Self-sustained oscillations emerge from a SIR model with realistic vital dynamics

JAVIER GUTIERREZ; KARINA LANERI; JUAN PABLO APARICIO

Bariloche

Seminario; Seminario del grupo de Teoría de Sólidos; 2016

Centro Atómico Bariloche

In reported SIR models with vital dynamics it is usually assumed that human mortality is an exponential probability density function that gives rise to constant death and birth rates. Such a formulation can only produce damped oscillations towards an equilibrium state. In this work we assume that human survivorship can be modeled with gamma distributed birth and death rates, which is a more realistic assumption in developed and developing countries. We show that self sustained oscillations emerge in a continuous transition from a damped oscillation regime trough a supercritical Hopf bifurcation, when the shape parameter of the gamma distribution is sufficiently high. The consideration of realistic vital dynamics can give rise to oscillations periods different form the ones reported, re-opening the discussion about the intrinsic feedbacks in many infectious diseases.