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Description
Spontaneous behavioural changes in response to an outbreak can significantly alter transmission dynamics. Recent studies \cite{ Omori2024JTB} have explored how the human perception of risk, and the subsequent reduction in contact rates, can be modelled as a function of epidemiological indicators. This study aims to provide a qualitative understanding of how such perception-based feedback shapes the emergence and characteristics of multi-wave epidemics.
We analyse an SIR-type model where the transmission rate depends on a non-linear function of past infection levels, reflecting the diminishing sensitivity of human behaviour to increasing incidence. To evaluate the oscillatory potential of the system, we employ a quasi-stationary approximation for the susceptible population. By linearizing the dynamics using logarithmic perturbations around the quasi-equilibrium, we derive the characteristic equation and analytically identify the conditions under which the interaction between the disease and behaviour leads to self-sustained oscillations. Our findings elucidate how the non-linear scaling of risk perception, combined with information lag, governs the fundamental frequency and damping of epidemic waves.
This analysis offers a theoretical basis for understanding the mechanisms by which behavioural-epidemiological interactions generate complex, multi-modal epidemic trajectories.
Bibliography
@article{Omori2024JTB, author = {Omori, Ryosuke and Ito, Koichi and Kanemitsu, Shunsuke and Kimura, Ryusuke and Iwasa, Yoh}, title = {Human movement avoidance decisions during Coronavirus disease 2019 in Japan}, journal = {Journal of Theoretical Biology}, volume = {585}, pages = {111795}, year = {2024}, month = {May}, doi = {10.1016/j.jtbi.2024.111795}, url = {https://doi.org/10.1016/j.jtbi.2024.111795} }
