Drug treatment, snail control, cercariae control, improved sanitation and health education are the effective strategies which are used to control the schistosomiasis. In this paper, we consider a deterministic model f...Drug treatment, snail control, cercariae control, improved sanitation and health education are the effective strategies which are used to control the schistosomiasis. In this paper, we consider a deterministic model for schistosomiasis transmission dynamics in order to explore the role of the several control strategies. The global stability of a schistosomiasis infection model that involves mating structure including male schistosomes, female schistosomes, paired schistosomes and snails is studied by constructing appropriate Lyapunov functions. We derive the basic reproduction number R0 for the deterministic model, and establish that the global dynamics are completely determined by the values of R0. We show that the disease can be eradicated when R0?≤1;otherwise, the system is persistent. In the case where ?R0?>1, we prove the existence, uniqueness and global asymptotic stability of an endemic steady state. Sensitivity analysis and simulations are carried out in order to determine the relative importance of different control strategies for disease transmission and prevalence. Next, optimal control theory is applied to investigate the control strategies for eliminating schistosomiasis using time dependent controls. The characterization of the optimal control is carried out via the Pontryagins Maximum Principle. The simulation results demonstrate that the insecticide is important in the control of schistosomiasis.展开更多
In this paper we show a boundary result of controllability by a new approach using a linear, continuous and surjective operator built from the solution of the heat system. And, subsequently, the border exact controlla...In this paper we show a boundary result of controllability by a new approach using a linear, continuous and surjective operator built from the solution of the heat system. And, subsequently, the border exact controllability of the 1D heat equation through a compactness criterion and the use of strategic zone actuators were established.展开更多
The aim of this work is to improve the minimum time of null controllability of the 1D heat equation by using the notion of strategic zone actuators. In fact, motivated by the work of Khodja on the null controllability...The aim of this work is to improve the minimum time of null controllability of the 1D heat equation by using the notion of strategic zone actuators. In fact, motivated by the work of Khodja on the null controllability of the heat equation and of El Jai on the controllability by the use of strategic zone actuators, we managed, in this work, to improve the minimal time of null controllability to the 1D heat equation. However, the restrictions and difficulties to establish the inequality of coercivity of the parabolic operator, require to seek other methods of internal control. Thus in this paper, a mixed method combining the method of moments and the notion of strategic profile was used to find a better minimal time of null controllability of the 1D heat equation.展开更多
Partial Differential Equations (PDEs) have been already widely used to simulate various complex phenomena in porous media. This paper is one of the first attempts to apply PDEs for simulating in real 3D structures. We...Partial Differential Equations (PDEs) have been already widely used to simulate various complex phenomena in porous media. This paper is one of the first attempts to apply PDEs for simulating in real 3D structures. We apply this scheme to the specific case study of the microbial decomposition of organic matter in soil pore space. We got a 3D geometrical representation of the pore space relating to a network of volume primitives. A mesh of the pore space is then created by using the network. PDEs system is solved by free finite elements solver Freefem3d in the particular mesh. We validate our PDEs model to experimental data with 3D Computed Tomography (CT) images of soil samples. Regarding the current state of art on soil organic matter decay models, our approach allows taking into account precise 3D spatialization of the decomposition process by a pore space geometry description.展开更多
文摘Drug treatment, snail control, cercariae control, improved sanitation and health education are the effective strategies which are used to control the schistosomiasis. In this paper, we consider a deterministic model for schistosomiasis transmission dynamics in order to explore the role of the several control strategies. The global stability of a schistosomiasis infection model that involves mating structure including male schistosomes, female schistosomes, paired schistosomes and snails is studied by constructing appropriate Lyapunov functions. We derive the basic reproduction number R0 for the deterministic model, and establish that the global dynamics are completely determined by the values of R0. We show that the disease can be eradicated when R0?≤1;otherwise, the system is persistent. In the case where ?R0?>1, we prove the existence, uniqueness and global asymptotic stability of an endemic steady state. Sensitivity analysis and simulations are carried out in order to determine the relative importance of different control strategies for disease transmission and prevalence. Next, optimal control theory is applied to investigate the control strategies for eliminating schistosomiasis using time dependent controls. The characterization of the optimal control is carried out via the Pontryagins Maximum Principle. The simulation results demonstrate that the insecticide is important in the control of schistosomiasis.
文摘In this paper we show a boundary result of controllability by a new approach using a linear, continuous and surjective operator built from the solution of the heat system. And, subsequently, the border exact controllability of the 1D heat equation through a compactness criterion and the use of strategic zone actuators were established.
文摘The aim of this work is to improve the minimum time of null controllability of the 1D heat equation by using the notion of strategic zone actuators. In fact, motivated by the work of Khodja on the null controllability of the heat equation and of El Jai on the controllability by the use of strategic zone actuators, we managed, in this work, to improve the minimal time of null controllability to the 1D heat equation. However, the restrictions and difficulties to establish the inequality of coercivity of the parabolic operator, require to seek other methods of internal control. Thus in this paper, a mixed method combining the method of moments and the notion of strategic profile was used to find a better minimal time of null controllability of the 1D heat equation.
文摘Partial Differential Equations (PDEs) have been already widely used to simulate various complex phenomena in porous media. This paper is one of the first attempts to apply PDEs for simulating in real 3D structures. We apply this scheme to the specific case study of the microbial decomposition of organic matter in soil pore space. We got a 3D geometrical representation of the pore space relating to a network of volume primitives. A mesh of the pore space is then created by using the network. PDEs system is solved by free finite elements solver Freefem3d in the particular mesh. We validate our PDEs model to experimental data with 3D Computed Tomography (CT) images of soil samples. Regarding the current state of art on soil organic matter decay models, our approach allows taking into account precise 3D spatialization of the decomposition process by a pore space geometry description.
