Oscillations in SIRS model with distributed delays

Details Oscillations in SIRS model with distributed delays Oscillations in SIRS model with distributed delays

2009-12-07

arxiv.org/abs/0912.1250v3

Eur. Phys. J. B 81 (2011) 363-371

Biology

Quantitative Biology

Populations and Evolution

18 pages, 12 figures

Scientific paper

10.1140/epjb/e2011-20054-9

The ubiquity of oscillations in epidemics presents a long standing challenge for the formulation of epidemic models. Whether they are external and seasonally driven, or arise from the intrinsic dynamics is an open problem. It is known that fixed time delays destabilize the steady state solution of the standard SIRS model, giving rise to stable oscillations for certain parameters values. In this contribution, starting from the classical SIRS model, we make a general treatment of the recovery and loss of immunity terms. We present oscillation diagrams (amplitude and period) in terms of the parameters of the model, showing how oscillations can be destabilized by the shape of the distributions of the two characteristic (infectious and immune) times. The formulation is made in terms of delay equation which are both numerical integrated and linearized. Results from simulation are included showing where they support the linear analysis and explaining why not where they do not. Considerations and comparison with real diseases are presented along.

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