arXiv subjects

Amira Rachah

Publications and source records attributed to Amira Rachah.

7 recordsLinked to original sources

arXiv2017

Analysis, simulation and optimal control of a SEIR model for Ebola virus with demographic effects

Ebola virus is one of the most virulent pathogens for humans. We present a mathematical description of different Susceptible-Exposed-Infectious-Recovered (SEIR) models. By using mathematical modeling and analysis, the latest major outbreak of Ebola virus in West Africa is described. Our aim is to study and discuss the properties of SEIR models with respect to Ebola virus, the information they provide, and when the models make sense. We added to the basic SEIR model demographic effects in order to analyze the equilibria with vital dynamics. Numerical simulations confirm the theoretical analysis. The control of the propagation of the virus through vaccination is investigated and the case study of Liberia is discussed in detail.

q-bio.PE↗

arXiv2016

Modeling, dynamics and optimal control of Ebola virus spread

We present a mathematical analysis of the early detection of Ebola virus. The propagation of the virus is analysed by using a Susceptible, Infected, Recovered (SIR) model. In order to provide useful predictions about the potential transmission of the virus, we analyse and simulate the SIR model with vital dynamics, by adding demographic effects and an induced death rate. Then, we compute the equilibria of the model. The numerical simulations confirm the theoretical analysis. Our study describes the 2015 detection of Ebola virus in Guinea, the parameters of the model being identified from the World Health Organization data. Finally, we consider an optimal control problem of the propagation of the Ebola virus, minimizing the number of infected individuals while taking into account the cost of vaccination.

q-bio.PE↗

arXiv2016

Dynamics and optimal control of Ebola transmission

A major Ebola outbreak occurs in West Africa since March 2014, being the deadliest epidemic in history. As an infectious disease epidemiology, Ebola is the most lethal and is moving faster than in previous outbreaks. On 8 August 2014, the World Health Organization (WHO) declared the outbreak a public health emergency of international concern. Last update on 7 July 2015 by WHO reports 27 609 cases of Ebola with a total of 11 261 deaths. In this work, we present a mathematical description of the spread of Ebola virus based on the SEIR (Susceptible-Exposed-Infective-Recovered) model and optimal strategies for Ebola control. In order to control the propagation of the virus and to predict the impact of vaccine programmes, we investigate several strategies of optimal control of the spread of Ebola: control infection by vaccination of susceptible; minimize exposed and infected; reduce Ebola infection by vaccination and education.

math.OC↗

arXiv2015

Optimal control strategies for the spread of Ebola in West Africa

The spread of Ebola virus in 2014 is unprecedented. The epidemic is still affecting West Africa, exacerbated by extraordinary socioeconomic disadvantages and health system inadequacies. With the aim of understanding, predicting, and control the propagation of the virus in the populations of affected countries, it is crucial to model the dynamics of the virus and study several strategies to control it. In this paper, we present a very simple mathematical model that describes quite well the spread of Ebola. Then, we discuss several strategies for the control of the propagation of this lethal virus into populations, in order to predict the impact of vaccine programmes, treatment, and the impact of educational campaigns.

math.OC↗

arXiv2015

Predicting and controlling the Ebola infection

We present a comparison between two different mathematical models used in the description of the Ebola virus propagation currently occurring in West Africa. In order to improve the prediction and the control of the propagation of the virus, numerical simulations and optimal control of the two models for Ebola are investigated. In particular, we study when the two models generate similar results.

q-bio.PE↗

arXiv2015

Mathematical Modelling, Simulation, and Optimal Control of the 2014 Ebola Outbreak in West Africa

The Ebola virus is currently one of the most virulent pathogens for humans. The latest major outbreak occurred in Guinea, Sierra Leonne and Liberia in 2014. With the aim of understanding the spread of infection in the affected countries, it is crucial to modelize the virus and simulate it. In this paper, we begin by studying a simple mathematical model that describes the 2014 Ebola outbreak in Liberia. Then, we use numerical simulations and available data provided by the World Health Organization to validate the obtained mathematical model. Moreover, we develop a new mathematical model including vaccination of individuals. We discuss different cases of vaccination in order to predict the effect of vaccination on the infected individuals over time. Finally, we apply optimal control to study the impact of vaccination on the spread of the Ebola virus. The optimal control problem is solved numerically by using a direct multi-shooting method.

q-bio.PE↗

arXiv2013

Optimal control of crystallization of alpha-lactose monohydrate

We present a mathematical model for solvated crystallization of alpha -lactose monohydrate in semi-batch mode. The process dynamics are governed by conservation laws including population, molar and energy balance equations. We present and discuss the model and then control the process with the goal to privilege the production of small particles in specific the range. We compare several specific and unspecific cost functions leading to optimal strategies with significantly different effects on product quality. Control inputs are temperature, feed rate, and the choice of an appropriate crystal seed.

math.OC↗