Seasonally Forced SIR Systems Applied to Respiratory Infectious Diseases, Bifurcations, and Chaos

STOLLENWERK, NICO; SPAZIANI, STEFANO; MAR, JAVIER; ARRIZABALAGA, IRATI EGUIGUREN; KNOPOFF, DAMIÁN; CUSIMANO, NICOLE; ANAM, VIZDA; SHRIVASTAVA, AKHIL; AGUIAR, MAÍRA

Computational and Mathematical Methods

Hindawi

Año: 2022 vol. 2022 p. 1 - 12

We investigate models to describe respiratory diseases with fast mutating virus pathogens such that after some years theaquired resistance is lost and hosts can be infected with new variants of the pathogen. Such models were initially suggested forrespiartory diseases like influenza, showing complex dynamics in reasonable parameter regions when comparing to historicempirical influenza like illness data, e.g., from Ille de France. The seasonal forcing typical for respiratory diseases gives rise tothe different rich dynamical scenarios with even small parameter changes. Especially the seasonality of the infection leads forsmall values already to period doubling bifurcations into chaos, besides additional coexisting attractors. Such models could inthe future also play a role in understanding the presently experienced COVID-19 pandemic, under emerging new variants andwith only limited vaccine efficacies against newly upcoming variants. From first period doubling bifurcations, we caneventually infer at which close by parameter regions complex dynamics including deterministic chaos can arise.