Abderrahman Iggidr

On the dynamics of a class of multi-group models for vector-borne diseases ☆

Abstract 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, there is an increasing interest in both multi-patch and multi-group models for such diseases. In this work, we study the dynamics of a vector borne disease within a class of multi-group models that extends the classical Bailey–Dietz model. This class includes many of the proposed models in the literature, and it can accommodate various functional forms of the infection force. For such models, the vector-host/host-vector contact network topology gives rise to a bipartite graph which has different properties from the ones usually found in directly transmitted diseases. Under the assumption that the contact network is strongly connected, we can define the basic reproductive number R 0 and show that this system has only two equilibria: the so called disease free equilibrium (DFE); and a unique interior equilibrium—usually termed the endemic equilibrium (EE)—that exists if, and only if, R 0 > 1 . We also show that, if R 0 ≤ 1 , then the DFE equilibrium is globally asymptotically stable, while when R 0 > 1 , we have that the EE is globally asymptotically stable.

Interval estimation of sequestered infected erythrocytes in malaria patients

The problem of estimation of sequestered parasites Plasmodium falciparum in malaria, based on measurements of circulating parasites, is addressed. It is assumed that all (death, transition, recruitment and infection) rates in the model of a patient are uncertain (just intervals of admissible values are given) and the measurements are subject to a bounded noise, then an interval observer is designed. Stability of the observer can be verified by a solution of LMI. The efficiency of the observer is demonstrated in simulation.

Observer design for a schistosomiasis model

This paper deals with the state estimation for a schistosomiasis infection dynamical model described by a continuous nonlinear system when only the infected human population is measured. The central idea is studied following two major angles. On the one hand, when all the parameters of the model are supposed to be well known, we construct a simple observer and a high-gain Luenberger observer based on a canonical controller form and conceived for the nonlinear dynamics where it is implemented. On the other hand, when the nonlinear uncertain continuous-time system is in a bounded-error context, we introduce a method for designing a guaranteed interval observer. Numerical simulations are included in order to test the behavior and the performance of the given observers.

Multi-patch and multi-group epidemic models: a new framework

We develop a multi-patch and multi-group model that captures the dynamics of an infectious disease when the host is structured into an arbitrary number of groups and interacts into an arbitrary number of patches where the infection takes place. In this framework, we model host mobility that depends on its epidemiological status, by a Lagrangian approach. This framework is applied to a general SEIRS model and the basic reproduction number

Multi-stage Vector-Borne Zoonoses Models: A Global Analysis

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Exponential Stabilization of Nonlinear Systems by an Estimated State Feedback

R0 is derived. The effects of heterogeneity in groups, patches and mobility patterns on

On the estimation of sequestered infected erythrocytes in Plasmodium falciparum malaria patients

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