Ousmane Seydi

Ecole Polytechnique de Thiès · Tronc Commun

We propose a general framework for simultaneously calculating the threshold value for population growth and determining the sign of the growth bound of the evolution family generated by the problem below dv(t) dt = Av(t) + F(t)v(t) − V(t)v(t), where A : D(A) ⊂ X → X is a Hille-Yosida linear operator (possibly unbounded, non-densely defined) on a Ba...

Bacteriophages or phages (viruses of bacteria) play numerous roles in shaping the diversity of bacterial communities within the human gut. Either a phage-infected bacterial cell immediately starts a lysis mechanisms (virulent/lytic infection), or it enters a stable state within the host as a prophage (lysogeny), until a trigger event, called Sponta...

Note: Please see pdf for full abstract with equations. We propose a general framework for simultaneously calculating the threshold value for population growth and determining the sign of the growth bound of the evolution family generated by the problem below dv(t)/dt = Av(t) + F(t)v(t) − V(t)v(t), where A : D(A) ⊂ X → X is a Hille-Yosida linear ope...

Understanding both the epidemiological and evolutionary dynamics of antimicrobial resistance is a major public health concern. In this paper, we propose a nested model, explicitly linking the within-and between-host scales, in which the level of resistance of the host population is viewed as a continuous quantitative trait. The within-host dynamics...

In this work, we find necessary and sufficient conditions in order that a family of sets {C(t), t ∈ J} be invariant for a Cauchy problem. We prove the existence and uniqueness of the solution using viability for time-dependent closed convex sets to the case of non densely defined Cauchy problem. Moreover, we propose several characterizations of con...

We propose a general framework for a sufficient condition for the existence of the principal eigenpair to the problem L[u] + H[u] = λu, (λ, u) ∈ R × X, where L : X → X is a linear, bounded, positive operator, and H : D(H) ⊂ X → X a 10 closed, possibly unbounded linear operator in the Banach space (X, ∥ · ∥). Criteria for (i) the existence of a prin...

Plasmodium species exhibit differential preferences for red blood cells (RBCs) of different ages. From a fundamental standpoint, we propose an age-structured within-host malaria model taking into account the variation in RBCs preference. We show that such a differential ecological characteristic of Plasmodium species within their human host is fund...

In this article we prove the existence of almost periodic solution for a class of non homogeneous and semilinear Cauchy problems. The main novelty is the fact that the linear part is non dense and is not Hille-Yosida.KeywordsNonautonomous dynamical systemsIntegrated semigroupsAlmost periodic solutionsExponential dichotomy

In this paper, we analyze a nonlocal spatial epidemic model presenting the diffusion process of a spore producing plant pathogens responsible of one of the most destructive cocoa pods disease. The global existence, compactness and dissipativity of the semiflow generated by the system are established. By defining a threshold number (the basic reprod...

A mathematical model of the dengue epidemic in the Philippines is developed to analyse the vaccination of children in 2016–2017. Reported case data and reported mortality data from the Philippines Department of Health is used to analyze quantitatively this vaccination program. The model compares the epidemic outcomes of no vaccination of children,...

We use the theory of semigroups to obtain the existence and uniqueness of solutions for multilayer diffusion models with possibly non linear reactions terms as well as local non-homogeneous boundary conditions on the first and the last layers. We also allow the possibility of having Dirichlet, Newman or mixed type conditions in the first and the la...

Studying asymptotic properties for non-autonomous partial differential equations is often a challenging question due to the lack of general theory. We prove in this paper some monotony properties of a class of general nonlinear non-autonomous size(age)-structured population dynamic models. Our results are applied to an example in order to show how...

We consider a compartmental model from which we incorporate a time-dependent health care capacity having a logistic growth. This allows us to take into account the Senegalese authorities response in anticipating the growing number of infected cases. We highlight the importance of anticipation and timing to avoid overwhelming that could impact consi...

This study develops a generalized notion of sub tangential condition to establish the positive invariance of a closed subset under the semiflow generated by a semi-linear non densely defined Cauchy problem. We also remark that the sufficient condition for the positivity of the semiflow implies our sub tangentiality condition. In other words, our su...

We investigate the age structured data for the COVID-19 outbreak in Japan. We consider a mathematical model for the epidemic with unreported infectious patient with and without age structure. In particular, we build a new mathematical model and a new computational method to fit the data by using age classes dependent exponential growth at the early...

We investigate the age structured data for the COVID-19 outbreak in Japan. We consider epidemic mathematical model with unreported infectious patient with and without age structure. In particular, we build a new mathematical model which allows to take into account differences in the response of patients to the disease according to their age. This m...

In this work, our team develops a differential equations model of COVID-19 epidemics. Our goal is to predict forward in time the future number of cases from early reported case data in regions throughout the world. Our model incorporates the following important elements of COVID-19 epidemics: (1) the number of asymptomatic infectious individuals (w...

