## Séminaire Sebastien Kolb

Jeudi 26 septembre 2019 (15h00, Salle G001)

Sébastien Kolb, MCF, Ecole de l'air.

Titre : Analyse non linéaire de la dynamique du vol grâce à la théorie des bifurcations.

Résumé : Certains phénomènes rencontrés en dynamique du vol sont fortement non linéaires. La théorie des bifurcations se révèle alors utile pour analyser, comprendre la dynamique sous-jacente et pour proposer des stratégies de récupération de pertes de contrôle. Concernant le vol longitudinal d'un avion de combat F-18, des bifurcations sont responsables de l'apparition d'oscillations périodiques et de la coexistence de plusieurs états d'équilibre. Pour ce qui est de la dynamique du vol d'un hélicoptère, l'état d'anneaux tourbillonnaires (formation d'anneaux tourbillonnaires à la périphérie du rotor) peut être caractérisé et délimité grâce au lieu des points de bifurcations. Il est possible également de proposer une stratégie afin de sortir de cette dangereuse région d'instabilité. En outre, le couplage aéronef-pilote peut également donner lieu à des oscillations (induites par le pilote) dont le déclenchement correspond à des bifurcations de cycles limites.

## Séminaire Ousmane Seydi

Jeudi 26 septembre 2019 (14h00, Salle G001)

Ousmane Seydi, Ecole Polytechnique de Thiès, Senegal.

Titre : Monotone abstract non densely defined Cauchy problems applied to age structured population dynamics models

Résumé : In this presentation we first derive some sufficient conditions to establish the monotonicity and comparison principles of the semi-flow generated by non-densely defined Cauchy problems. We apply our results to a class of age structured population models. As a consequence we obtain a monotone semiflow theory and some comparison principles for age structured models.

## Séminaire Léna Tendeng

Jeudi 14 novembre 2019 (14h00, Salle G001)

Titre : An Optimal Control for A Transmission Model of Bilharzia

Résumé : Bilharzia or schistosomiasis is one of the most widespread human parasitic infections. In term of socioeconomic and public health impact, bilharzia is second only to malaria as the most devastating parasitic desease in tropical countries. In this work, we consider a non linear system of Bilharzia transmission. We prove local controllability at the equilibrium points and find an optimal con- trol by maximum principle of Pontryagin. We study the global controllability and test the controlled system by numerical simulations. Key-words: bilharzia, local controllability, global controllability, non linear system, Pontryagin maximum principle.

## Séminaire Cédric Hameni

Jeudi 28 novembre 2019 (14h00, Salle G001)

Cédric Hameni, Université de Douala, Cameroun.

Titre : Dynamics and optimal control of Ebola virus disease transmission

Résumé : Ebola is one of the major public health concerns, especially after the disasters that occurred in 2013-2015 and his recent outbreak in Democratic Republic of Congo. This study deals with the problem of dynamics and optimal control strategies of Ebola virus diseases (EVD). We first formulate a deterministic mathematical model for the dynamic transmission of the Ebola virus. We then provide the theoretical study of the model. We calculate the disease-free equilibrium (DFE), derive the basic reproduction number R0, and show that there is a threshold parameter \xi such that when R0 <\xi1, the disease disappears, regardless of the initial size populations. We use this result to study the impact of imperfect random mass vaccination and decreased immunity within a community affected by EVD. After, optimal control theory is applied to study an optimal strategy to control the spread of disease using vaccination and education campaigns of susceptible individuals as control variables. The numerical results show the utility of optimization strategies in the EVD control and prevention process.

## Séminaire Benjamin Ambrosio

Jeudi 17 octobre 2019 (14h00, Salle G001)

Benjamin Ambrosio , LMAH.

Titre : On a Feedforward Chain of Periodically Kicked FitzHugh-Nagumo Neurons

Résumé : In this talk I will discuss a recent model unidirectionally coupled chain of FHN equations. At one end of the chain, the neuron receives kicks which are propagated along the chain. Existence of periodic solutions result from a fixed point argument for both $\epsilon$ zero or small. Varying the period of kicks lead to mixed mode oscillations. Numerical simulations illustrate that this behavior relates on concurrence between speed along fast fibers and speed along slow manifolds for close trajectories.