Numerical simulation of the SIR and Lotka-Volterra models used in biology

Arabi, Inasse El; Chafi, Anas; Alami, Salaheddine Kammouri

doi:10.1109/isacs48493.2019.9068876

Cited by 2 publications

(3 citation statements)

References 6 publications

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“…Using the previous finite difference schemes, the corresponding division scheme for solving the 1D advection-diffusion-reaction equation by the Splitting method is [4], [5], [6]:…”

Section: The Splitting Methodsmentioning

confidence: 99%

Numerical simulation of the advection-diffusion-reaction equation using finite difference and operator splitting methods: Application on the 1D transport problem of contaminant in saturated porous media

2022

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The combined advection-diffusion-reaction (ADR) equation, which describe the transport problem of a contaminant in porous medium, does not generally admit an analytical solution. In general, when solving the ADR equation, the numerical methods (such as finite differences, finite elements, splitting), for most practical problems, the ADR equation is too difficult to solve analytically. The finite difference method is the oldest and most commonly used method for the numerical solution of this kind of equation. Although newer techniques, such as those based on finite elements and splitting are appropriate for the solution of equilibrium-type problems, the finite difference remains the most appropriate for the solution of time-dependent phenomena. The transport of a contaminant can also be written by the ADR equation; hence, our objective is to choose the most efficient method to study the 1D transport problem of a contaminant and its evolution in a porous medium. In this work, we will simulate the ADR equation using two different methods: those of finite difference and splitting ones. The numerical result will be compared with the analytical solution in order to discuss the stability and the convergence of each of them using those two different methods. In the end, we will show that the splitting technical method is more efficient for solving this kind of problems in comparison with the finite difference method despite the fact that the latter is the most widely used by researchers. The validation of the efficiency of this method, implemented in this simulation, is tested on a 1D-transport problem of contaminant in a saturated porous medium.

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“…Using the previous finite difference schemes, the corresponding division scheme for solving the 1D advection-diffusion-reaction equation by the Splitting method is [4], [5], [6]:…”

Section: The Splitting Methodsmentioning

confidence: 99%

Numerical simulation of the advection-diffusion-reaction equation using finite difference and operator splitting methods: Application on the 1D transport problem of contaminant in saturated porous media

2022

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“…El Arabi et al performed the numerical simulation of the SIR and the Lotka-Volterra models used to describe the dynamics of predator-prey biological systems, the evolution of an infectious disease in any population, and bacterial growth in a given environment. These models formed a system of non-linear and coupled equations, which required special numerical processing [21]. Bouaine and Rachik established an improved spatiotemporal discrete LV model, including different species occupying a three-dimensional area and obeying any complex marine food chain.…”

Section: Related Workmentioning

confidence: 99%

“…After the model's establishment, the system's equilibrium point can be obtained according to the model, and the stability of the equilibrium point can be judged [21]. In solving the equilibrium point, we must set each equation to zero.…”

Section: Equilibrium Points and Stability Analysismentioning

confidence: 99%

Ecosystem Stability Analysis and Numerical Simulation via Three Improved Lotka-Volterra Models

Wang,

Zhou,

Wang

2023

Fuzzy Systems and Data Mining IX

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This study analyzed the stability of predator-prey ecosystem (including the sensitivity of the initial value and coefficient) via the original Lotka-Volterra model and three improved models. The first improved model considered the impact of hunting and internal competition on the ecosystem, the second introduced the second prey to the original model, while the third added the second-type predator and the second-type prey to the original system. The performed numerical simulation of the original and three improved models proved instability of the ecosystem represented by the original Lotka-Volterra model and the stability of those represented by all three improved models.

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Numerical simulation of the SIR and Lotka-Volterra models used in biology

Cited by 2 publications

References 6 publications

Numerical simulation of the advection-diffusion-reaction equation using finite difference and operator splitting methods: Application on the 1D transport problem of contaminant in saturated porous media

Numerical simulation of the advection-diffusion-reaction equation using finite difference and operator splitting methods: Application on the 1D transport problem of contaminant in saturated porous media

Ecosystem Stability Analysis and Numerical Simulation via Three Improved Lotka-Volterra Models

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