We model the COVID-19 coronavirus epidemic in China. We use early reported case data to predict the cumulative number of reported cases to a final size. The key features of our model are the timing of implementation of major public policies restricting social movement, the identification and isolation of unreported cases, and the impact of asymptom...

At the beginning of a COVID-19 infection, there is a period of time known as the exposed or latency period, before an infected person is capable of transmitting the infection to another person. We develop two differential equations models to account for this period. The first is a model that incorporates infected persons in the exposed class, befor...

We model the COVID-19 coronavirus epidemic in China. We use early reported case data to predict the cumulative number of reported cases to a final size. The key features of our model are the timing of implementation of major public policies restricting social movement, the identification and isolation of unreported cases, and the impact of asymptom...

We develop a mathematical model to provide epidemic predictions for the COVID-19 epidemic in Wuhan, China. We use reported case data up to 31 January 2020 from the Chinese Center for Disease Control and Prevention and the Wuhan Municipal Health Commission to parameterize the model. From the parameterized model, we identify the number of unreported...

We model the COVID-19 coronavirus epidemic in China. We use early reported case data to predict the cumulative number of reported cases to a final size. The key features of our model are the timing of implementation of major public policies restricting social movement, the identification and isolation of unreported cases, and the impact of asymptom...

We model the COVID-19 coronavirus epidemic in China. We use early reported case data to predict the cumulative number of reported cases to a final size. The key features of our model are the timing of implementation of major public policies restricting social movement, the identification and isolation of unreported cases, and the impact of asymptom...

In this paper we propose a two-group SIR age of infection epidemic model by incorporating periodical behavioral changes for both susceptible and infected individuals. Our model allows different incubation periods for the two groups. It is proved in this paper that the persistence and extinction of the disease are determined by a threshold condition...

In this article we prove the positive invariance of a closed subset by the semiflow generated by a semi-linear non densely Cauchy problem. The condition impose to obtain such a property is a so called sub-tangential condition. We apply our results to a class of age structured population models.

In this article we prove the positive invariance of a closed subset by the semiflow generated by a semi-linear non densely Cauchy problem. The condition impose to obtain such a property is a so called sub-tangential condition. We apply our results to a class of age structured population models.

In this article 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 semi-flow theory and some comparison principles for age struc...

We consider a system of non densely defined Cauchy problems and we investigate the persistence of normally hyperbolic manifolds. The notion of exponential dichotomy is used to characterize the normal hyperbolicity and a generalized Lyapunov-Perron approach is used in order to prove our main result. The result presented in this article extend the pr...

In this article 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 semi-flow theory and some comparison principles for age struc...

A model of an epidemic outbreak incorporating multiple subgroups of susceptible and infected individuals is investigated. The asymptotic behavior of the model is analyzed and it is proved that the infected classes all converge to 0. A computational algorithm is developed for the cumulative final size of infected individuals over the course of the e...

This work is devoted to the study of a class of singularly perturbed non-densely defined abstract Cauchy problems. We extend the Tikhonov's theorem for ordinary differential equations to the case of abstract Cauchy problems. Roughly speaking we prove that the solutions rapidly evolve and stay in some neighbourhood of the slow manifold. As a consequ...

In this paper we prove a variation of constants formula for a non autonomous and non homogeneous Cauchy problems whenever the linear part is not densely defined and is not a Hille-Yosida operator. By using this variation of constants formula we derive a necessary and sufficient conditions for the existence of exponential dichotomy for the evolution...

In this paper we consider a two-group SIR epidemic model. We study the finale size of the epidemic for each sub-population. The qualitative behavior of the infected classes at the earlier stage of the epidemic is described with respect to the basic reproduction number. Numerical simulations are also preformed to illustrate our results.

In this article we revisit the perturbation of exponential trichotomy of linear difference equation in Banach space by using a Perron-Lyapunov fixed point formulation for the perturbed evolution operator. This approach allows us to directly re-construct the perturbed semiflow without using shift spectrum arguments. These arguments are presented to...

In this article we consider a model describing hospital acquired infections. The model derived is a system of delay differential equations. The state variable is formed by the patients and the healthcare workers components. The system is a slow-fast system where the fast equation corresponds to the healthcare workers equation. The question addresse...

A differential equations model is developed for the 2014 Ebola epidemics in Sierra Leone, Liberia, and Guinea. The model describes the dynamic interactions of the susceptible and infected populations of these countries. The model incorporates the principle features of contact tracing, namely, the number of contacts per identified infectious case, t...

In this article we study exponential trichotomy for infinite dimen-sional discrete time dynamical systems. The goal of this article is to prove that finite time exponential trichotomy conditions allow to derive exponential trichotomy for any times. We present an application to the case of pseudo orbits in some neighborhood of a normally hyperbolic...

In this article, we derive Ricker's [22, 23] type nonlinear boundary con-dition for an age structured population dynamic model by using a singular perturbation. The question addressed in this paper is the convergence of the singularly perturbed system. We first obtain a finite time convergence for a fixed initial distribution. Then we focus on the...