Performances optimales d'une allocation globale de ressources radio dans des réseaux hétérogènes

L'évolution des réseaux sans fil et mobiles devient de plus en plus rapide, ainsi l'allocation optimale de ressources radio est un problème qui s'impose. Ce développement de réseaux de télécommunications est accompagné d'un déploiement efficient de réseaux sans fil tels que le Wireless Fidelity et des réseaux mobiles comme le LongTerm Evolution(LTE). Dans cet article, nous proposons un algorithme améliorant l'allocation globale de ressources radio dans le cadre d'un système hétérogène de réseaux sans fil et mobile à l'aide de la programmation dynamique notamment le principe d'optimalité de Bellman. Nous avons pris en compte la mobilité des utilisateurs en utilisant le modèle 2D Fluid Flow pour obtenir de meilleures performances testées numériquement par le Network Simulator 3(NS3)

Performances optimales d'une allocation globale de ressources radio dans des réseaux hétérogènes

L'évolution des réseaux sans fil et mobiles devient de plus en plus rapide, ainsi l'allocation optimale de ressources radio est un problème qui s'impose. Ce développement de réseaux de télécommunications est accompagné d'un déploiement efficient de réseaux sans fil tels que le Wireless Fidelity et des réseaux mobiles comme le LongTerm Evolution(LTE). Dans cet article, nous proposons un algorithme améliorant l'allocation globale de ressources radio dans le cadre d'un système hétérogène de réseaux sans fil et mobile à l'aide de la programmation dynamique notamment le principe d'optimalité de Bellman. Nous avons pris en compte la mobilité des utilisateurs en utilisant le modèle 2D Fluid Flow pour obtenir de meilleures performances testées numériquement par le Network Simulator 3(NS3)

On the Optimal Control of Intervention Strategies for Hepatitis B Model

Hepatitis B is one of the leading causes of morbidity and mortality, affecting hundreds of millions of people worldwide. Thus, this paper focuses on three control measures as the best way to intervene against the hepatitis B viral infection. These measures are condom use, testing and treatment, and vaccination to stop the disease from spreading over a community. The model comprises seven (7) compartments that include susceptible individuals, latent individuals, acute-infected individuals, chronic-infected individuals, infected by carrier individuals, recovered individuals from the disease, and the vaccinated population. We mathematically established a nonlinear differential equation to study the dynamics of the model. The disease-free equilibrium (DFE) and endemic equilibrium (EE) are reached. The basic reproduction numbers, R0A, R0H, and R0C, determine the transmission of the disease and thus are gotten. We perform sensitivity analysis on the reproduction numbers to identify the factors that affect the reproduction numbers. The results of the sensitivity analysis paved a way for introducing a controlled system which was solved using Pontryagin’s maximum principle (PMP) and the optimality system got. The optimality system was then solved numerically using the forward and backward sweep approach, and graphs were generated, establishing the conditions for local and global stability of the disease-free equilibrium using the Routh-Hurwitz criterion and Castillo-Chavez approach, respectively. We also used Pontryagin’s maximum principle to determine the optimality system. The result of the analysis of the stability of the disease-free equilibrium states that hepatitis B virus can be completely wiped out if the rate of infection is kept at a number less than unity. A numerical simulation of the model was carried out and showed that hepatitis B virus transmission can best be controlled when condom use, testing and treatment, and vaccination are implemented

Mathematical analysis and optimal control interventions for sex structured syphilis model with three stages of infection and loss of immunity

Abstract In this study, we develop a nonlinear ordinary differential equation to study the dynamics of syphilis transmission incorporating controls, namely prevention and treatment of the infected males and females. We obtain syphilis-free equilibrium (SFE) and syphilis-present equilibrium (SPE). We obtain the basic reproduction number, which can be used to control the transmission of the disease, and thus establish the conditions for local and global stability of the syphilis-free equilibrium. The stability results show that the model is locally asymptotically stable if the Routh–Hurwitz criteria are satisfied and globally asymptotically stable. The bifurcation analysis result reveals that the model exhibits backward bifurcation. We adopted Pontryagin’s maximum principle to determine the optimality system for the syphilis model, which was solved numerically to show that syphilis transmission can be optimally best control using a combination of condoms usage and treatment in the primary stage of infection in both infected male and female populations