Autor(es): Lemos-Silva, Márcia ; Vaz, Sandra ; Torres, Delfim F.M.
Data: 2025
Identificador Persistente: http://hdl.handle.net/10773/42576
Origem: RIA - Repositório Institucional da Universidade de Aveiro
Assunto(s): Compartmental models; Nonlinear epidemiological systems; Mickens method; Local stability; Exact solution of a SIR discrete-time system; Consistent discretization
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-time model available in the literature, our new model is simultaneously mathematically and biologically sound.
