Chaos in a seasonally perturbed SIR model: avian influenza in a seabird colony as a paradigm

Abstract

Seasonality is a complex force in nature that affects multiple processes in wild animal populations. In particular, seasonal variations in demographic processes may considerably affect the persistence of a pathogen in these populations. Furthermore, it has been long observed in computer simulations that under seasonal perturbations, a host-pathogen system can exhibit complex dynamics, including the transition to chaos, as the magnitude of the seasonal perturbation increases. In this paper, we develop a seasonally perturbed Susceptible-Infected-Recovered model of avian influenza in a seabird colony. Numerical simulations of the model give rise to chaotic recurrent epidemics for parameters that reflect the ecology of avian influenza in a seabird population, thereby providing a case study for chaos in a host- pathogen system. We give a computer-assisted exposition of the existence of chaos in the model using methods that are based on the concept of topological hyperbolicity. Our approach elucidates the geometry of the chaos in the phase space of the model, thereby offering a mechanism for the persistence of the infection. Finally, the methods described in this paper may be immediately extended to other infections and hosts, including humans.

Seasonal forcing in a host–macroparasite system

“…Also, our results indicate several regions of (apparently) chaotic behaviour, due to the many period-doubling bifurcation curves which can give rise to period-doubling cascades (Aron and Schwartz, 1984). This multitude of period-doubling cascades is not readily observed in other seasonal systems (O'Regan et al, 2013;Rinaldi et al, 1993). Our study also shows that period-halving can occur, which has not been reported in previous studies of seasonally forced models.…”

FPGA Realizations of Chaotic Epidemic and Disease Models Including Covid-19

“…In this section, we describe the four models that are considered in this work. The details of these models and their respective derivation assumptions can be found in [11], [13], [25] and [34].…”

How can contemporary climate research help understand epidemic dynamics? Ensemble approach and snapshot attractors

“…There are observations, for example in childhood diseases or avian influenza, that do not show damped characteristics rather (ir)regular cycles instead. This phenomenon can be linked to seasonal variation in contact rate b(t) or in recruitment rate g 19 . It has already been noticed that in case of periodic forcing, b 0 (t) = b 0 =const.…”

“…Sufficiently large seasonal forcing or different mixing rates between sub-populations can cause large oscillations and also period doubling cascades [12][13][14][15][16][17][18] . It has also been demonstrated that for certain values of system parameters the nonautonomous models of recurrent epidemics (measles, mumps, rubella, H5N1 avian influenza) show chaotic behavior 6,[19][20][21] . Traditional SIR-like epidemic models are dissipative nonlinear low-dimensional systems with constant, periodic, quasiperiodic 22 , or term-time 3,23 external forcing whose dynamics a) Electronic mail: tkovacs@general.elte.hu is governed by (chaotic) attractors in phase space.…”