3 documents found, page 1 of 1
Exact solution for a discrete-time SIR model
Lemos-Silva, Márcia; Vaz, Sandra; Torres, Delfim F.M.We propose a nonstandard finite difference scheme for the Susceptible–Infected–Removed (SIR) continuous model. We prove that our discretized system is dynamically consistent with its continuous counterpart and we derive its exact solution. We end with the analysis of the long-term behavior of susceptible, infected and removed individuals, illustrating our results with examples. In contrast with the SIR discrete...
The Lotka-Volterra dynamical system and its discretization
Lemos-Silva, Márcia; Torres, Delfim F. M.Dynamical systems are a valuable asset for the study of population dynamics. On this topic, much has been done since Lotka and Volterra presented the very first continuous system to understand how the interaction between two species – the prey and the predator – influences the growth of both populations. The definition of time is crucial and, among options, one can have continuous time and discrete time. The ch...
A note on a prey-predator model with constant-effort harvesting
Lemos-Silva, Márcia; Torres, Delfim F. M.We study a prey-predator model based on the classical Lotka–Volterra system with Leslie–Gower and Holling IV schemes and a constant-effort harvesting. Our goal is twofold: to present the model proposed by Cheng and Zhang in 2021, pointing out some inconsistencies; to analyse the number and type of equilibrium points of the model. We end by proving the stability of the meaningful equilibrium point, according to ...