Karam Allali

Bio: Karam Allali is an academic researcher from University of Hassan II Casablanca. The author has contributed to research in topics: Natural convection & Darcy's law. The author has an hindex of 12, co-authored 82 publications receiving 446 citations. Previous affiliations of Karam Allali include Claude Bernard University Lyon 1 & University of Lyon.

Mathematical analysis of a fractional differential model of HBV infection with antibody immune response

Abstract: Fractional differential mathematical model describing the dynamics of hepatitis B viral infection with DNA-containing capsids, the liver hepatocytes and the humoral immune response is presented and investigated in this paper. The humoral immunity is represented by antibodies, the principal role of those antibodies is to attack the free viruses. In order to describe the time needed for the interaction between biological liver cells and viral particles and also the time needed for the activation of the humoral immune response, a memory term represented by a fractional derivative will be added in each equation of our suggested model. The positivity and boundedness of all solutions with non negative initial condition will be proved which is consistent biologically. Moreover, the disease-free equilibrium, the infection steady state without humoral immunity and the infection steady state with humoral immunity are given. By constructing some suitable Lyapunov functionals, the global stability of all equilibria are proven depending on the basic reproduction number and on the antibody immune response reproduction number. Finally, different numerical simulations using the multistage generalized differential method are established in order to illustrate our theoretical findings. It was revealed from both the theoretical and the numerical results that the order of the fractional derivative has no effect on the three equilibria stability. However, for increased values of the fractional derivative order, which describes the long memory behavior, each solution converge more rapidly to its stationary state.

Global dynamics of a multi-strain SEIR epidemic model with general incidence rates: application to COVID-19 pandemic.

Abstract: This paper investigates the global stability analysis of two-strain epidemic model with two general incidence rates. The problem is modelled by a system of six nonlinear ordinary differential equations describing the evolution of susceptible, exposed, infected and removed individuals. The wellposedness of the suggested model is established in terms of existence, positivity and boundedness of solutions. Four equilibrium points are given, namely the disease-free equilibrium, the endemic equilibrium with respect to strain 1, the endemic equilibrium with respect to strain 2, and the last endemic equilibrium with respect to both strains. By constructing suitable Lyapunov functional, the global stability of the disease-free equilibrium is proved depending on the basic reproduction number $$R_0$$ . Furthermore, using other appropriate Lyapunov functionals, the global stability results of the endemic equilibria are established depending on the strain 1 reproduction number $$R^{1}_0$$ and the strain 2 reproduction number $$R^{2}_0$$ . Numerical simulations are performed in order to confirm the different theoretical results. It was observed that the model with a generalized incidence functions encompasses a large number of models with classical incidence functions and it gives a significant wide view about the equilibria stability. Numerical comparison between the model results and COVID-19 clinical data was conducted. Good fit of the model to the real clinical data was remarked. The impact of the quarantine strategy on controlling the infection spread is discussed. The generalization of the problem to a more complex compartmental model is illustrated at the end of this paper.

Mathematical analysis and simulation of a stochastic COVID-19 Lévy jump model with isolation strategy.

Abstract: This paper investigates the dynamics of a COVID-19 stochastic model with isolation strategy. The white noise as well as the Levy jump perturbations are incorporated in all compartments of the suggested model. First, the existence and uniqueness of a global positive solution are proven. Next, the stochastic dynamic properties of the stochastic solution around the deterministic model equilibria are investigated. Finally, the theoretical results are reinforced by some numerical simulations.

Solving Permutation Flow Shop Scheduling Problem with Sequence-Independent Setup Time

Abstract: In this paper, we study the resolution of a permutation flow shop problem with sequence-independent setup time. The objective is to minimize the maximum of job completion time, also called the makespan. In this contribution, we propose three methods of resolution, a mixed-integer linear programming (MILP) model; two heuristics, the first based on Johnson’s rule and the second based on the NEH algorithm; and finally two metaheuristics, the iterative local search algorithm and the iterated greedy algorithm. A set of test problems is simulated numerically to validate the effectiveness of our resolution approaches. For relatively small-size problems, it has been revealed that the adapted NEH heuristic has the best performance than that of the Johnson-based heuristic. For the relatively medium and large problems, the comparative study between the two metaheuristics based on the exploration of the neighborhood shows that the iterated greedy algorithm records the best performances.

Global stability analysis of a two-strain epidemic model with non-monotone incidence rates

Abstract: In this paper, we study an epidemic model describing two strains with non-monotone incidence rates. The model consists of six ordinary differential equations illustrating the interaction between the susceptible, the exposed, the infected and the removed individuals. The system of equations has four equilibrium points, disease-free equilibrium, endemic equilibrium with respect to strain 1, endemic equilibrium with respect to strain 2, and the last endemic equilibrium with respect to both strains. The global stability analysis of the equilibrium points was carried out through the use of suitable Lyapunov functions. Two basic reproduction numbers R 0 1 and R 0 2 are found; we have shown that if both are less than one, the disease dies out. It was established that the global stability of each endemic equilibrium depends on both basic reproduction numbers and also on the strain inhibitory effect reproduction number(s) Rm and/or Rk. It was also shown that any strain with highest basic reproduction number will automatically dominate the other strain. Numerical simulations were carried out to support the analytic results and to show the effect of different problem parameters on the infection spread.