November 2, 2023

Research Seminar – Dynamic SIR Models with an Exact Solution

Title: Dynamic SIR Models with an Exact Solution

Speaker: Prof. Dr. Delfim F. M. Torres

Affiliation: University of Aveiro, Portugal

Abstract: We investigate an epidemic model based on Bailey’s continuous differential system. In the continuous time domain, we extend the classical model to time-dependent coefficients and present an alternative solution method to Gleissner’s approach. If the coefficients are constant, both solution methods yield the same result. In the discrete case, this provides the solution to a new discrete epidemic system. However, the biological significance is not maintained. To address the problem, we derive a nonstandard finite difference scheme for Bailey’s Susceptible-Infected-Removed 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 simulations.