(ANAP) Chaotic dynamics and bifurcations in modified SIR models

(ANAP) Chaotic dynamics and bifurcations in modified SIR models

Laboratório 4, DMat, UMinho, pólo de Gualtar

2024-05-29 - 15:45

Orador: João Maurício de Carvalho (FCUP, CMUP)

Título: Chaotic dynamics and bifurcations in modified SIR models

Data: quarta-feira, 29 de Maio de 2024, 15h45min

Local: Laboratório 4, DMat, UMinho, pólo de Gualtar

Grupo: Análise e Aplicações

Resumo: This presentation is divided into three parts:

In the first part we analyze a periodically forced SIR model. We prove that for R0 < 1 the system exhibits multiple endemic equilibria -- backward bifurcation. Using the theory of strange attractors, we prove the persistence of strange attractors for an open subset in the parameter space where R0 < 1.

In the second part, we address a modified SIR model with a constant vaccination strategy and the bifurcations it unfolds.  We explicitly prove that the endemic equilibrium is a codimension two singularity in the parameter space (R0, p), where R0 is the basic reproduction number and p is the proportion of susceptible individuals successfully vaccinated at birth. The analytical expressions of the bifurcation curves as a function of R0 and p estimate the proportion of vaccinated susceptible individuals necessary for the disease to be eliminated from the population.  

In the third part we present our ongoing work. We focus on two main topics: (i) in the absence of seasonality, the endemic (and unique) equilibrium point undergoes supercritical and subcritical Hopf bifurcations; (ii) in the presence of seasonality, we conjecture that, via the torus breakdown theory, the system exhibits chaotic dynamics. 

This seminar will be in portuguese and is a joint work with Alexandre Rodrigues (ISEG, CEMAPRE).

(Este seminário será precedido de outro com uma pequena pausa.)