Department of Information Technology
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Browsing Department of Information Technology by Subject "Hopf bifurcation"
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Item Bifurcation analysis of waning-boosting epidemiological models with repeat infections and varying immunity periods(Elsevier, 2024-04) Opoku-Sarkodie, R.; Bartha, F.A; Polner, M.; Röst, G.We consider the SIRWJS epidemiological model that includes the waning and boosting of immunity via secondary infections. We carry out combined analytical and numerical investigations of the dynamics. The formulae describing the existence and stability of equilibria are derived. Combining this analysis with numerical continuation techniques, we construct global bifurcation diagrams with respect to several epidemiological parameters. The bifurcation analysis reveals a very rich structure of possible global dynamics. We show that backward bifurcation is possible at the critical value of the basic reproduction number, 0 = 1. Furthermore, we find stability switches and Hopf bifurcations from steady states forming multiple endemic bubbles, and saddle–node bifurcations of periodic orbits. Regions of bistability are also found, where either two stable steady states, or a stable steady state and a stable periodic orbit coexist. This work provides an insight to the rich and complicated infectious disease dynamics that can emerge from the waning and boosting of immunity.Item Dynamics of an SIRWS model with waning of immunity and varying immune boosting period(Journal of Biological Dynamics, 2022-07-29) Opoku-Sarkodie, Richmond; Bartha, Ferenc A.; Polner, Mónika; Röst, GergelySIRS models capture transmission dynamics of infectious diseases for which immunity is not lifelong. Extending these models by a W compartment for individuals with waning immunity, the boosting of the immune system upon repeated exposure may be incorporated. Previous analyses assumed identical waning rates from R to W and from W to S. This implicitly assumes equal length for the period of fullimmunityandofwanedimmunity.Werelaxthisrestriction,andallowan asymmetric partitioning of the total immune period. Stability switches of the endemic equilibrium are investigated with a combination of analytic and numerical tools. Then, continuation methods are applied to track bifurcations along the equilibrium branch. We find rich dynamics: Hopf bifurcations, endemic double bubbles, and regions of biostability. Our results highlight that the length of the period in which waning immunity can be boosted is a crucial parameter significantly influencing long term epidemiological dynamics.