Abderrahman Iggidr

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The conjecture of Arino and van den Driessche (2003) that a SIS type model in a mover-stayer epidemic model is globally asymptotically stable is confirmed analytically. If the basic reproduction number R 0 ≤ 1, then the disease free equilibrium is globally asymptotically stable. If R 0 > 1, then there exists a unique endemic equilibrium which is globally(More)
The resurgence of vector-borne diseases is an increasing public health concern, and there is a need for a better understanding of their dynamics. For a number of diseases, e.g. dengue and chikungunya, this resurgence occurs mostly in urban environments, which are naturally very heterogeneous, particularly due to population circulation. In this scenario,(More)
We consider an age-structured model of a harvested population. This model is a discrete-time system that includes a nonlinear stock-recruitment relationship. Our purpose is to estimate the stock state. To achieve this goal, we built an observer, which is an auxiliary system that uses the total number of fish caught over each season and gives a dynamical(More)
We provide a global analysis of systems of within-host parasitic infections. The systems studied have parallel classes of different length of latently infected target cells. These systems can also be thought as systems arising from within-host parasitic systems with distributed continuous delays. We compute the basic reproduction ratio R0 for the systems(More)
In this paper, the analysis of a schistosomiasis infection model that involves human and intermediate snail hosts as well as an additional mammalian host and a competitor snail species is studied by constructing Lyapunov functions and using a Krasnoselkii sublinearity trick. We derive the basic reproduction number R 0 for the deterministic model, and(More)
We introduce classes of differential susceptibility and infectivity epidemic models. These models address the problem of flows between the different susceptible, infectious and infected compartments and differential death rates as well. We prove the global stability of the disease free equilibrium when the basic reproduction ratio R0≤1 and the existence and(More)
The purpose of the paper is to design a fishing strategy in order to regulate an exploited fish population. To this end, we use a stage-structured model of a harvested fish population that has been derived in [5]. We give a formula for the fishing effort as a feedback control that allows to stabilize the system. * travail réalisé avec la contributionfinancì(More)
The aim of this article is to present some new stability suucient conditions for discrete-time nonlinear systems. It shows how to use nonnegative semi-deenite functions as Lyapunov functions instead of positive deenite ones for studying the stability of a given system. Several examples and some applications to control theory are presented to illustrate the(More)