4 citations · 10 across the 7 of their papers we have counts for
7 papers
Exact solution for a quantum SIR model
Márcia Lemos-Silva, Sandra Vaz, Delfim F. M. Torres
Based on the classical continuous system initially proposed by Bailey in 1975, we present a novel Susceptible--Infected--Removed (SIR) model defined in quantum time, where the temp…
A consistent SIR model on time scales with exact solution
Márcia Lemos-Silva, Sandra Vaz, Delfim F. M. Torres
We propose a new dynamic SIR model that, in contrast with the available model on time scales, is biological relevant. For the new SIR model we obtain an explicit solution, we prove…
The Omega Calculus of Variations
Márcia Lemos-Silva, Delfim F. M. Torres
We prove a necessary optimality condition of Euler--Lagrange type for the calculus of variations with Omega derivatives, which turns out to be sufficient under jointly convexity of…
Exact solution for a discrete-time SIR model
Márcia Lemos-Silva, Sandra Vaz, Delfim F. M. Torres
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 i…
Stability analysis and optimal control of the logistic equation
Márcia Lemos-Silva, Sandra Vaz, Delfim F. M. Torres
We consider the unexploited/exploited logistic equation and study the stability of equilibrium points through Lyapunov functions. Then, we apply first and second order optimality c…
The Lotka-Volterra Dynamical System and its Discretization
Márcia Lemos-Silva, Delfim F. M. Torres
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 t…
A note on a prey-predator model with constant-effort harvesting
Márcia Lemos-Silva, Delfim F. M. Torres
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 prese…