is to present some results on the distribution and abundance of a malaria-vector Anopheles mosquito population, taking into account environmental parameters such as wind and temperature, and its response to Sterile Insect Technique (SIT) control. To do so, we consider a compartmental approach to account for the interactions between groups of individuals within the population, and we model the dispersal of each compartment via an advection-diffusion-reaction process based on biological and behavioural assumptions. The resulting mathematical model is formulated by a system of partial differential equations which accounts for temporal variations of the population abundance and spatial heterogeneity. We then carry out numerical simulations for the dispersal of mosquitoes and simulate various SIT control scenarios. We show that environmental factors have a significant influence on the distribution of mosquitoes and the efficiency of the control method. (Texte integral)
Anopheles mosquito is a vector responsible for the transmission of diseases like Malaria which a_ect many people. Hence its control is a major prevention strategy. Sterile Insect Technology (SIT) is a nonpolluting method of insect control that relies on the release of sterile males. Mating of the released sterile males with wild females leads to non hatching eggs. Thus, if sterile males are released in su_cient numbers or over a su_cient period of time, it can leads to the local reduction or elimination of the wild population. We study the e_ectiveness of the application of SIT for control of Anopheles mosquito via mathematical modeling. Our main result is that there exists a threshold release rate ^_ depending only on the basic o_spring number R and the wild mosquito equilibrium for males such that a release rate higher than ^_ results in elimination of the mosquito population irrespective of its initial size. A release rate _ which is lower than ^_ eliminates the mosquito populations only if it is su_ciently small. If the population is at the wild equilibrium it is reduced by a percentage depending on _ and R only. (Resume d'auteur)
A convergence structure generalizing the order convergence structure on the set of Hausdorff continuous interval functions is defined on the set of minimal usco maps. The properties of the obtained convergence space are investigated and essential links with the pointwise convergence and the order convergence are revealed. The convergence structure can be extended to a uniform convergence structure so that the convergence space is complete. The important issue of the denseness of the subset of all continuous functions is also addressed.
In the last decades, the development of sustainable insect control methods, like sterile insect technique (SIT), has become one of the most challenging issue to reduce the risk of human vector-borne diseases, like malaria, dengue, chikungunya or crop pests, like fruit flies. control generally consists of massive releases of sterile insects in the targeted area with the aim to reach elimination or to lower the pest population under a certain threshold. Practically, due to e.g. manufacturing limitations/constraints and the (economic) cost of such operations, massive releases of sterile males are only possible for a short period of time. Despite that restriction, the main issue is to quantify the size and the duration of massive releases, before, eventually, shift to a low level and more sustainable releases of sterile insects, in order to reach elimination or maintain wild insects below an epidemiological risk threshold. Mathematical modelling can be a powerful tool to provide insights in the long-term dynamics of complex systems, like wild insects population experiencing control. In this poster, we present minimalistic entomo-mathematical models for wild insect population when is taken into account. Using Mathematical analysis and simulations, we show that different strategies can be developed, like, for instance a strategy that maintains the wild population under a certain threshold, for a permanent and sustainable low level of control and ensuing their elimination in the long-term dynamics. Taking into account the spatial component in the previous strategy, we also show that it can be used to stop a pest/vector invasion and eventually push them back. This work is partly supported by the SIT feasibility project against Aedes albopictus in Reunion Island phase 2B, jointly funded by the French Ministry of Health and the European Regional Development Fund (ERDF). The authors were supported by the DST/NRF SARChI Chair M2B3, in Mathematical Models and Methods in Biosciences and Bioengineering, at the University of Pretoria (grant 82770).
We consider a compartmental model for the Bartonella infection on rodents. More precisely, on the co‐occurring populations of Rattus rattus and Rattus norvegicus where the vectors are two species of ectoparasites, namely ticks and fleas. As usual for such models a key stage is the modelling of the forces of infection. While the vital dynamics and the progression of the infection within each of the four species are sufficiently well known to determine the rest of the transfer rates, there is practically no data on the probability of infection. In order to determine appropriate values for the coefficients of the forces of infection we solve an optimal control problem where the objective function is the norm of the difference between the observed and the predicted by the model equilibrium infection prevalence rates in the four species. Within this setting the conjecture that the higher prevalence of the infection in Rattus norvegicus can be explained solely by their higher ectoparasite load is tested and disproved.
Abstract We present two results on the analysis of discrete dynamical systems and finite difference discretizations of continuous dynamical systems, which preserve their dynamics and essential properties. The first result provides a sufficient condition for forward invariance of a set under discrete dynamical systems of specific type, namely time-reversible ones. The condition involves only the boundary of the set. It is a discrete analog of the widely used tangent condition for continuous systems ( viz. the vector field points either inwards or is tangent to the boundary of the set). The second result is nonstandard finite difference (NSFD) scheme for dynamical systems defined by systems of ordinary differential equations. The NSFD scheme preserves the hyperbolic equilibria of the continuous system as well as their stability. Further, the scheme is time reversible and, through the first result, inherits from the continuous model the forward invariance of the domain. We show that the scheme is of second order, thereby solving a pending problem on the construction of higher-order nonstandard schemes without spurious solutions. It is shown that the new scheme applies directly for mass action-based models of biological and chemical processes. The application of these results, including some numerical simulations for invariant sets, is exemplified on a general Susceptible-Infective-Recovered/Removed (SIR)-type epidemiological model, which may have arbitrary large number of infective or recovered/removed compartments.
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