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- Title
Relaxation Oscillations in an SIS Epidemic Model with a Nonsmooth Incidence.
- Authors
Zhang, Yingying; Niu, Ruijuan
- Abstract
In this study, we extend an SIS epidemic model by introducing a piecewise smooth incidence rate. By assuming that the demographic parameters are much smaller than the disease-related ones, the proposed model is converted to a slow–fast system. Utilizing the geometrical singular perturbation theory and entry-exit function, we prove the coexistence of two relaxation oscillations surrounding the unique positive equilibrium of the model. Numerical simulations are performed to verify our theoretical results. The phenomenon presented in this study can be a potential explanation for that several infectious diseases can re-emerge many years after being almost extinct.
- Subjects
SINGULAR perturbations; OSCILLATIONS; PERTURBATION theory; EPIDEMICS; COMMUNICABLE diseases
- Publication
International Journal of Bifurcation & Chaos in Applied Sciences & Engineering, 2023, Vol 33, Issue 16, p1
- ISSN
0218-1274
- Publication type
Article
- DOI
10.1142/S0218127423501882