Abderrahman Iggidr

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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)
The conjecture of Arino and van den Driessche (2003) that a SIS type model in a moverstayer epidemic model is globally asymptotically stable is confirmed analytically. If the basic reproduction number R0 ≤ 1, then the disease free equilibrium is globally asymptotically stable. If R0 > 1, then there exists a unique endemic equilibrium which is globally(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)
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)
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)
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 R0 for the deterministic model, and(More)
We consider a stage-structured model of a harvested fish population and we are interested in the problem of estimating the unknown stock state for each class. The model used in this work to describe the dynamical evolution of the population is a discrete time system including a nonlinear recruitment relationship. To estimate the stock state, we build an(More)
The aim of this paper is to give an estimation of total parasite burden of the patient and the rate of infection in a malaria’s intra-host model by using control theory tools. More precisely, we use an auxiliary system called observer whose solutions tend exponentially to those of the original model. This observer uses only the available measurable data(More)